Dominic Ford

The Patrick Moore

The

Observer’s

Guide to

Planetary

Motion

Explaining the Cycles

of the Night Sky

The Patrick Moore Practical Astronomy Series

For further volumes: http://www.springer.com/series/3192

The Observer’s Guide to Planetary Motion

Explaining the Cycles of the Night Sky

Dominic Ford

ISSN 1431-9756 ISSN 2197-6562 (electronic)ISBN 978-1-4939-0628-4 ISBN 978-1-4939-0629-1 (eBook) DOI 10.1007/978-1-4939-0629-1 Springer New York Heidelberg Dordrecht London

Library of Congress Control Number: 2014937791

© Springer Science+Business Media, LLC 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifi cally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfi lms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifi cally for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specifi c statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.

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Dominic Ford The Naked Scientists Cambridge , UK

v

About the Author

Dominic Ford is a science radio presenter and producer at the Naked Scientists , where he presents the monthly podcast Naked Astronomy . He is also a regular guest on BBC and ABC radio stations, talking about the latest astronomical news. In his spare time, he runs In-The-Sky.org , a website which lists forthcoming astronomical events, and manages the website of the British Astronomical Association (BAA).

Dominic previously worked as a professional astronomer at the University of Cambridge, where he completed a doctorate on the processes by which stars form. He went on to design components of the computer software needed to process observations made by the Square Kilometre Array (SKA). When it commences operations in around 2019 this will be the world’s largest radio telescope, split over two sites in Southern Africa and Australasia.

Dominic also works on open-source software projects for the amateur community. In 2005, he wrote GrepNova , an automated image-comparison tool for supernova hunters which has assisted in the discovery of over 50 events to date. Among its users is the British supernova hunter Tom Boles, who presently holds the world record for the largest number of supernova discoveries made by any single indi-vidual. More recently, Dominic has worked as the lead author of the vector graphics package Pyxplot , which was used to produce most of the line diagrams in this book.

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Pref ace

Astronomy is among the oldest recorded human activities, and the planets have always held a special fascination. As seen by the unaided eye, their motion across the night sky is the only way in which the heavens appear to change noticeably from one century to the next. While the patterns of the constellations have remained largely unchanged for thousands of years, the Sun, Moon and five naked-eye plan-ets have always been the seven exceptions to the rule. Efforts to understand their motion date back to at least 1500 BC , when Babylonian court astronomers were already compiling systematic tables of observed planetary positions and trying to formulate mathematical procedures to predict their future paths. More recently, as we shall see, it was this same problem that motivated Isaac Newton to formulate his laws of motion and gravity.

This book is about the ways in which the orbits of the planets produce complex patterns in their brightnesses, sizes and positions from one week to the next. It tells the story of how mankind has struggled to understand those orbits over the past centuries, and what they can tell us today about the Universe we live in. For active observers, it provides tabulated almanacs of significant events and alignments in the paths of all the planets over the period 2010–2050. In the cases of rarer events, I have been able to cover much longer time periods still, sometimes extending to 2200. These tables serve not only as catalogs of examples of each of the types of events that will be described, but also as a long-term handbook for active observers, which can be used to plan suitable dates for future star parties, for preparing ‘sky diary’ columns in advance, or simply for personal use.

Since the computer revolution, the role of printed celestial almanacs has changed considerably. Nowadays, almost every amateur astronomer has access to a com-puter, and there is no need to look far to find out where the planets are on any given

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night. There is a wide range of planetarium programs to choose from, ranging from freely available packages such as Stellarium and Google Sky to deluxe paid-for packages such as The Sky and Starry Night , to countless astronomy apps that are available for each and every type of smartphone or tablet computer.

Few astronomers would now choose to pore over printed tables of planetary positions to find out where they might find Mars on any particular night. The only reason why they might is that such planetarium software remains, for the time being at least, accessible only on devices with backlit screens. Holding a planetarium program up to the night sky is a fun way to navigate when learning the constella-tions and bright stars, but at a dark site it can take several minutes to reacquire night vision after using one. Nonetheless, just as printed encyclopedias have had to evolve in response to the wealth of information that Wikipedia places at the finger-tips of anyone with access to a web browser, so too printed ephemerides have had to evolve.

The drawback of planetarium software is that having so much information avail-able can make it difficult to see the wood for the trees. A recurring theme in this book is that there are long-term cycles in the positions and visibilities of the planets. Some, such as eclipses and the phases of the Moon, are very evident. Others, such as ocean tides, are no less evident, but it is not immediately obvious that they are triggered by astronomical mechanisms. The vast majority, however, are rather more subtle and can only be spotted by compiling detailed observations over long time periods. In light of this, it is rather remarkable that there is extensive evidence that ancient civilizations were very familiar with many of them. The Babylonians, for example, were fully aware by 1500 BC that days can vary in length by up to 30 s, depending on the time of year (see Chap. 4 ).

It remains interesting to study such patterns, not just to better understand when and where the planets will appear in the sky, but also to understand the gravitational and geometric mechanisms which lie behind them. Why does Saturn sometimes remain unfavorably placed for northern-hemisphere observers for several years at a time? Why does Mars appear much brighter at some oppositions than others? Why does Venus move from the evening sky to the morning sky in only 4–5 months, but take over a year to make the return journey? Such are the questions with which astronomers have had to grapple over the centuries in working out the three- dimensional structure of the solar system and the gravitational forces that act between the planets.

As we shall see, in modern times, new questions have been added to the list. Why did the solar system form with all of its gas giants further from the Sun than its terrestrial planets? Are Saturn’s rings a permanent structure, or a temporary result of some recent event? Why do we sometimes have to insert leap seconds into our system of timekeeping?

This book is free from equations, relying instead on diagrams of the physical geometry of the solar system, so as to be accessible to readers with little or no mathematical background. It is intended both for amateur astronomers who are

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interested in the mechanics which underlie the motion of the solar system and also for science students who are interested in the historical and observational origin of the physical models of gravity and planetary motion that remain in use by astronomers.

Cambridge, UK Dominic FordMarch 2013

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Acknowledgments

Many people helped me during the writing of this book. My proof-readers—David Ansell, Ross Church, Rachel Holdforth, Alby Reid, Matthew Smith and Thomas Williams—not only spotted numerous misprints, but also sparked discussion which led to my being able to expand and clarify many sections. Special thanks are due to Ross Church, who shared his expertise on the fast-developing subject of planet formation in the light of which I was able to include the most recent developments in Chap. 3 . At Springer, I am grateful to my editors, Maury Solomon in New York and John Watson in London, for seeing this book to press.

Where photographs and drawings have been taken from elsewhere, individual credits are made in figure captions. Particular thanks are due to David Arditti for his willingness to allow me to use his extensive library of astronomical images, and to Richard Ray for supplying maps of the Earth’s ocean tides.

Cambridge, UK Dominic Ford March 2013

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Contents

1 Introduction ............................................................................................. 1

2 The Earth as an Observatory ................................................................. 23

3 The Formation of the Solar System ....................................................... 49

4 Measuring Time ...................................................................................... 61

5 The Moon ................................................................................................. 77

6 The Outer Planets ................................................................................... 115

7 Mars ......................................................................................................... 155

8 The Inner Planets .................................................................................... 177

9 The Deep Sky ........................................................................................... 199

10 Extrasolar Planets ................................................................................... 205

Appendix A: Astronomical Imaging .............................................................. 215

Appendix B: Sources ....................................................................................... 229

Glossary ........................................................................................................... 231

Index ................................................................................................................. 237

1D. Ford, The Observer’s Guide to Planetary Motion: Explaining the Cycles of the Night Sky,The Patrick Moore Practical Astronomy Series, DOI 10.1007/978-1-4939-0629-1_1,© Springer Science+Business Media, LLC 2014

Introduction

The patterns of stars that we see in the night sky today have remained virtually unchanged since the earliest recorded human history. Archaeologists often face a long and difficult task to uncover the terrestrial sights that might have been familiar to people in ancient civilizations, but we can be remarkably certain of what those same people would the have seen, thousands of years ago, when they looked up at night. In this way, the stars provide an unparalleled connection with the past.

It is not merely hypothetical to assume that ancient communities might ever have looked up at the night sky. In fact, we have direct archaeological evidence for a historical interest in astronomy that dates back to at least the second millennium BC , because observers wrote descriptions and drew depictions of what they saw. The archaeological records range greatly in style. In Babylon, systematic tables of astronomical data were amassed over a period of more than a thousand years, as part of a tradition that was already well established by 1500 BC . Elsewhere, observ-ers produced artistic representations of what they saw, such as the elaborate decora-tions found in the tomb of Tutankhamun (c. 1320 BC ). We can guess that, in all likelihood, there were many earlier generations of observers who either didn’t keep written records, or who wrote and drew on less durable materials which have since decayed. Some have speculated that cave paintings at Lascaux in southern France, which date from 15000 BC , may resemble astronomical objects, though any likeness is difficult to prove. When looking at the stars of the Big Dipper, Orion, or Cassiopeia, it is remarkable to think that their patterns would have been quite rec-ognizable to the philosophers of ancient Greece, the builders of the Egyptian pyra-mids, and in all probability even the cave dwellers of prehistoric millennia.

Among the objects of the night sky, the Sun, Moon and planets have always held a particular fascination. These are the seven exceptions to the rule—seven objects

Chapter 1

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that not only move, but do so appreciably from one week to the next. To ancient observers, all but the Sun and Moon were no more than moving points of light, and it was impossible to do more than wonder what their motion meant. Since the advent of the astronomical telescope in 1609, they have come to be understood as whole separate worlds akin to the Earth, with markings visible on their surfaces. In the space age, it has become possible to take high-resolution images of them from above the distorting effects of the Earth’s atmosphere, to compile detailed maps of their surfaces, and to find out what chemical materials they are made from.

In the light of this information, it has become reasonable to compare them to the Earth, although the conclusion of any such comparisons has been that, even though some of our closest neighbors may once have been quite Earth-like in the distant past, they have all now evolved into radically different and unique environments. Of particular interest has been the question of whether any of the other planets might be inhabited—although to the contrary, they have all turned out to be far from hospitable places. This discovery came as a profound disappointment when it first became apparent in the 1960s—crushing centuries of speculation by science fiction writers about men from the Moon, Mars or Venus—but it is a discovery which in more recent times has enabled us to much better understand the special set of cir-cumstances which has made our own planet well-suited for life.

The most recent step in our growing understanding of the Earth as a member of a family of similar objects has been the detection of many hundreds of planets orbiting around other stars—so called extrasolar planets or exoplanets . Since the discovery of the first exoplanet in 1992, the rate of discoveries has steadily increased, and now a handful are usually found every month. It has become possi-ble for the first time to understand our solar system not just as an isolated specimen, but as one of a kind. We can ask whether it is normal for stars to have planets orbit-ing around them, or whether it is a peculiarity of our own Sun. We can ask whether, among planetary systems, ours is typical, or whether it has any unusual features which have made it possible for life to develop on Earth. While the search for extra- terrestrial life in the Universe was once directed almost exclusively at our near neighbor Mars, attention has now shifted to other planetary systems. Since 2000, we have learnt that a small but significant proportion of such systems do appear to include planets which resemble the Earth, at least on the basis of the limited infor-mation we have about them: their sizes and the amounts of heat that they receive from their host stars.

The opening chapters of this book cover topics which are common to all the planets—the celestial coordinate system which is used to describe the positions of astronomical objects, and our current best ideas of how the solar system formed in the first place. We will then look at the orbit of the Earth itself, since even if it is not often a target for amateur observers, it is the ever-moving platform from which all observations are made, whose motion defines the cycle of night and day and the daily rotation of the positions of the stars above us. In order to describe the motion of any of the other planets over time, astronomers need to be able to know what the time is. The most basic unit of timekeeping—the day—is traditionally defined by

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the Earth’s rotation, but as we shall see, irregulaties in the Earth’s own orbit have forced astronomers to look for time standards that tick with better regularity.

The middle chapters then work through the planets in groups, describing how each group moves across the sky, what this means for anyone who is trying to observe them, and what it reveals about the structure of the solar system. Almanacs are provided for each of the planets, listing their apparitions in coming decades. A final chapter covers the fast-developing search for extrasolar planets and the first clues which have been gleaned about how typical our own planetary system is in comparison to others.

As we have already seen, the story of humanity’s fascination with the motion of the planets is a long one. Over the past 3,000 years, it has not only caught the atten-tion of astrologers seeking to tell the future from the sky, but has also driven the development of large parts of modern mathematics and physics. It is that historical story that we turn to first.

The Fixed Stars

How true is it to say that ancient civilizations saw the same sky that we see today? It is certainly true that the vast majority of the constellations we see today have been perfectly recognizable in their present configurations for a very long time. For example, the familiar shapes of Orion and Cassiopeia are formed from very distant groupings of stars, which have changed little over many thousands of years. Even though the Orion Nebula (M42) is itself a site of very active star formation, a pro-cess that is rather rapid by astronomical standards, even this takes millions of years to progress and appears frozen in time when viewed over human timescales. But there are nevertheless a few constellations that have undergone gradual changes. Perhaps the best known example is the Big Dipper, whose handle, made up of the stars Alkaid, Mizar and Alioth, would have appeared a little less bent 10,000 years ago. These not only form a bright and conspicuous grouping of stars, but are also relatively nearby neighbors of the Sun, which means that they only need to move a short distance through space to appear to have drifted a large distance across the sky. Just as distant objects on the horizon appear to move very slowly when seen from a high-speed train, so stars, drifting through the Milky Way galaxy, appear to crawl across the sky when seen at astronomical distances. But our nearest neighbors are able to rush past like the trees at the side of the track.

The Big Dipper is the best known example of a group of stars which are very nearby, but there are a few stars which are closer still, and that appear to drift across the sky more quickly still. The fastest of these—said to have large proper motions , the technical term for a star’s rate of drift across the sky—can cover perceptible distances across the sky from one decade to the next. However, of these fast movers, none are particularly bright and all have been discovered only in modern times. An especially famous example is Barnard’s star, which moves by around a Moon-width every 180 years, a rate of proper motion that it achieves only by being the fourth

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closest known star to the Sun, while simultaneously moving relative to us at a speed of around ten times that typical among other stars. It can presently be found in Ophiuchus, but at ninth magnitude is beyond the reach of both the unaided eye and even binoculars.

Since they are so close, it is easy to assume that fast-movers like Barnard’s star should appear bright in the night sky, outshining the much more distant stars behind them. Instead, Barnard’s star is a challenging telescopic target, which is difficult to pick out from all of the other much more distant stars that appear around it. As this example demonstrates, it is far from true that the stars which appear brightest in the night sky are those that are closest to us. Stars have a huge range of luminosities, and giant stars like Betelgeuse produce nearly 50 million times more light than humble red dwarf stars like Barnard’s star. Small, faint stars are thought to be much more common than giants, but even if such a dwarf is very nearby, much more distant giants can easily appear to outshine it. As a result, many of the brightest stars in the night sky are relatively distant giants, and it is likely that vast numbers of dwarf stars may lie between us and them, unknown to astronomers because they shine so faintly as to be entirely inaccessible even to the world’s largest telescopes.

With the advent of modern cosmology, we know that the Sun and all of the stars around us are in constant motion, orbiting around the center of the Milky Way. Our galaxy is a swirling mass of stars, each having to move with a phenomenal speed of around 220 km/s to remain in orbit around the galaxy’s center and avoid falling into it. That isn’t quite a fair estimate of how fast stars move relative to one another, since most of the Sun’s near neighbors are moving through the galaxy as a group, with similar speeds and in similar directions, but their individual speeds still differ relative to one another by a few tens of kilometers per second, leading them to gradually drift apart.

It is only because of the vast size of the Milky Way—and in particular the vast distances between its stars—that it can take thousands of years for this drift in the relative positions of stars to cause them to appear to shift appreciable distances across the sky. The distances involved are so large that they are rather difficult to grasp. Light travels at a speed of 300,000 km each second, and yet it takes light tens of years to travel from even our nearest neighbor stars to the Earth. From more distant stars like Betelgeuse and Rigel, the journey takes well over a 100 years. The Sun takes hundreds of millions of years to complete a single circuit around the center of the galaxy, even though it travels along its orbit at a speed of 220 km/s. The total distance it covers along each circuit is 150,000 light-years.

If stars appear to crawl very slowly across the sky only because they are very distant, the planets are different in that they are very much closer to the Earth, at distances of light-minutes and light-hours, rather than tens of light-years. Even though the planets appear to drift across the sky thousands of times faster than even the fastest stars, the physical speeds at which they circle around the Sun are much slower than the speeds at which stars orbit around the Milky Way. The Earth, for example, circles the Sun at a comparatively relaxed pace of 30 km/s—a mere 15 % of the Sun’s own orbital speed around the galaxy—and the outer planets progress along their orbits much more slowly still.

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The planets orbit around the Sun at much smaller distances than those that separate the stars in our galaxy, and so they are many thousands of times closer to the Earth than even the Sun’s nearest neighbor stars. In other words, the galaxy is a rather empty place. Planetary systems are minute in comparison to the vast tracts of interstellar space that separate them. We can draw a comparison between how empty the galaxy is, versus how empty the solar system is. We think of the solar system as being rather empty: there are vast tracts of space between the planets, which it takes spacecraft on interplanetary missions months or years to traverse. To put a number to just how empty it is, the scale of the Earth’s orbit around the Sun is roughly 23,000 times larger than the Earth’s own radius. By contrast, if we compare the scale of the solar system to the distance of our nearest neighbor star, Proxima Centauri, that distance is around 270,000 times larger than the Earth–Sun distance. The solar system, viewed on the scale of interstellar distances, appears as an even smaller speck than the Earth appears when viewed on the scale of interplanetary distances. If the solar system is empty, the galaxy is around ten times emptier still.

Practical Uses of Astronomy

Throughout history, people have been drawn to observe the night sky for many reasons. Although we now know astronomical objects to be very distant, and, con-trary to the beliefs of astrologers, to have little or no direct effect on our day-to-day lives, there have always been sound practical reasons for wanting to be familiar with the night sky.

At night, the constellations provide directional reference points for navigators at sea. In the northern hemisphere, the pole star Polaris always lies almost directly above the observer’s northern horizon, and its altitude above that horizon is a mea-sure of the latitude from which it is being observed. In antiquity, celestial way- markers such as this may have been used by visual instinct alone. For example, as early as the second millennium BC , the inhabitants of Polynesia were almost cer-tainly using the stars to navigate between the thousand-or-so islands that they occupied in the south Pacific. While little is known of the methods they used, it is generally assumed that their instruments were primitive at best. Over time, tools developed which made the process of observing these reference points more precise. The sextant and the mariner’s astrolabe are two common examples, and both were often specially adapted for use on the rolling deck of a ship. In later medieval times, the nocturnal developed as a simple instrument for telling the time at night using the orientation of either the Big Dipper (part of Ursa Major) or the Little Dipper (Ursa Minor) relative to the pole star. The use of sextants for navigation at sea was not entirely superseded until the advent of satellite navigation, beginning in the 1960s with the early precursors to the modern Global Positioning System (GPS).

On dry land, with larger and sturdier instruments, the same techniques have provided the most accurate means of identifying the exact cardinal points. While making exact alignments has rarely been necessary for human survival, it

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has often been required by custom, whether it be to bury the dead facing the rising Sun—a common custom among early Christians and many others—to orientate an Egyptian pyramid with sides facing precisely north–south–east–west, or to orientate a church to face east. The Islamic tradition of orientating mosques to face Mecca is trickier to get right, requiring not only a compass but also a very good map. As has happened repeatedly through history, satisfying a religious custom necessitated scientific development and, in this case, led to the development of new cartographic techniques which were accurate over ever-longer distances as the Islamic empire spread beyond Arabia in the seventh century.

Different constellations are visible at different times of year, providing farming communities with an easy way to keep track of the passage of the seasons. As the year progresses, new constellations appear in the pre-dawn sky. Day by day, these new constellations rise around 4 min earlier each night, becoming gradually more readily visible before dawn twilight. Eventually, they rise several hours before dawn, then at dusk, and then even before night has even fallen. In ancient Egypt, a series of groupings of stars called decans were identified, which were chosen to rise at steady intervals through the night. Each morning, any astronomer who had a clear eastern horizon could look for any new decans which had become visible in the pre-dawn sky, but which had not been visible the previous morning. Each decan would come into view on around the same day each year—called the day of the decan’s heliacal rising —providing a simple calendar of the seasons. The decans could also be used to tell the time at night, by watching them gradually rise one-by- one in sequence as the night progressed.

Though the star groupings used varied from place to place, the principle of tell-ing the time of year, and time of night, in this way was widespread and still current in Roman and much later times. One very plausible translation of the Biblical ‘star in the east’ is as a star making a heliacal rising, since observing the eastern dawn sky would have been the staple day-to-day work of the astronomers of the time.

The Sky’s Visual Appeal

Aside from any practical concern, however, perhaps the most fundamental and enduring draw of the night sky is the simple fact that it is a remarkably beautiful sight. Even with the interference of modern light pollution, stars appear to form mesmerizing patterns like the Big Dipper. Throughout the ages, people have played connect-the-dots to find patterns resembling objects familiar to their cultures. Where ancient civilizations saw an archer (Sagittarius), many modern amateur astronomers see the likeness of a teapot. Close to where ancient cultures saw an arrow (Sagitta), modern astronomers can find the likeness of a coat hanger (Brocchi’s cluster; Cr 399). Whether the Big Dipper resembles a ladle, a plow, or a bear remains a matter of American–European–Babylonian disagreement.

In the absence of light pollution, the Milky Way emerges from the haze and the sky is more than a world of dots. Even to the naked eye, the galaxy’s knotted band of light is quite apparent, superimposed with dark nebulae. Once again, the human

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eye is adept at finding patterns in complex structures that are reminiscent of familiar objects; to the astronomers of ancient Egypt, and to many cultures since, the Milky Way appeared to depict a river. Given its bright appearance, Greek myth supposed it to be a river of milk, an idea that has lived on into the English language.

In modern telescopic astronomy, the visual appeal of the night sky is just as present. A pair of binoculars or a telescope opens up the world of several thousand ‘faint fuzzy’ objects that litter the sky, while the Milky Way is revealed as a sea of countless stars. To an even greater extent, there are geometrical patterns that form the likenesses of everyday objects, and these associations have been turned into popular names for nebulae. Many such names originated from descriptions left by nineteenth-century pioneers of deep sky observation, especially John Herschel (1792–1871). In the open cluster NGC 4755, Herschel saw ‘a casket of variously coloured precious stones’; the cluster remains known as the ‘jewel box’. Similarly, Herschel was the first to apply the monikers ‘trifid’ to M20, ‘dumbbell’ to M27, and ‘hourglass’ to a detail within M8, amongst others. Nonetheless, the art of pro-ducing new monikers still remains alive and well, as evidenced by the ‘soap bubble nebula’ discovered in Cygnus in 2008 (see Fig. 1.1 ).

Fig. 1.1 The soap bubble nebula (PN G75.5 + 1.7), discovered in 2008, demonstrates that the tradition of giving nebulae monikers lives on. Image courtesy of Keith Quattrocchi and Mel Helm (see http://www.lostvalleyobservatory.com/ )

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Before the seventeenth century, astronomers had very little idea what they were looking at. Complex structures with no apparent purpose seemed an extravagance of nature that demanded explanation. Since the earliest recorded astronomy, the sky has held a sense of other-worldliness. In the absence of other clues, Plato mused that ‘astronomy compels the soul to look upwards and leads us from this world to another’. Plato and Aristotle went further, taking the traditional four worldly elements of air, fire, earth and water, and adding a fifth divine element, ether. This was the material of heavenly perfection from which the sky was made; it was where the gods lived. In Greek astronomy, the planets had to orbit in circles, because they were the only shapes with perfect symmetry. The metaphor between heaven and the heavens remains strong: in western art, angels are still often to be seen depicted among the clouds.

Astrology

Among the historical reasons for observing the night sky, astrology has undoubtedly been among the most enduring, and a common source of funding and patronage for astronomers. The Babylonian court astronomers who compiled tables of the posi-tions of the planets reported to priests, who in turn reported omens to the king. There was little science here: in compiling such omens, the priests were just as interested in the entrails of sheep as they were in the planets. The Babylonian astronomers, who laid many of the foundations of modern astronomy, owed their existence to royal superstition and interest in horoscopes. In ancient Egypt, star maps painted in the tombs of the pharaohs were not scientific attempts at cosmol-ogy, but part of elaborate campaigns to ensure that each recently departed pharaoh would take his place among the gods in the sky.

It is perhaps little wonder that people should have questioned whether the move-ments of the planets affected human affairs, given the strong associations they believed to exist between the sky and the gods. In fact, there is nothing strictly unscientific about asking whether such connections exist: science is about looking for regular patterns in nature, and testing whether they reliably and consistently repeat themselves. Of course, most astrology is bunkum, and in modern times is little more than a play on the gullibility of patrons. Nonetheless, a few genuine patterns do exist which link terrestrial and celestial events, over short periods at least. Many celestial events occur at regular intervals, meaning that the sky can be thought of as a giant and very accurate gravitational clock.

Many cultures have come to associate the Moon with human fertility, and given that its phases cycle with a 29-day period, it is easy to understand why. Werewolves may be mythical, but there is evidence that many animals, both predators and prey, behave differently around full moon, when there is no cover of darkness, from how they behave around new moon, when there is almost complete darkness. As we shall see in later chapters, each of the planets moves through the constellations with a characteristic speed—for example, Jupiter completes a circuit of the celestial

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sphere every 12 years, and Saturn does so every 30 years. Likewise, many events on Earth happen at regular intervals. The El Niño oscillation in the Pacific Ocean leads to weather systems along the American Pacific coast that repeat every 5 years, while periodical cicadas emerge in large numbers at any given location only once every 13 or 17 years.

At a more fundamental level, as we have already seen, different constellations are visible at different times of year. Conversely, it is possible to tell the time of year by observing the night sky. To complement their system of decans, ancient Egyptian astronomers had an even simpler way to predict when the Nile was going to flood. They looked for the day when Sirius—the brightest star in the sky—made its helia-cal rising, as it does each year in early August. When it did so, they knew that the floods—which always take place in late summer—could be expected within a few weeks. The Egyptian astronomers went further, believing that the annual flooding of the Nile was caused by the appearance of Sirius. That belief is harder to recon-cile with modern science, but as a predictive tool, it was remarkably effective.

Scientific Astronomy

It is only since the early seventeenth century that astronomers have had much meaningful grasp of what the physical structures are that produce the light that they observe. Before that time, it was not even universally accepted that the stars were other Suns like our own. Some of the basic facts of astronomy have been learnt much more recently still: the idea that the Milky Way is but one galaxy among many, separated by distances of millions of light-years, was not universally accepted until the 1920s. Yet even if the mystical ideas of the past have now been replaced by a solid physical understanding of what the objects are that shine in the night sky—what they’re made of, how big they are and how hot they are—the cos-mos seems if anything more, rather than less, remarkable.

As we have already seen, the scales involved are incomprehensibly large. Light from even the closest stars to the Sun takes several years to reach us. One of the reasons why astronomers took so long to agree that many nebulae were entire gal-axies of stars outside our own Milky Way was that this implied what seemed to them an improbably large scale for the Universe. Geometrical hazes which were once called ‘spiral nebulae’ have indeed now revealed themselves to be vast struc-tures that it takes even light 50,000 years to cross, and whose light takes at least a couple of million years to reach us, even in the case of our very near neighbor Andromeda (M31). Light from the most distant galaxies in the Universe can take more than 10 billion years to reach us.

More recently still, we have begun to piece together an understanding of the long process by which our solar system formed. As we shall see in Chap. 3 , this began with the formation of the chemical elements that we find distributed throughout the solar system—carbon, nitrogen and oxygen, amongst others—most likely by nuclear fusion in the hot interiors of the some of the first stars to form in the

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Universe. These materials would initially have been confined to the inner cores of the stars in which they formed, but in time became widely distributed through inter-stellar space, quite possibly as a result of being ejected in huge supernova explo-sions at the ends of the lives of those stars. About 5 billion years ago, that material gravitated together to form a new star—the Sun—and a system of planets around it.

The modern campaign of observing the night sky to scientifically learn about the physical structure of the Universe began in earnest with the work of the Danish astronomer Tycho Brahe (1546–1601). Though Tycho’s greatest achievement was in making accurate measurements of the paths of the planets across the sky, which later allowed Johannes Kepler to show that they orbited the Sun following elliptical rather than circular paths, his first great achievement was in the deep sky.

Many astronomers can name a particularly spectacular sight that inspired their interest in astronomy—whether it be a shooting star or a bright comet. Tycho was unusually lucky in that his interest was sparked in 1572 by the sight of a supernova—a stellar explosion which triggered a previously faint and unseen star to flare, in this case to rival Venus in brightness. Such events are rather rare, and are more normally spotted only in distant galaxies rather than any closer to home. Tycho’s supernova, as it is now known, was one of only five such events that were close enough to the Earth to be visible to the unaided eye in the past millennium, and there has only been one other such event since.

Tycho realized that this event provided a perfect opportunity to test one of the central ideas of ancient Greek astronomy, still widely accepted at the time. Aristotle’s idea that the night sky was made of the perfect ether implied that it was timeless and could not change. Yet the supernova had clearly changed its appear-ance in a very short space of time, leading traditional wisdom to dictate that it could not be a celestial object. The appearance of new comets had long been explained away by supposing them to be atmospheric phenomena—stones flung up from the Earth or some effect of the weather—and it seemed natural to Tycho’s contempo-raries to explain away the appearance of a supernova in the same way.

Tycho realized that he could test that idea by measuring the supernova’s parallax . He proposed to travel around Europe measuring its position relative to background stars. If the supernova was indeed atmospheric, Tycho would expect it to appear in different parts of the sky from different locations, and by determining how far it shifted across the night sky for each mile traveled along the ground, Tycho could calculate its altitude. Instead, Tycho found that he could not detect any parallax at all, which implied that the supernova was in fact very distant—more distant even than the Moon—and it was therefore plainly a celestial object.

Five years later, in 1577, the sky offered Tycho another opportunity to test clas-sical astronomy. This time, the event was the appearance of a bright comet, and as before, the traditional interpretation was that the new object had to be within the Earth’s atmosphere. Once again, Tycho attempted to determine the new object’s parallax, this time with little expectation of success, and once again he concluded that it was very distant and therefore celestial. With one long-held aspect of classical astronomy now in serious doubt, Tycho began to question the validity of other clas-sical ideas about how the planets moved across the night sky. These had remained

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in use largely unchanged since the work of Ptolemy in the second century AD . In fact, over a decade earlier in 1563, Tycho had observed a conjunction between Jupiter and Saturn as a student, and had found himself frustrated that even the most state-of-the-art planetary tables were awry in their predictions of the event’s timing by 2 whole days. Older thirteenth century tables, meanwhile, were wrong by a full month. At the very least, the tables were clearly based on inaccurate observations. Were the underlying models perhaps also wrong? To find out, Tycho embarked on a night-by-night campaign to make precise measurements of the movement of the planets.

Tycho was in a unique position to fund this campaign because by birth right, he was a Danish nobleman in the service of King Frederick II. Etiquette dictated that Tycho’s royal service would be rewarded with the offer of a fiefdom, but Tycho’s hopes of a scientific career led him to diplomatically decline such offers as were made. To Tycho’s good fortune, however, Frederick II was sympathetic, and wanted Denmark to become a center of learning. He was anxious to retain Tycho, despite the difficulty in finding a suitable role for him. In 1576, he struck upon the idea of offering Tycho the small island of Hven, in the Øresund straight, to be his observa-tory. This was an offer that Tycho could hardly refuse, and without delay he set about building an observatory and research institute on the island.

Over the following two decades, Uraniborg , as Tycho named it, grew into an extensive research complex. Companies today talk of vertical integration—manufacturing components in-house rather than buying them in from elsewhere, to avoid unreliable supply chains. Tycho was an early pioneer of this approach. He did not trust European printers to reproduce his tracts without leaking his ideas to his rivals, and so he installed a printing press of his own on Hven. Later, when paper shortages threatened his ability to keep these presses running, he added his own paper mill to the complex. In Uraniborg’s workshops, Tycho took standard designs for the astronomical instruments used at the time—quadrants for measuring the altitudes of objects in the sky and sextants for measuring the distances between them—and systematically refined them to achieve the greatest possible accuracy. When it became clear that the mounts for his instrument were being shaken when-ever the wind blew, he dug a new underground observatory, Stjerneborg , where they would be protected from the elements.

In all of this work, Tycho was restricted to working entirely with the naked eye. The astronomical telescope would not be invented until 1609, and so we must assume that sharp eyesight was a prerequisite for anyone hoping to become one of Tycho’s observing assistants. Tycho was pushing naked-eye astronomy very close to the limit of what is theoretically achievable. Tycho’s observations of the posi-tions of the planets are typically accurate to within two arcminutes—one fifteenth of the diameter of a full moon—and at times more accurate still. The small size of the human eye limits its angular resolution, even for the best naked-eye observer, to a theoretical limit of around one arcminute.

By the 1590s, Tycho had completed two tasks out of three. He had designed the best observing instruments in the world, and he had amassed a vast collection of data from them. However, the paperwork of reducing the data into a standard form

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and analyzing it still lay ahead. At this crucial stage, Tycho ran into a string of problems, which eventually led to the analysis being left unfinished at his death. Because of this, the name that we now associate with the laws of planetary motion is that of Tycho’s successor, Johannes Kepler (1571–1630).

The problems came from several directions at once. Tycho had trouble recruiting high-caliber staff. More seriously, Denmark had a new monarch, Christian IV, who lacked his predecessor’s enthusiasm for Tycho’s cause. By 1597, relations with the Danish court had ebbed to such a low that Tycho fled Hven. After a series of brief sojourns elsewhere, he eventually traveled south to Prague in June 1599, where he sought and received the patronage of the Holy Roman Emperor, Rudolf II. His stay in Prague was short-lived—he died there in October 1601—but it was in these final 2 years that he invited Kepler to join him as a mathematical assistant. Such was Kepler’s obvious talent that he succeeded Tycho to the title of imperial mathemati-cian in 1601, and over the following decade completed the mammoth task of ana-lyzing Uraniborg’s legacy of observations.

The two mathematicians took very different approaches. Kepler was a Copernican, who believed that the Earth circled around the Sun, principally on the grounds that this approach led to simpler planetary models. Tycho had his own planetary theory, in which the Sun and Moon circled around the Earth, but the other planets circled around the Sun. The two theories were observationally very similar: they both predicted that the planets should move across they sky in much the same way, and they only differed in their definition of which object was at rest. But Tycho’s conviction that the Earth was at rest was founded on a deeper philosophical point. It stemmed from a similar argument to that he had used to show that the supernova of 1572 and comet of 1577 were celestial.

If, over the course of the year, the Earth traveled a circular path around the Sun, that meant that it moved relative to other nearby stars, whose positions might be assumed to be fixed relative to the Sun. Tycho had shown that the supernova of 1572 was clearly celestial on the basis of his inability to detect any parallax in its position when comparing observations taken from different locations around Europe. By a similar argument, if the Earth circled around the Sun, observations made at different times of year—from different points along the Earth’s orbit—would reveal a parallax in the positions of nearby stars (see Fig. 1.2 ). The fact that none could be detected implied one of two things. Either the Earth was at rest—Tycho’s preferred option—or the stars were so very much further away than the Sun that their parallaxes were smaller than Tycho could measure, which we now know to be the case. Tycho, however, rejected the latter option on the grounds that it seemed to imply a preposterously large scale for the Universe.

Regardless of this philosophical point, one thing Tycho and Kepler could agree on was that Mars posed a problem for both of their models. In time, Mars’s motion would prove to be the key to the resolving disagreement between the two mathema-ticians, albeit only some years after Tycho’s death and much to the chagrin of his heirs. Put simply, Kepler was quite unable to fit Tycho’s observations of its motion to any satisfactory circular orbit. Even his best attempts ended up deviating from Tycho’s observations by up to eight arcminutes. Given the accuracy Tycho that had

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managed to achieve elsewhere, it was quite implausible that his observations should have been so consistently awry here. Kepler’s battle with the problem was eventu-ally resolved in 1605, when he struck on the idea that the shapes of planetary orbits around the Sun might be ellipses rather than circles. His publication of the idea was delayed by the disapproval it met with from Tycho’s heirs, who were horrified that Tycho’s own data was being used to argue the case for a heliocentric planetary model, which was so contrary to Tycho’s own cosmological ideas. However, they were eventually published to the world in 1609, in Kepler’s New Astronomy .

The Telescope

In that same year, another revolution took place in astronomy. Nearly simultane-ously, the Englishman Thomas Harriot (c. 1560–1621), and the Florentine Galileo Galilei (1564–1642), built the first astronomical telescopes and turned them to the sky. Within 2 years of their first observations, Galileo had used his new magnified view of the sky to make a series of discoveries which comprehensively demon-strated the inadequacy of classical astronomy. On the Moon’s surface he saw an imperfect, rugged and cratered surface: hardly the perfect sphere demanded by Greek philosophy. Close to Jupiter he discovered four moons, plainly in orbit around it, putting an end to any ideas that all bodies in the cosmos orbited around the central Earth. Venus’s disk showed phases like those of the Moon, demonstrat-ing that it was plainly in orbit around the Sun. When he magnified the Milky Way, he saw a sea of pinpoints of light—vast numbers of stars that had been invisible to previous generations—demonstrating that there was much in the sky that remained unstudied and which could only be revealed using new high-precision instruments.

Fig. 1.2 The parallax of an object is a measure of how much its position in the sky appears to wobble over the course of the year as the Earth orbits the Sun. Nearby objects show large parallaxes, while more distant objects show much smaller parallaxes

TheSun JulyJanuary

Background stars

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The discovery of additional planets took considerably longer, for want of knowing where to look, but eventually came in 1781 when William Herschel stumbled upon Uranus. In so doing, Herschel became the first person in recorded history to dis-cover a new planet.

To understand how the arrival of telescopes changed astronomy, it is necessary to understand how they help astronomers. Most people, if asked, tend to say that telescopes are instruments that magnify the night sky, allowing small structures to be enlarged and brought into view. This is not untrue, but it is only half of what a telescope does. A telescope is also an instrument that can reveal faint structures in the night sky by collecting a large amount of light—all of the light that falls across their large front aperture—and bringing it all together to form a single bright image. Telescopes effectively enlarge the pupil of the observer’s eye from a few millime-ters across to many centimeters or even meters across. The reason why Uranus is invisible to the unaided eye is simply that it is too faint to be seen. A pair of binocu-lars does not have the magnification to resolve it into anything more than a point of light, but they are nonetheless able to bring it into view by collecting much more light than the unaided eye is able to do by itself.

Similarly, we now know that the brightest nebulae of the night sky were not inaccessible to medieval astronomers because they are particularly small in size, but because of the faintness of their light. Our closest large companion galaxy, the Andromeda Galaxy (M31), measures five or six times the diameter of a full moon from side to side, sprawling across its namesake constellation. Even more distant galaxies like the Whirlpool Galaxy (M51) still measure a respectable third-of-a- Moon-width across.

However, even if it was the light-gathering power of telescopes that led to the discovery of new planets—and eventually asteroids—it was their magnification which led to some of Galileo’s most important discoveries—lunar craters and the moons of Jupiter—and which would lead to ever-more-accurate observations of the paths of the planets across the sky.

The Force of Gravity

Even after the work of Kepler, the question remained of what physical force caused the planets to turn in their orbits. Kepler himself favored a magnetic force, believing that the Sun produced a magnetic field which interacted in some way with the Earth’s. The connection had not yet been made been made between the force that causes apples to fall from trees, and the force that keeps the Moon and planets turn-ing in their orbits—so called universal gravitation , gravity that acted on everything in the Universe. Though this stroke of insight is commonly attributed to Isaac Newton (1642–1727), it first appeared in Robert Hooke’s Attempt to Prove the Motion of the Earth in 1674.

However, Hooke was a physicist rather than a mathematician, and to test this idea against observations would prove a very difficult mathematical problem. Hooke was not up to it, but the same could not be said of Newton. Within a few

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years, Newton had found a mathematical proof that if there was a force of attraction towards the Sun that grew weaker with distance in a particular manner called an inverse square law, the result would be that the planets would follow elliptical orbits, exactly as Kepler had found. Moreover, he had found that such a model could simultaneously explain not only the orbits of the planets, but also the latest observations of how the known moons of Jupiter and Saturn circled around their parent planets. These moons seemed to form small-scale models of the solar sys-tem, obeying exactly the same laws of physics.

However, Newton had not yet fully grasped Hooke’s idea of universal gravitation. He believed that the Sun exerted a pull on the planets, and that the planets exerted a pull on their moons. But he was unsure whether there were any other connections. Did the moons of Jupiter and Saturn exert pulls back on their parent planets? Did the Sun exert a pull on moons? Newton preferred simplicity, and so favored a model in which gravity was selective in the bodies it acted upon. In his mind, the planets felt a gravitational pull from the Sun, but the Sun felt no gravitational pull back from the planets. Likewise, the moons of Jupiter felt a gravitational pull from Jupiter, but Jupiter felt no gravitational pull from its moons. However, even if this model was simple in the sense that it included the minimum number of forces needed to repro-duce observations, Newton found himself confronted with a confusing hierarchy of bodies that attracted one another, which seemed to defy easy explanation.

In 1684 he struck upon the idea that Hooke had had a decade earlier, that all celes-tial bodies exert a pull on all other bodies. He immediately went further in quantifying the strength of gravity’s pull. He formulated a theory in which the strength of the pull between any two bodies was in proportion to how massive the objects were, and grew weaker the further apart they were. The reason why everything in the solar system circled around the Sun—either as a planet circling around it, or as a moon following a planet around it—was that the Sun was by far the most massive body in the solar system. The reason why we, on the surface of the Earth, are much more strongly attracted towards the Earth than towards the Sun is that we are so much closer to it.

There were promising signs: when Newton came to consider the motion of the Earth’s own Moon, he found that the gravitational pull experienced on the surface of the Earth—that which caused apples to fall from trees—had exactly the strength that was needed for the Earth to keep the Moon in a gravitational orbit at a distance of 60 Earth radii (400,000 km), with an orbital period of one revolution per month. Newton had given universal gravitation the mathematical rigor that Hooke’s specu-lation had been unable to provide, and he published his calculations in the Philosophiae Naturalis Principia Mathematica , or Principia , in 1687. Hooke, meanwhile, was left bitterly feeling that his idea had been stolen.

Halley’s Comet

In the Principia , Newton analyzed not only the orbits of the planets and their moons, but also those of comets. These, he argued, must also be subject to universal gravitation, but rather than traveling in ellipses that were very nearly circular, they

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traveled in highly elongated ellipses. If this line of reasoning was correct, it seemed likely that if one waited long enough it would be possible to see the same comet come back around.

Historical records did not seem abundant with such examples, and we can now understand why. Comets are cold icy bodies that are made from a mixture of snow and rock, sometimes referred to as dirty snowballs. They spend most of their time far from the Sun in the outer solar system, but on each orbit they briefly plunge in towards the Sun before shooting past it to return to the outer solar system. They form tails when this brief exposure to the Sun’s heat rapidly warms their surfaces. Some of the snow on their surfaces begins to turn to steam, which is lost to space and forms a trail of gas and dust which is directed away from the Sun by the pressure of the Sun’s light.

Each time a comet goes through this process—called making a return —it vents an appreciable mass of snow to space. Its surface becomes increasingly rock- covered, since the rocky component is only lost in small quantities that become airborne as dust in the rising steam. This means that, even aside from the fact that comets sometimes disintegrate entirely, their lifetimes are limited. Each successive apparition is likely to be less impressive than the previous, unless the comet under-goes structural collapse or disintegration to expose fresh snow to the surface. Many of the most spectacular comets are those that have not made recent ventures into the inner solar system, and which still have relatively fresh surfaces. Comets that make regular apparitions tend to be faint, because their surfaces are rocky.

Looking through the catalogs of historical comets, Edmond Halley (1656–1742) could, however, identify one strong candidate for a periodic comet, which had been sighted in 1456, 1531, 1607, and 1682. All of these comet sightings seemed to have much in common, and he predicted that the comet would next return in 1757. Sadly this was too far in the future for Halley to live to search for the comet himself. By the time the comet arrived, mathematical techniques had improved so as to allow Halley’s prediction to be refined to spring 1758. The comet was first sighted on Christmas Day 1757, and has been known as Halley’s Comet ever since. Its modern classification number, P1, indicates that it was the first comet to be shown to be periodic. Newton’s theory of gravity had made a prediction, which had been borne out by observation. Physics appeared to be on the right track.

The Mathematical Age

Why, even 10 years after Hooke had published the idea of universal gravitation, did Newton take so long to grasp it? Why did he struggle for so long with a model in which the planets and their moons formed a seemingly arbitrary hierarchy of attrac-tion, rather than realizing that all bodies attracted one another?

Unlike Hooke, Newton was a mathematician, and for him it was important that any planetary model should allow exact calculations to be made to find out how the planets would move in the future. Though he had been able to show that any planet, moving under the influence of the Sun’s gravity alone, would follow an elliptical path around it, he realized that each planet would slightly deviate from an elliptical

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path if the other planets also exerted secondary pulls on it. In order to work out the precise path that the Earth followed, for example, it would be necessary to take into account not only the Sun’s gravity, but also the weaker pulls of all the other planets. These secondary pulls are known as perturbations .

We now know that this is an intractable problem. It is not possible to solve an equation that describes how each planet moves in response to the gravity of not only the Sun, but also of every other body in the solar system, right down to the smallest asteroid. Instead, various groups around the world make predictions of where the planets will be in coming years by taking their current observed posi-tions, and running computer simulations of how they will move in the future under the force of gravity. Most notable among these teams is that based at the Jet Propulsion Laboratory (JPL) in California, who produce the ephemerides that guide all of NASA’s interplanetary space missions, and whose DE405 ephemeris is used as the basis for most of the tabulated almanacs in this book.

However, these predictions can only be made over a finite period into the future. If there is any uncertainty about the current positions of the planets—which there inevitably is—this uncertainty grows over time as the simulations progress. As the positions of the planets become more uncertain the further one looks into the future, the perturbations which they exert on one another also become more uncertain. This triggers a snowball effect—because we don’t know exactly where the planets will be, we also don’t know exactly what forces they will exert on one another—and at some point in the future this causes the simulations to rapidly lose all certainty of where the planets will lie along their orbits. At this point, it becomes useless to run them any further. In modern mathematical terminology, planetary orbits are said to be chaotic . With present observations, however, predictions can be made for long enough into the future for all practical purposes: for around the next 100,000 years.

Chaos theory was not well understood until the twentieth century, but Newton was aware that perturbations produced a mathematical problem that he could not solve, and grew to accept their reality only very reluctantly. He only became con-vinced of the need for them when he came to study the Moon’s orbit, which Tycho’s data had shown to deviate from a neat ellipse, in a way which nobody before Newton had managed to satisfactorily explain. Newton found that the Moon felt a complicated mixture of the Earth’s gravity with that of the Sun, and that when both pulls were taken into account, he was able to reproduce exactly the deviation that Tycho observed. Nonetheless, even with this evidence in hand, the theory ran against Newton’s mathematical instincts. He complained that ‘To consider simulta-neously all these causes of motion and to define these motions by exact laws admit-ting of easy calculation exceed, if I am not mistaken, the force of any human mind’.

To go any further in understanding the perturbations of planetary orbits required not only the most powerful mathematical tools available at the time, but also the development of entirely new ones. Newton himself developed the branch of mathematics we today call calculus in response to the problem, but much would be left to later generations. Over the next 200 years, astronomy became a highly mathematical subject, and a field of mathematics called analytical mechanics grew up to analyze the problem of these planetary perturbations.

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The problem of knowing where the planets were going to be in the future was not just one of purely abstract interest. As we have seen, the stars had been used by sailors since ancient times to navigate at sea. In ancient Egypt, the system of decans had been devised to tell the time at night. By the eighteenth century, the Royal Greenwich Observatory was the center of timekeeping in Britain, measuring time by recording the exact moments when particular stars crossed the north–south line running through the observatory, the Greenwich meridian.

However, sailors still faced the pressing problem that while it was easy to mea-sure a ship’s latitude, by measuring the altitude of the pole star in the sky, it was very difficult to determine a ship’s longitude around the globe. What they needed was a way to find out by how much the Sun’s east–west motion, as observed on the decks of their ships, was advanced or retarded in comparison to its east–west motion as observed at the same instant at Greenwich. In modern terms, they needed to know what time zone their ships were in. This could be done if they could find out, at any given instant, what the present time was at Greenwich, which they could compare with their local time, as determined by where they observed the Sun to be in the sky.

This problem was eventually solved in the mid-eighteenth century by John Harrison (1693–1776), who devised a clock which could withstand the pitching and rolling of a ship. So long as this clock was accurately set before the ship set sail, it would continue to read Greenwich time throughout the voyage. Before this, how-ever, various astronomical means of telling the time were considered. Jupiter’s moons periodically disappear behind its disk, and reappear a few hours later. The times of these events could be predicted with accuracy, and while they did not hap-pen to order, they potentially offered a few fixed moments in time when far-flung observers could determine the present time at Greenwich. This technique proved effective for determining the longitudes of land-based colonial settlements, but sighting Jupiter through any telescope mounted on the deck of a ship proved impos-sible in all but the calmest conditions.

More promising was an idea to make use of the Moon’s path across the night sky, since the Moon has to move by roughly one moon-width each hour relative to the stars behind it in order to complete a full circuit around the sky each month. Given a table of lunar and stellar positions, the Moon’s movement relative to other stars could be used as a crude clock. This idea could have worked, had such tables existed, but by the time the required accuracy was achieved, Harrison’s clocks had already achieved better accuracy than could be hoped for from lunar observation.

The Discovery of Neptune

The most notable scientific achievement of this mathematical era of predicting planetary positions was the discovery of Neptune by the Berlin Observatory in 1846. At this time, celestial mechanics faced two challenges, from the orbits of

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Mercury and Uranus. Both showed deviations from the straightforward elliptical orbits which theory said they should follow, and these could not be accounted for by perturbations that any mathematician could identify. In the 1830s this was a very topical subject—Uranus had only been discovered 50 years earlier, by William Herschel in 1781—and it had taken this long for Uranus to travel far enough along its orbit for observations to show that it was tracing out the wrong shape.

In 1845, two mathematicians derived models using the assumption that Uranus’s orbit was being perturbed by another as-yet undiscovered planet. Urbain Le Verrier (1811–1877) of the Paris Observatory presented his work to the Paris Academy of Sciences, making an estimate of the planet’s position good to a few degrees, and by the following year he had persuaded the Berlin Observatory to take up the search. John Couch Adams (1819–1892), at Cambridge, had started work on the problem earlier, arrived at a similar conclusion, and eventually convinced Cambridge profes-sor of astronomy James Challis (1803–1882) to take up his own search. However, though he had a head start, Challis delayed, and Berlin took the discovery on September 23. Models of planetary orbits had become so accurate that the second new planet to be discovered in the telescopic era was first detected not by its light, but by its tiny gravitational influence on its neighbors.

Spurred on by his success with Uranus, Le Verrier turned his attention to Mercury. By 1859, he had worked out a model which could explain the anomalies in Mercury’s orbit by attributing them to a planet of similar size to Mercury, but which orbited at half its distance from the Sun. He supposed it to have hitherto evaded discovery as a result of being perpetually lost in the Sun’s glare, and pro-posed the name Vulcan for it.

However, Heinrich Schwabe (1789–1875) had already made a search for such a planet over a decade earlier, noting that even if it were perpetually lost in the Sun’s glare, it was likely to pass in front of the Sun on a regular basis. From 1826 until 1843, Schwabe observed the Sun on every clear day to search for such transits, without success. In the process, however, he compiled a systematic catalogue of sunspots—to avoid confusing them with planetary transits—and thereby discov-ered the regular 11-year variation in their number.

The problem of identifying what was actually disrupting Mercury’s orbit was not resolved until 1915, when Albert Einstein (1879–1955) published a revised theory of gravity—his general theory of relativity —and demonstrated that Mercury’s orbit is sufficiently close to the Sun for relativistic effects to become minutely detectable.

The Space Age

Interest in planetary positions waned after the discovery of Neptune, and the failure to discover Vulcan, because the scientific potential of the subject seemed to have been exhausted. While it seemed possible, in principle, to make ever more accurate

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determinations of the trajectories of the planets, it was unclear that this would be of any practical use. The next major advance came in 1961, when inter-planetary radar was used to make the most accurate measurement ever made of the distance to Venus.

The concept of radar—using a transmitter to produce high-powered pulses of radio waves and a receiver to detect the return of reflections of these pulses from distant objects—was proposed in the 1920s, and came into widespread use during World War II. At the end of the war, demobilized technicians began to look for civilian applications for the technology. Bouncing signals off the Moon presented itself as an obvious challenge within reach of the technology available, and was achieved by the US Army Signal Corps on January 10, 1946, under the direction of John DeWitt. A Hungarian team led by Zoltan Bay independently achieved the same feat on February 6.

Initially, the interest in such work was not motivated by any interest in the Moon and planets themselves. Both teams saw atmospheric research as the principal sci-entific motivation for what they were doing. The radio waves were traveling through the Earth’s upper atmosphere twice on their return journey to the Moon, and the attenuation of the pulses recorded information about the environment they had traveled through. Early on, for example, it became clear that meteor trails in the upper atmosphere were highly reflective to radio waves; the technique of detecting meteor impacts using radio receivers is still used by amateur meteor spotters today. Commercial applications were also identified for lunar radar bounces: in an age before satellite communications, bouncing signals off the Earth’s natural satellite seemed an attractive way to communicate over large distances. The US Naval Research Laboratory (NRL) built a one-megawatt transmitter for the purpose, which transmitted its first Morse code message on October 21, 1951. Voice com-munication was later achieved in 1954.

Such projects were given new impetus in 1957 with the Soviet launch of Sputnik 1 , and the foundation of NASA in the following year. Both Soviets and Americans needed to rapidly develop facilities for communicating with satellites in orbit. Moreover, in order to contemplate sending space probes to the planets, it would be vital to know exactly where the planets were. Very little work had been done to determine planetary positions in the preceding century, but now there was a sudden new demand for high precision.

Detecting radar reflections from the planets would make it possible to determine their distances with unprecedented accuracy. At its closest approach to the Earth, Venus comes closer to the Earth than any other planet, and so this was the first target to try, but the expected strength of the reflections was still so low that new more sensitive receivers would be needed. The US military was already researching the same problem in order to meet demands for long-range defensive radar, and new maser receivers reached the performance demanded within a few years. After two false starts—a group at MIT erroneously believed it had bounced radio waves off Venus in 1958, and Jodrell Bank made a similar claim in 1959—the first unam-biguous detection of such reflections was by the Jet Propulsion Laboratory (JPL) on March 10, 1961.

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The work of making such measurements, feeding them into computer simulations of how the planets move under gravity, and using these simulations to determine the paths of the planets, has remained a staple part of the work of JPL since. The accu-racy of the predictions made by these simulations varies between the planets, and depends in large part on how many recent space missions have been sent to each planet, for which accurate new data will have had to be collected. The most precise data is for Mars, which has been the intended destination for over 30 spacecraft, whose position we now know to within an accuracy of a few hundred meters, cor-responding to a position on the sky which is accurate to around a one thousandth of an arcsecond.

The Space Age

23D. Ford, The Observer’s Guide to Planetary Motion: Explaining the Cycles of the Night Sky,The Patrick Moore Practical Astronomy Series, DOI 10.1007/978-1-4939-0629-1_2,© Springer Science+Business Media, LLC 2014

The Earth as an Observatory

Our view of the Universe is complicated by the fact that we live on a planet that spins on its axis each day and which travels in circles around the Sun each year. The Earth’s rotation means that an observer on the equator is forever being carried around the Earth’s center at a speed of almost a 1,000 miles per hour. The Earth itself is forever hurtling around the Sun at a speed of almost 30 km/s. In turn, the Sun orbits the center of the Milky Way at a speed of around 220 km/s. The illusion that the Earth is stationary is a very convincing one, because everything around us is moving through space with us with exactly the same speed, rather like the furni-ture on an aircraft. But what is the effect of observing the Universe from the surface of a moving astronomical body?

The Structure of the Solar System

The solar system is a flat structure, similar in shape to a DVD, within which all of the planets orbit the Sun in almost exactly the same plane. It is fairly accurate to picture the solar system as a series of marbles on a dinner plate, with the Sun at the plate’s center and the planets rolling in circles around it—though in practice the planets are tens of thousands of times smaller than the gaps which separate them, meaning that microscopic marbles would be needed to make such a model to scale.

While the network of stars around the Sun, or the network of galaxies around the Milky Way, are spread throughout three-dimensional space in a way that is difficult to represent on a two-dimensional sheet of paper, it is comparatively easy to repre-sent the three-dimensional orbits of the planets on a flat sheet of paper. Figure 2.1 shows the orbits of the planets projected onto the plane of the ecliptic—the plane of the Earth’s orbit around the Sun—and taking this picture at face value, supposing

Chapter 2

24

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2 The Earth as an Observatory

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that all the planets really do orbit exactly within the plane of the page, gives a fairly accurate picture of their true motion. In practice, they might be found at most a few millimeters above or below it at the scale to which it is drawn.

The scale of Fig. 2.1 is indicated in astronomical units (AU), a unit of distance equal to the average separation of the Earth from the Sun. The top panel shows the solar system’s central 3 AU, including the orbits of the terrestrial planets Mercury, Venus, Earth and Mars. The bottom panel extends the view out to 35 AU, to include the orbits of the gas giants Jupiter, Saturn, Uranus and Neptune. See also Table 2.1 for a list of the planets.

Not shown in Fig. 2.1 , the asteroid belt lies in the large gap between the orbits of Mars and Jupiter, and consists of millions of rocky fragments which range in size from a few kilometers across down to microscopic particles. To date, over 100,000 individual objects have been cataloged in this swarm of material. There is a second, larger collection of such objects beyond the orbit of Neptune, at a distance of 30–50 AU from the Sun, called the Kuiper belt. Much further out still, at a distance of around 50,000 AU from the Sun—around a light-year away—lies the Oort cloud, a still-larger collection of icier bodies, some of which occasionally career into the inner solar system to become comets.

Some further characteristics of the solar system are apparent in Fig. 2.1 beyond its flatness. The spacings between the planets grow larger with distance from the Sun—roughly speaking, each of the gas giants orbits the Sun at twice the distance of its inner neighbor, while the terrestrial planets are a little more closely packed. This observation is loosely known as Bode’s Law, though it remains a matter of considerable debate to what extent it arose as an inevitable consequence of the process by which the solar system formed (see Chap. 3 ), and to what extent it is a peculiarity of the particular planetary system in which we live.

Although all of the planets follow almost circular orbits, most of them are suf-ficiently elliptical that they are visibly skewed, even in a small diagram such as Fig. 2.1 . The technical term for the degree to which an orbit deviates from a circle is its eccentricity . To aid the eye in picking out of eccentricities of each of the orbits, the point where each makes its closest approach to the Sun is labeled P (for perihelion), while its furthest point from the Sun is labeled A (for aphelion).

Table 2.1 The planets of the solar system

Planet Mass/Earth mass Radius/Earth radius Semi-major axis of orbit/AU

Mercury 0.055 0.383 0.387 Venus 0.815 0.95 0.723 Earth 1 1 1 Mars 0.105 0.532 1.52 Jupiter 318 11 5.2 Saturn 95.2 8.5 9.58 Uranus 14.5 3.97 19.2 Neptune 17.1 3.86 30.1

Quantities are expressed relative to the Earth’s mass, radius, and orbital distance from the Sun (1 AU)

The Structure of the Solar System

26

Of the planets shown, Mercury and Mars have the most eccentric orbits, the latter’s appearing especially obviously non-circular on account of lying right next to the Earth’s much more circular orbit.

The Earth’s orbit is labeled with the positions that the Earth passes through on the first day of each month, and also its position on the dates of the northern autum-nal equinox (AE; aligned upwards), the northern spring equinox—also called the vernal equinox (VE)—and the northern summer and winter solstices (SS and WS). Even the orbit of the Earth, the planet with the third most perfectly circular orbit in the solar system after those of Venus and Neptune, quite clearly passes inside the vertical gridline marking 1 AU to the left of the Sun—around the time of its peri-helion in January—and outside the vertical gridline marking 1 AU to the right of the Sun—around the time of its aphelion in early July.

Figure 2.1 does not show how fast the planets turn in their orbits, but their periods are listed in Table 2.1 . The outer planets turn much more slowly in their orbits than the inner planets, for two reasons. The first is quite simple: the orbits of the outer planets have much longer circumferences, and so these planets have to cover much greater distances before they come back to their starting points. The second involves Newton’s law of gravity: the strength of the Sun’s gravitational field decreases with distance, and so the inner planets feel a stronger pull towards the Sun and need to move along their orbits at much faster speeds in order to avoid falling inwards. One way to demonstrate this at home is to try tying a tennis ball to the end of a piece of rope and whirling it (carefully!) around your head. The faster you whirl the ball around, the harder it tries to pull the rope from you. The inner planets feel a strong inward pull from the Sun and are like a ball being whirled quickly, whereas the outer planets feel much weaker pulls and circle the Sun more slowly (see Fig. 2.2 ).

Synodic Periods

Just as trees appear to fly past the windows of a moving train, the Earth’s motion through space affects the way that objects appear to move across the night sky. As we shall see in Chap. 4 , the Earth’s motion is also central to way we define and measure the time. The concept of annual parallax (see Fig. 1.2 ) was previously introduced in Chap. 1 —that as the Earth circles around the Sun, nearby objects appear to wobble back-and-forth across the sky with a 12-month period. For stars, that wobbling motion is so small that it is virtually impossible to detect, because their distances—even in the case of the Sun’s nearest neighbors—are vastly larger than the scale of the Earth’s orbit. But the same is far from true for the solar system’s other planets.

The Earth’s orbit around the Sun measures 2 AU (300 million km) across, and pairs of images taken 6 months apart represent two perspectives on the Universe taken from points 2 AU apart. One way to visualize the effect that this every- changing vantage point has on our view of the solar system is to plot charts of the orbits of the planets, centered not on the middle of the solar system, but rather on the Earth (see Fig. 2.3 ). Rather than moving in simple circles, the planets appear to trace out paths more like spirograph patterns.

2 The Earth as an Observatory

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Fig. 2.2 The inner planets circle around the Sun much more quickly than the outer planets, a pattern which is called differential rotation

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Synodic Periods

28

The distance of each planet from the Earth varies according to whether it is on the same side of the solar system as the Earth, or on the far side. For example, while Jupiter’s average distance from the Sun is around 5.2 AU, its distance from the Earth is 1 AU less than this when the Sun, Earth and Jupiter are lined up with the Earth in the middle, but 1 AU more than this when they form a line with the Sun in the middle. Because Jupiter takes 12 years to complete a single orbit about the Sun, Jupiter’s distance wobbles between 4 and 6 AU nearly a dozen times on each orbit.

This means that the apparent sizes of the planets also change over time. Figure 2.4 shows how the distances to each of the naked-eye planets will fluctuate between 2015 and 2020 (left vertical axis), and how this will affect their apparent diameters (right vertical axis). The details of these patterns will be covered in later chapters, but some trends are very apparent. The fluctuation is greatest for the plan-ets that are closest to the Earth—especially Venus and Mars. Venus, for example, orbits the Sun at an average distance of 0.72 AU, and can pass within a mere 0.3 AU of the Earth when overtaking it on the inside, but can recede to a distance of 1.7 AU when on the far side of the Sun. The variation in the distance to Mars is equally pronounced, as is apparent in the Earth-centered view of its orbit shown in Fig. 2.3 .

The apparent sizes of the planets don’t all fluctuate with the same period. Jupiter and Saturn make their closest approaches to the Earth roughly once each year, but Venus and Mars do so only once every 2 years. Circling in their orbits, all in the same direction but moving more slowly the further they are from the Sun, the plan-ets are like runners on a celestial racetrack. How often they overtake one another depends on how much their speeds differ.

The outer gas giants move very slowly around their orbits. Each time the Earth completes an orbit, these planets have not moved very far from where they were a year earlier, and so the Earth overtakes them roughly once a year. At the opposite extreme, Mercury circles the Sun once every 88 days, after which time the Earth has completed less than a quarter of a revolution. Mercury overtakes the Earth every 116 days, the additional 28 days being needed for it to catch up with the Earth’s own orbital progress in the intervening time. This period—the time interval between any planet’s closest approaches to the Earth—is called its synodic period. As we shall see, it is also the time period over which each planet cycles between being readily visible in the night sky, and being lost amid the Sun’s glare.

Those planets which are closest to the Earth—especially Venus and Mars—have very long synodic periods. This is because they orbit the Sun at speeds very similar to that of the Earth. If there were to be another planet that orbited the Sun at exactly the same distance as the Earth, it would orbit the Sun at exactly the same rate as the Earth and never overtake it—its synodic period would be infinitely long.

Figure 2.5 shows how the synodic periods of the planets depend on their dis-tances from the Sun. To make the pattern clearer, a line has been added to show what the hypothetical synodic periods would be for planets in circular orbits at any arbitrary distance from the Sun, as computed from Kepler’s laws of orbital motion.

2 The Earth as an Observatory

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The Two-Dimensional Sky

To get any further in describing the apparent motion of the planets, it is necessary to have a system for describing their positions. Charts like Fig. 2.3 are useful for illustrating the mechanics of how the planets move through the solar system, but

(e) Saturn

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The Two-Dimensional Sky

30

they present the view that would be seen by a hypothetical observer floating above the solar system, not that of somebody on Earth. In everyday life it is possible to walk around one’s surroundings to gain a three-dimensional spatial understanding of them, but astronomers must, for the most part, make do with the one vantage point that they have. For those grounded on the Earth, astronomy is in essence about observing the unchanging two-dimensional view of the Universe seen above, a view that might as well be projected on a giant spherical screen around the Earth.

The information on a star chart is about how, in the three-dimensional sea of stars around the Sun, different stars lie in different directions; it says nothing about how far away those stars are. It makes sense for positions to be specified as two- dimensional directions in space, as this is what an astronomer needs to know when pointing a telescope to a particular altitude above the horizon, and to a particular azimuth (bearing) relative to north—that is, to a two-dimensional position on the sky. For this reason, astronomers find it convenient to specify the positions of astronomical objects as if they really did lie on a large imaginary spherical surface surrounding the Earth, called the celestial sphere.

To get from a two-dimensional map of the Universe to a three-dimensional structure, an additional piece of information is needed—the distance to each object. To what extent are the distances to astronomical objects known, and how can they be measured? As we have seen, the distances to the planets have been determined with great accuracy since the 1950s by the use of interplanetary radar and by send-ing spacecraft into orbit around them. The planets, however, are only our very nearest neighbors in the Universe.

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2 The Earth as an Observatory

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Moving outward, a small handful of the closest stars do have annual parallaxes which are measurable with very well calibrated ground-based telescopes. The first was detected by Friedrich Bessel (1784–1846) for the star 61 Cygni in 1838. The principal problem with making such measurements from ground-based observato-ries is that the parallaxes of even the nearest stars are barely larger than the scales on which the distorting effect of the Earth’s atmosphere become significant—around one arcsecond at best. In recent decades, the advent of space-based obser-vatories have made these measurements more feasible. The Hipparcos space observatory (1989–1993) measured distances to over a 100,000 stars, including most of those visible to the unaided eye. The Gaia observatory, launched in 2013, is anticipated to reach out much further, to stars at least a quarter of the way across our galaxy, mapping out the Milky Way’s spiral arms in unprecedented detail.

Moving out even further, the distances to galaxies can be estimated by referring to cosmological models. It is relatively easy to determine from an object’s spectrum how rapidly it is moving towards or away from the Earth, using a phenomenon called the Doppler effect. We know that the Universe is expanding, and as it does so, more distant objects recede from the Earth more rapidly, since they are sepa-rated from us by larger expanses of expanding space. This leads to Hubble’s law: that the distance to a galaxy is directly proportional to its recession velocity. Modern cosmological models are more complicated than this, taking into account historical changes in the rate of expansion of the Universe over the time taken for a galaxy’s light to reach us—often billions of years. However, all such models rely as their starting point on knowing how rapidly the universe is expanding in the first place. Determining this requires some galaxies to have had their distances mea-sured by independent means. Making such measurements was one of the initial scientific aims of the Hubble Space Telescope (HST; 1990–), and it is largely due to early observations using the HST that such distances are now thought to be accu-rate to within around 4 %.

Despite these advances, which have allowed precise estimates of the scale of the Universe to be made in the past few decades, distance estimates are still—with the single exception of radar measurements of the distances of the planets—considerably more uncertain than the directions in which they lie. Furthermore, in some cases genuine debate remains over the validity of particular distance measures. For this reason, the celestial sphere continues to serve astronomers well, as a tool for separating the distance coordinate which may be controversial from the two easily measurable direction coordinates.

The Earth’s Rotation

So far we have only looked at the Earth’s orbital motion around the Sun. A far more apparent movement is the Earth’s daily rotation about its polar axis, and the daily rotation of the stars around the night sky that this produces. At the beginning of this chapter, I said that an observer on the equator is hurtling through space at a

The Earth’s Rotation

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perpetual speed of over a 1,000 miles per hour in order to complete a full circuit about the Earth’s axis each day.

Other than the motion of the stars across the night sky, this rotational movement is very difficult to detect. Though an observer on the equator is rocking back-and- forth by a distance of over 12,700 km—the diameter of the Earth—few astronomi-cal bodies are close enough to show any detectable parallax over that distance. At its closest approach, for example, Mars can be observed to rock from side to side daily by around 30 arcseconds, but this is difficult to detect without an exception-ally good star chart. The Moon, by contrast, wobbles back and forth by up to a full 2°—four times its diameter—providing the only easily-observable verification that the observer is indeed decidedly not at rest (see Fig. 2.6 ).

Even though it is the Earth that spins, and the stars that are at rest, it is often easier to talk—informally at least—in terms of the celestial sphere rotating about the observer rather than vice versa. This is, after all, what any observer sees from a rotating standpoint. An observer at the north or south pole sees the sky appear to rotate around the zenith—the point directly overhead—because his sense of vertical is exactly aligned with the Earth’s rotation axis. To observers at other latitudes, the rotation appears to be tipped from the vertical to the north or to the south, as shown in Fig. 2.7 . However, some details are the same at all latitudes. All observers can agree that any particular object appears highest in the sky when it crosses the lines

The Earth

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Fig. 2.6 Each night, the Moon appears to wobble in its position by up to 2°—four times its width—due to the observer’s changing position in space as the Earth rotates. Here, the Earth is drawn looking down on its north pole, about which it appears to rotate counterclockwise. Two observers on the equator, separated in longitude by 180° see the Moon in front of different background stars (not drawn to scale)

2 The Earth as an Observatory

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that connects the cardinal points north and south on the horizon through the zenith; this line is called the meridian. When an object crosses it, it is said to transit the meridian, or simply transit. Such events are relatively easy to time accurately by mounting a telescope firmly to a north–south line and waiting until the object

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The Earth’s Rotation

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crosses the telescope’s cross-hairs; this technique was long used by observatories such as the Royal Greenwich Observatory (RGO) to provide time standards, of especial importance in the measurement of longitude.

Directions between objects in the sky can be specified using bearings (compass directions), with north pointing towards the north celestial pole, in a way which is very similar to how we specify directions between places on the Earth’s surface. However, there is one important difference between the Earth’s surface and the sky. Specifically, we look at the sky from below and the Earth’s surface from above. If a word is written on a piece of glass, and the glass is turned over, the word appears back-to-front. Similarly if one imagines drawing the cardinal points onto the out-side of the celestial sphere, and then looking at it from the inside, those cardinal points would appear in mirror image.

Whereas a map of the world is drawn with east to the right and west to the left, maps of the sky are drawn in mirror image, with east to the left and west to the right. If this is not done, the sky appears back-to-front in comparison to how it is observed. As an example, imagine standing in the northern hemisphere, facing south and looking up at the sky. Since the celestial north pole is directly behind, the direction of celestial north in the sky is aligned upwards when looking due south. Objects which are rising above eastern horizon are to the east of objects which are just setting below the western horizon, yet they would appear to the left-hand side.

Returning to Fig. 2.7 , the sky at any given location can be divided into three distinct regions. At a latitude of 50°N (the top panel), the northernmost part of the sky never rises or sets, but only circles around the north celestial pole. Objects in this part of the sky are said to be circumpolar. The southernmost part of the sky never rises above the observer’s southern horizon, but always remains below it. The area of sky in between spends some of its time above the horizon, and some of its time below the horizon. Dotted lines separate these three regions.

The sky’s motion is fastest at the celestial equator and slows to a standstill at the poles. Even at mid-latitudes, it is fast enough that long-exposure photographs of much more than 20 s begin to show stars not as points but as streaks, called star trails. To capture photographs of objects that are too faint to be apparent in the 20-s expo-sure, it is necessary to mount the camera in a piggy-back configuration on the back of a driven telescope mount that rotates with the sky. Meanwhile, long exposures of an hour or more, showing stars forming arcs of light around the pole star Polaris, have become one of the classic artistic images of the night sky (see Fig. 2.8 ).

The Constellations

The daily rotation of the sky presents a difficulty to astronomers who want to describe the locations of objects in the night sky. For example, it is only sufficient to say that an object is ‘in the west’ if the exact time and date of the observation are also specified. The simplest visual solution to this problem, dating back to antiq-uity, is to identify easily-recognizable patterns of stars, give them names (constel-lations), and use them as way-markers.

2 The Earth as an Observatory

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Some of the constellations we know today date back to Babylonian astronomy—especially the zodiacal 12. Many others, though, are much newer. In particular, the southern hemisphere was only systematically surveyed in the eighteenth century, and 14 of the present-day southern constellations were introduced by the French astronomer Abbé Nicolas Louis de Lacaille (1713–1762). Their modern origins are quite apparent in the associations that Lacaille chose—not mythical beings, but rather an air pump (antlia), a microscope (microscopium) and a telescope (telesco-pium), amongst others.

All of the constellations have had their boundaries refined as recently as the twentieth century, and the present set of 88 was only formally adopted by the International Astronomical Union (IAU) in 1922 and given rigid boundaries in 1930. Figure 2.9 is a chart of these modern constellations. As with any map of the world, however, any attempt to represent the curved spherical surface of the night sky on a flat piece of paper suffers distortion. Here, a Gall–Peters projection has been used, which is an equal area projection—the areas of each of the constella-tions is faithfully reproduced—but their shapes are stretched horizontally around the poles, and vertically around the equator.

Fig. 2.8 An image of star trails. The tower in the foreground is a disused water tower that now acts as an observing plinth at the Lund Observatory. Image courtesy of Francois Polito

The Constellations

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Where more exact positions are required, the names or catalog numbers of a nearby star within each constellation can be used. These have never been used with greater effect than by the English amateur astronomer George Alcock (1912–2000), who memorized the names of over 1,000 stars visible to the naked eye. Using this encyclopedic knowledge of the night sky, he was able to efficiently record the paths of meteors across the sky in the 1930s and 1940s. By having his star catalogue committed to memory, he was able to do so at great speed, minimizing the length of time that it took him to record each observation, when his eyes were directed at his notebook rather than the sky, and when he couldn’t be on the look-out for more meteors. Moreover, he completely eliminated the need to consult a star chart with a torch, which would have potentially impaired his night vision. By comparing his positional measurements with those made by another observer—Manning Prentice—60 miles away, he was able to triangulate the heights of the meteor trails in the atmosphere, producing many of the earliest measurements of the altitudes at which meteors burn up.

Alcock later went on to extend his knowledge of the sky by memorizing the visual patterns that were formed by the stars visible through a pair of binoculars—over 30,000 such stars. Over five decades from the 1950s until the 1990s, he was able to discover five new comets and six novae, which he was able to pick out by instinctively recognizing whenever a familiar pattern of stars appeared to have been disrupted by a newcomer.

Celestial Coordinates

For most purposes, however, it is far preferable to have a regular grid of coordinates for describing positions on the sky. As we have already seen, the problem of describing the positions of objects on the celestial sphere is similar to that of describing where places are on the spherical surface of the Earth. Cartographers mapping the Earth use latitude and longitude as their coordinate grid. Doing this requires two reference points to be chosen, which provide the zero points of each coordinate. For the zero of latitude, the choice is straightforward: the equator is the midpoint between the Earth’s north and south poles, and is physically defined by the Earth’s rotation axis.

The choice of a zero point for longitude—called the prime meridian—is more arbitrary: the longitude of the Royal Greenwich Observatory in London, histori-cally the reference point used for determining the longitudes of British colonies. This has been used internationally since the International Meridian Conference of 1884, held in Washington DC at the request of US President Chester Arthur. Until that time, various conventions had been used in different regions, the most notable alternative being the Paris meridian, which had served a similar historical role in the French Empire.

The coordinate system used to describe the positions of objects on the celestial sphere is very similar to that used by cartographers. On star charts, the latitude

Celestial Coordinates

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coordinate of world maps becomes declination. Objects at a declinations of 90° and −90° appear at the celestial north and south poles—i.e. the would appear directly overhead if observed from the respective poles. Objects at a declination of zero, meanwhile, appear directly overhead at the Earth’s equator.

The longitude coordinate of star charts, called right ascension, is usually divided into a scale of 24 h rather than 360°. This is a convenient unit to use, since the sky completes roughly one revolution every 24 h. The difference in the right ascensions of two objects, when expressed in hours, equals the time interval between their respective transits. For two objects at the same declination, it also equals the time interval between the moments when they rise or set, though this is not true for objects at differing declinations, since objects at different declinations spend differ-ent lengths of time above the horizon.

The use of degrees to express declination, and hours to express right ascension, leads to a confusing clash of terminology when these units come to be subdivided. Just as the hours of the day are each divided into 60 min, so too are hours of right ascension. In turn, each of these is divided into 60 s. When writing declinations, each degree is commonly divided into 60 arcminutes, and each of these is further subdivided into 60 arcseconds. However, it must be remembered that a minute of right ascension is 15 times larger than an arcminute of declination.

Both of these conventions are ancient in origin, dating back to the same Babylonian astronomers who gave us many of the constellations that are still in use. They used an arithmetic system—highly advanced for its time—which counted in base 60. In modern decimal (i.e. base 10) arithmetic, numbers are written using a units column that counts from zero to nine. After it reaches nine, a one is added to the tens column and the units column reverts to zero. In the Babylonian sexagesi-mal (i.e. base 60) system, the arcseconds column counted up to 60, before a one was placed in the arcminutes column. This system, more than 3,500 years old, continues to be used in everyday life in the way we tell the time and the way we divide a circle into 360°. It has the advantage over decimal systems that the number 60 is evenly divisible by many integers—2, 3, 4, 5, 6, 10, 12, 15, 20 and 30—such that an hour can be evenly divided into two 30-min blocks, or three 20-min blocks, and so forth.

To complete the celestial coordinate system, the only remaining task is to make a choice of zero point for right ascension. By ancient convention, the point that is chosen is the position where the Sun appears in the night sky at the moment of the March equinox, and so before going any further, the path that the Sun takes across the sky must be investigated.

The Path of the Sun

The Earth’s orbit around the Sun remains virtually unchanged over periods of bil-lions of years, and barring any cosmic calamities is unlikely to change significantly over the remaining 5-billion-year lifetime of the solar system. Year after year, the

2 The Earth as an Observatory

39

Earth turns around the Sun at an almost constant rate, remaining almost exactly within the same plane. As it does so, a hypothetical observer sitting on the Sun would see the Earth appear to track a single circuit around the night sky each year relative to the stars behind it. An observer on the Earth, looking back in the opposite direction, likewise sees the Sun appear to track a single circuit around the night sky each year, also following almost exactly the same path year after year. This path across the sky is called the ecliptic (see Fig. 2.10 ).

The Earth’s sightline to the Sun always lies within the plane of its orbit. If you point your arm towards any star which lies along the path of the ecliptic, and sweep your arm along the ecliptic’s line, your arm is sweeping out a physical plane in space which is that of the Earth’s orbit. At different times of day, that plane appears in different orientations relative to the Earth’s surface because the Earth is continu-ally rotating. But relative to fixed reference directions in space, especially the sightlines from the Earth to very distant galaxies, this plane has remained virtually unchanged since the solar system’s earliest history.

The path that the ecliptic follows through the constellations is shown in Fig. 2.11 . Even though it traces out a straight line across the sky—called a great

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Fig. 2.10 As seen from the Earth, the Sun appears to track a single circuit around the night sky each year, following a path called the ecliptic. This figure shows a slice through the celestial sphere in the plane of the Earth’s orbit, listing the constellations that the Sun passes through, and the dates on which it moves from one to the next. The Sun remains stationary at the center of the diagram, while the Earth circles around it

The Path of the Sun

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2 The Earth as an Observatory

41

circle—this appears as a curved line when projected onto a grid of right ascension and declination, because of the inevitable distortion that is introduced by any attempt to map the spherical night sky onto a flat piece of paper.

Another way of visualizing the path of the Sun across the sky is to draw the three-dimensional geometry of the Earth’s rotation axis with respect to its orbit around the Sun, which is done in Fig. 2.12 . The line through the Earth indicates its rotation axis. As we have already seen, the system of right ascension and declina-tion is defined with respect to the Earth’s rotation axis. If the Earth’s rotation axis points directly towards a particular star, it appears close to the north celestial pole, at a declination close to 90°N. The celestial equator lies perpendicular to the Earth’s rotation axis. Because the ecliptic is tipped up relative to the Earth’s equator, the declination of the Sun changes as the year progresses.

It is this fact that gives rise to the Earth’s seasons. For example, when the Earth is on the left-hand side of Fig. 2.12 , its north pole is tipped towards the Sun, and the Sun lies to the north of the celestial equator, on the border of Taurus and Gemini. This means that the Sun spends longer than 12 h above the horizon in the northern hemisphere and less than 12 h above the horizon in the southern hemi-sphere. For half of the world it is summer, and for the other half it is winter. The tables are reversed when the Earth is on the right-hand side of Fig. 2.12 , when the Earth’s south pole is tipped towards the Sun. At the two intermediate points, the equinoxes, the Earth’s sightline to the Sun passes through the celestial equator; the Sun momentarily appears to have a declination of 0°.

The Sun’s path across the sky, vital for ensuring a new supply of food and clem-ent weather each spring, has always held a special cultural significance. Long before the whole sky had been systematically divided up into constellations with well-defined boundaries, the Babylonians had divided the ecliptic into 12 zodiacal constellations, each of which contained an equal 30° segment of the Sun’s path. It took the Sun roughly a month to traverse each of these segments—Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricornus, Aquarius and

N

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The SunWinterSolstice

SummerSolstice

VernalEquinox

AutumnalEquinox

Fig. 2.12 The Earth’s rotation axis is inclined with respect to the plane of its orbit around the Sun, giving rise to the Earth’s seasons

The Path of the Sun

42

Pisces. The series began with Aries, the constellation that the Sun entered at the moment of the March equinox, an important moment in the year, marking the beginning of spring as defined by astronomers. To this day, the point on the sky where the Sun crosses the celestial equator in March is known as the first point of Aries, and this is the point which is defined to have a right ascension of zero.

The Precession of the Equinoxes

Since the time of the Babylonians, the constellations have been redefined. No lon-ger are the zodiacal constellations of equal sizes. Today they have well-defined boundaries, which in some cases have rather jagged edges (see Fig. 2.9 ) to ensure that all of the objects which have traditionally been associated with each of them lie within the right constellation’s boundary. The Sun still passes through the 12 traditional zodiacal constellations, which now have varying sizes, but it also passes through the additional constellation of Ophiuchus for 2 weeks in early December.

However, the changes in the positions of the constellations have gone beyond a mere tweaking of their boundaries. In the first millennium BC , the Sun entered the constellation of Aries on March 21, and remained in Aries for around a month. Hence, as we have seen, the Sun’s location at the moment of the March equinox was called the ‘first point of Aries’. In the twenty-first century, the Sun enters the modern constellation of Aries almost a full month later, on April 19. Astrologers still cling to the constellation boundaries of old, assigning a star sign of Aries to anyone born between March 20 and April 19. But a quick look at a chart of the night sky reveals that on March 20, the Sun is some 30° away from the stars that make up the likeness of a ram. That is to say, the modern so-called ‘first point of Aries’—the position of the Sun at the March equinox—now lies in the constellation of Pisces, some 30° away from Aries.

What has happened over the intervening 2,000 years? The problem is called the precession of the equinoxes, and stems from the fact that the direction of Earth’s rotation axis in space changes slowly over time. While the plane of the Earth’s orbit in space is broadly-speaking fixed, the direction of the Earth’s rotation axis is more variable. The cause of this variability is a combination of the Sun’s gravitational field, and the fact that the Earth is not quite perfectly spherical. The Earth’s surface is slightly higher around the equator, and lower at the poles, by about 20 km. In other words, the Earth is shaped like an M&M—a shape technically called an oblate spheroid—with a bulge around the equator. This spheroidal shape is a result of the Earth’s rotation: material on the equator is revolving at high speed around the Earth’s center, and feels an outward centrifugal force—rather like a car perpetually turning around a corner. The material at the two poles, meanwhile, moves no dis-tance at all as the Earth rotates.

The Sun’s gravity pulls on different parts of the Earth with different strengths. Specifically, the force of the Sun’s gravity decreases with distance from the Sun. For the Earth’s two equatorial bulges, drawn in Fig. 2.13 at around the time of the

2 The Earth as an Observatory

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winter solstice, this means that the bulge on the side of the Earth closest to the Sun feels a slightly stronger gravitational pull than the bulge on the Earth’s far side. The net result of these two unbalanced forces is that the Sun’s gravity acts to turn the Earth’s rotation axis towards the north ecliptic pole—the line perpendicular to the plane of the Earth’s orbit.

Precession of Gyroscopes

The Earth responds to this tug in the same way as a gyroscope—a generic term for any fast-rotating object mounted in low-friction bearings, of which the Earth is a good example. One classic demonstration of the counter-intuitive ways in which gyroscopes can behave is to balance one, tipped to one side, on the top of a small tower (see Fig. 2.14 ). Intuitively, it is natural to expect that the gyroscope will fall to the side under the force of gravity. Instead, the gyroscope gradually turns in circles around the tower, with its rotation axis always at a constant angle to the vertical, but with its direction slowly rotating around the vertical.

This effect is known as precession. To understand what happens to the Earth’s rotation axis in response to the Sun’s pull, it is not strictly necessary to understand how precession arises—as we are about to see, what is important is that the Earth behaves in exactly the same counterintuitive way as the gyroscope shown in Fig. 2.14 . Nonetheless, the next two paragraphs briefly summarize the physics of pre-cession. The gyroscope appears to defy gravity because it has a large amount of rotational energy stored within it. Associated with this is a quantity that physicists call angular momentum, which describes the fact that the rotation has a particular direction—the gyroscope’s axis of rotation—associated with it. The gyroscope

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Direction of theEcliptic North Pole

Direction of theEcliptic South Pole

Fig. 2.13 The Earth is not perfectly spherical, since centrifugal forces cause it to bulge around the equator. The side of the bulge which is nearest to the Sun feels a fractionally stronger gravi-tational pull than that on the far side, trying to turn the Earth clockwise as depicted here

The Precession of the Equinoxes

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resists gravity’s attempts to make it fall sideways off its mount, because this would mean tipping the axis of the gyroscope’s rotation sideways. It takes a large pull to take an object that is rotating quickly in one direction, and to cause it to start turning instead around a different axis.

In Fig. 2.14 , gravity is trying to impart its own rotational motion onto the gyro-scope. It is trying to cause the gyroscope to tip counterclockwise, so as to fall off the tower to the left-hand side. In other words, gravity is trying to add its own rotational motion, on top of that which the gyroscope already has. Why does the gyroscope remain at the same angle to the vertical, and instead of falling to the side, turn its rotation axis in circles around the vertical? The answer can be found by thinking about what actually happens if the top of the gyroscope moves either into or out of the page as shown in Fig. 2.14 . While its rotor is seen almost exactly edge- on at the moment when Fig. 2.14 was taken, a little while later when it has pre-cessed some distance, the rotor will have turned itself a little way towards appearing face-on as seen from this camera angle. Whereas the photographer could not mean-ingfully say whether the gyroscope’s rotor appeared to be going clockwise or counterclockwise at the moment when it was edge on, now the rotor appears from his viewing angle to be going round either one way or the other. What gravity was

Fig. 2.14 If a gyroscope is balanced at an angle on top of a small tower, instead of falling sideways off the tower as might be expected, it appears to defy gravity by remaining at a roughly constant tilt away from the vertical. However, its rotation axis gradually rotates in a circle around the vertical axis, due to an effect called precession . The Earth behaves in exactly the same way, and this is why the orientation of its rotation axis changes over time

2 The Earth as an Observatory

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trying to do, at the moment when Fig. 2.14 was taken, was to make the gyroscope tip counterclockwise. Seconds later, the gyroscope will have turned its rotor towards the camera, and that rotor will appear to be turning counterclockwise. Gravity has gotten its way, but not in the intuitive way one might expect.

The Earth as a Gyroscope

The Earth is exactly analogous to the gyroscope discussed above. The difference between the strength of the Sun’s gravitational field on the daylight and night-time sides of the Earth is always trying to tip the Earth’s axis of rotation towards the north ecliptic pole—the vertical as seen in Fig. 2.13 . This is in the opposite direc-tion to that discussed in the example above, but the effect is the same. The Earth has a large amount of rotational energy and momentum, and just like a gyroscope, it responds to gravity in a counter-intuitive way. Instead of the whole planet tipping clockwise as seen in Fig. 2.13 , it turns its rotation axis so that the Earth appears, as seen from the camera angle shown in Fig. 2.13 , to be turning clockwise. In other words, it remains tilted at roughly the same angle, 23.5°, to the ecliptic plane, but its rotation axis rotates around the NEP. This happens once every 26,000 years.

Effects on Celestial Coordinate Systems

As a result of the precession of the equinoxes, the celestial coordinate system of right ascension and declination is not as unchanging as might ideally be liked. The coordinate system they form is defined relative to the direction in space to which the Earth’s rotation axis points, but as we have just seen this gradually drifts across the sky over time. Although the ecliptic is—more or less—an unchanging plane in space which has always passed through the same set of constellations, the Earth’s rotation axis precesses relative to it. The position of the north celestial pole moves by 19 arcseconds each year; its path across the sky in past and coming centuries is shown in Fig. 2.15 .

One way to visualize why this path has the shape it does is to draw a flat projec-tion of the sky—exactly as we have already done in charts such as Fig. 2.9 —but this time, instead of drawing it so that the celestial equator runs horizontally across the middle of the chart, we rotate the sky so that the ecliptic does so. In other words, instead of using a grid of right ascension along the horizontal axis and declination up the vertical axis, we use a grid of ecliptic longitude and ecliptic latitude. On such a chart, the ecliptic north pole lies at the top of the map, and the ecliptic south pole lies at the bottom of the map (see Fig. 2.16 ). It is exactly equivalent to a star chart plotted in right ascension and declination, except that the whole sky has been rotated by 23.5°, and that ecliptic longitudes are customarily written in degrees rather than hours.

The Precession of the Equinoxes

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As the Earth’s rotation axis precesses around the north ecliptic pole, it always remains at an ecliptic latitude of 66.5° on Fig. 2.16 —at an angle of 23.5° from the ecliptic pole. However, its ecliptic longitude decreases—it moves to the right across Fig. 2.16 —at a rate of around 50 arcseconds per year. As it moves to the right, the line of the equator follows it, and so the two points where the ecliptic and the celes-tial equator intersect move along the ecliptic at the same rate of 50 arcseconds per year to the left.

The aim of setting up a system of celestial coordinates was to provide a means of writing down the positions of objects like the Pleiades—as right ascension 3 h and 47 min, declination 24°N—safe in the knowledge that those coordinates would remain constant regardless of the time of day or time of year. Unfortunately, the system of right ascension and declination chosen has not perfectly answered that need. Over long time periods, the zero points of both right ascension and declination drift across the sky, and the whole sky appears to rotate relative to the coordinate system.

In other words, it is still necessary for observers to specify which position in the night sky they are taking to be the north celestial pole, and which position they are

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CepheusCepheusCepheusCepheusCepheusCepheusCepheusCepheusCepheus

Corona BorealisCorona BorealisCorona BorealisCorona BorealisCorona BorealisCorona BorealisCorona BorealisCorona BorealisCorona Borealis

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Fig. 2.15 The movement of the north celestial pole over time due to the precession of the equinoxes. Over a period of 26,000 years, it turns in circles with a radius of 23.5° around the north ecliptic pole, which lies in Draco. Polaris is only temporarily the pole star; in the second millennium BC , it was 10° away from the pole

2 The Earth as an Observatory

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The Precession of the Equinoxes

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taking to be the first point of Aries. This is customarily done by specifying the epoch at which the chosen points was aligned with the Earth’s true rotation axis and the ecliptic’s vernal equinox, as the celestial pole drifts ever left-ward across Fig. 2.15 . At the time of writing, the most common choice of epoch is midnight on January 1, 2000, designated as J2000.0. In the past, an epoch of midday on January 1, 1950 was commonly used—B1950.0—and in due course it is likely that the year 2050 will come to be used.

One consequence of the accumulated precession of the equinoxes over the past 50 years is apparent from the boundaries of the constellations, as drawn in Fig. 2.9 . The modern boundaries of the constellations appear to be made up from a mixture of almost-horizontal and almost-vertical line segments. Wherever constellation boundaries need to move in roughly diagonal lines—as in the case of the northern boundaries of Antlia and Pyxis—they are instead made up from a sequence of hori-zontal and vertical sections, which form a stepped end result. However, it is also apparent that these line segments are not quite straight, especially around the poles. The reason for this is historical: the constellations were given fixed boundaries in 1930, when a historical epoch was used to define the right ascensions and declina-tions of objects. In 1930, boundaries were chosen that, for simplicity, were made entirely out of lines of constant right ascension—vertical lines—and lines of con-stant declination—horizontal lines. However, now that J2000.0 has become the preferred standard epoch for specifying right ascensions and declinations, these once straight lines are now based around a historical position of the north celestial pole, which is a quarter of a degree from the present position of the pole.

2 The Earth as an Observatory

49D. Ford, The Observer’s Guide to Planetary Motion: Explaining the Cycles of the Night Sky,The Patrick Moore Practical Astronomy Series, DOI 10.1007/978-1-4939-0629-1_3,© Springer Science+Business Media, LLC 2014

The Formation of the Solar System

The Sun and the solar system formed together around 4.6 billion years ago, when the Universe was around 8 billion years old. At the beginning of this process, the starting material was a large interstellar gas cloud, which suddenly collapsed inwards under the pull of its own gravitational self-attraction until it was a fraction of its original size. This decisive event in the planetary system’s earliest history took place so long ago that there are limits in how much can be learned about it by studying the solar system itself, and most of what is known about it has come from studying other nearby star-forming clouds that are still at various stages of ongoing collapse.

Nevertheless, even if 4.6 billion years of intervening history have obscured the detailed mechanics of how the solar system formed, it still retains an organized structure which appears to have been shaped by processes which operated at this earliest time in its history. The answers to why all of the planets orbit in roughly the same plane, why the gas giants are all further from the Sun than the terrestrial plan-ets, and why the space between the orbits of Mars and Jupiter is filled with asteroids, all lie right back at the time when the solar system formed. This chapter turns to the mechanical processes that operated at this time, and which have determined how the solar system has looked ever since.

The Life Cycle of the Sun

The solar system formed from a vast diffuse interstellar gas cloud, which would have been composed mostly of hydrogen gas—by far the most abundant substance in the Universe—mixed with a little helium and traces of other materials such as

Chapter 3

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carbon, nitrogen and oxygen. One can guess that it may originally have measured tens of light-years across and have had many thousands of times the mass of the Sun. In interstellar space, clouds of this size are quite common, and go by the name of giant molecular clouds . Inside them, two forces lie in fine balance. First, the cloud’s own gravity pulls all parts of it inward towards its center, trying to make the cloud contract. The resulting weight of the cloud’s outer layers, pushing inward on its interior, produces a counterbalancing force: the gas at the center becomes com-pressed and pressurized like the air inside a balloon, producing an outward pressure which tries to make the cloud disperse.

Stars form when something happens to upset the balance in such a cloud, caus-ing gravity to win the tussle suddenly and decisively. More on what that something may have been shortly, but for the moment its consequences are more important. Initially, the cloud begins to contract under the force of its own gravity. As it does so, it loses gravitational energy, which is converted to heat, and the gas becomes hot. When it reaches a temperature of around 6,000 °C, hydrogen atoms—made of an electron orbiting around a proton—are no longer stable, and fall apart into a sea of free-floating protons and electrons called a plasma. Whereas hydrogen gas is transparent, light cannot travel through a plasma without interacting with its con-stituent particles. Suddenly the gas cloud takes on a cloudy appearance, and more-over begins to shine brightly, since as well as being opaque it is also red hot.

At this point, the gas cloud resembles a hot luminous star for the first time, hav-ing suddenly been transformed from a transparent cloud of gas to an opaque glow-ing fireball. But that fireball has a serious shortage of energy. It is continuously radiating energy away in the form of light from its hot surface, but it can only replenish that energy by shrinking further under gravity. Unless it can find a new source of energy, it is bound to carry on shrinking forever.

As the star continues to contract, its core becomes ever hotter. The protons that make up the bulk of its material have a natural tendency to repel one another, because of their positive electrostatic charge, but as they get hotter they collide with one another with ever-increasing violence. Eventually, when they reach a tempera-ture of around 15 million Kelvin, and are compressed together to a density of 150 times that of water, the collisions become so violent that the protons can stick together to form heavier atomic nuclei—specifically helium—by a process called nuclear fusion. Each time protons fuse together to form helium, a considerable amount of nuclear energy is released, and as this process becomes established, a large new flow of energy is unleashed into the cloud’s core. In time, the center of the star is heated by this nuclear power source to the point where it has enough internal pressure to put a stop its collapse.

By the time this happens, however, the cloud has shrunk from its initial size by a factor of a thousand or more, all within a period of a million years. The final product is a condensation of gas which is still losing energy from its hot glowing surface, but which is able to replenish it using a nuclear reactor in its core, which is constantly sticking protons together to form helium nuclei. With this energy bal-ance established, the star is able to delicately avoid collapsing any further: it constantly stays hot enough that its internal pressure can counterbalance its ten-dency to want to collapse inwards under the force of its own gravity.

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Stars spend the vast majority of their lives in this state. The Sun, for example, has been paying its energy bills by fusing protons together into helium nuclei for the past 5 billion years, and it will continue to do so for the next 5 billion years. Nevertheless, even if this defense against collapse can be long-lived, it cannot last forever. It relies on the Sun having a plentiful supply of protons to turn into helium nuclei, and even if the mass of gas in the Sun sounds like a lot of material by human standards—it’s around a couple of billion billion billion tons—even this large amount of fuel must run out eventually. To date, the Sun has fused almost half of the protons at its center into helium, and the remaining half are being fused at a rate of around 600 million tons per second. In around 5 billion years’ time, this supply will be exhausted, setting in train a complex sequence of events as the Sun will once again find itself short of energy.

The Red Giant Phase

As the Sun nears the end of its hydrogen-fusing life, its core—which by this point will be composed of almost pure helium—will contract a little. The layers of gas just outside its core will become hotter as a result of this release of gravitational energy. This in turn will permit nuclear fusion to transfer smoothly from the Sun’s center to a thin shell, sitting on top of its inert central core of helium. In tandem with this change, the Sun’s outer layers will expand and cool, forming a red giant star. In time, the outer envelope of the Sun will grow so large that it will engulf Mercury and Venus. As the Sun expands in this way, the rate at which it consumes hydrogen will increase, and the growth of its central helium core will accelerate.

Eventually, the temperature of the Sun’s core will rise to a sufficient temperature that the helium nuclei themselves can stick together to form carbon atoms, yielding an additional, though short-lived, new source of energy. In the enormously dense environment of the center of a red giant star, helium fusion does not occur in a steady manner, but as explosive momentary releases of energy. For a few brief seconds, the energy output of the core of the Sun may be comparable to that of all of the other stars in the Milky Way put together. The heat produced by these bursts, however, will remain trapped deep within the Sun’s blanketing envelope, stabilizing its core once more against gravitational collapse.

Even helium fusion, however, will prove to be no more than a temporary fix to the Sun’s lack of a sustainable long-term source of energy. It will not be a perma-nent way to stop the Sun’s inward gravitational collapse. Once its central helium reserve is exhausted—after a mere 130 million years—the Sun’s core will once again begin to contract, while its outer layers will puff outward as before. This time, the Earth will not escape being engulfed, and it is likely that Mars will also suffer the same fate. This outward expansion of the Sun’s outer layers will weaken the gravitational pull of the Sun’s core on its extended, tenuous envelope, and the solar wind—likely to be quite strong at this point in the Sun’s old age—will blast the remainder of the Sun’s hydrogen and helium supplies out into interstellar space, forming a planetary nebula (see Fig. 3.1 ).

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Simultaneously the Sun’s core, now comprised almost entirely of carbon and oxygen, will contract until it reaches a density where each cubic centimeter of its material weighs around a ton. At this point, quantum mechanical repulsion between electrons in the plasma will become significant, and at last the Sun will be able to prevent further gravitational collapse for the indefinite future. The Sun will have become a white dwarf star, similar in size to the Earth, yet incredibly dense. As it cools over billions of years, it will slowly fade from the night sky for the last time.

Star Formation

Going right back to the beginning of this story, though, what initial catastrophic event might have upset the balance of gravity and internal pressure in a giant molecular cloud to set this tale of gravitational collapse into motion? Much of the understanding of the stability of such clouds is built on the work of the astronomer–mathematician James Jeans (1877–1946). Jeans proved that internal pressure tends to be stronger than gravity in diffuse clouds, causing them to disperse, but that if a cloud exceeds a critical density, gravity overpowers its internal pressure and the cloud contracts. Since this only increases the cloud’s density further, the result is a runaway collapse, eventually resulting in the formation of a star.

Fig. 3.1 Planetary nebulae, which form from the expelled outer envelopes of stars as their cores turn into white dwarfs, take on a wide range of contrasting geometric patterns. It is not well understood how these patterns arise. Left : The Ring Nebula (M57). Right : The Dumbbell Nebula (M27). Both images courtesy of David Arditti, http://staglaneobservatory.co.uk/

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This is a process that we see repeating itself time and again in countless deep sky objects, though it is such a slow process that any particular star-forming region appears to be frozen in time when observed on human timescales. To see the whole process, many different regions must be observed and compared, in the hope that we might be able to place them into an evolutionary sequence—a sequence in which we might expect the younger objects to one day mature to look more like the older objects. Just as paleontologists are able to dig up fossils and infer the life cycles and evolutionary sequences of creatures without being able to see individu-als grow from birth to death, so astronomers can piece together the life cycles of stars by looking at specimens young and old.

For example, the Pillars of Creation (see Fig. 3.2 )—undoubtedly one of the most iconic images ever taken by the Hubble Space Telescope—is an image of a small detail from the Eagle Nebula (M16), a giant molecular cloud (GMC) in Serpens. The gas in the Eagle Nebula has fragmented into a large number of dense cores,

Fig. 3.2 The Pillars of Creation, an iconic detail in the Eagle Nebula (M16) observed by the Hubble Space Telescope in 1995. The largest of the pillars is roughly 4 light-years long. Credit : NASA/HST

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some of which have already formed into stars. The pillars themselves are stellar nurseries—sites where condensations of material are in the process of turning into stars. They appear dark because the gas is mixed with a small fraction of a material called interstellar dust—solid grit- and soot-like particles measuring up to a micrometer across, which are formed in the outer envelopes of stars and vented into interstellar space much like smoke. Though this dust is tenuous enough that it is almost invisible in diffuse clouds, once those clouds collapse it reaches a density that is high enough for it to become almost entirely opaque.

At the tip of each pillar is a structure called an evaporating gaseous globule (EGG)—a condensation of gas which may one day turn into a star. However, the pillars exist in a harsh environment, exposed to the intense radiation of hot young near-neighbor stars which have already formed out of the Eagle Nebula. The radia-tion of these stars heats the outer layers of each EGG, causing some of the gas to have enough thermal pressure to escape the globule’s gravitational field—to ‘evaporate’. It is this billowing flow of gas, escaping the surface of each globule, that creates the pillar structures. Star formation will not continue for much longer in the Eagle Nebula; the EGGs in the pillars of creation are already in a race against time to form stars before all of their gas evaporates, and it is unlikely that further new EGGs will form in such a hot environment.

On the opposite side of the sky, the Orion Nebula (M42) is a star-forming region at a similar stage in its development. Many hundreds of stars have already formed from it, and their heat is gradually forcing the remaining gas in the nebula to dis-sipate. Other deep sky objects show later stages in the process: most of the open clusters in the night sky are groupings of stars which once upon a time formed from a common molecular cloud, and which still remain in close proximity to one another, but which will eventually drift apart. The Pleiades (M45) is one such example—a loose cluster that is around 100 million years old. Other open clusters such as M36, M37 and M38 in Auriga are grouped around surviving molecular clouds in which there are still some sites of active star formation that remain.

Several of the stars of the Big Dipper form part of a still-later stage of such a cluster’s evolution: they are a moving group. In the past, they would have been more tightly grouped together as an open cluster, but this has since fallen apart. Now their common heritage can only be inferred from their common age and direc-tion of travel through the Milky Way.

Planetary Systems

Not all of the material in a giant molecular cloud ends up forming into stars. In fact, at most 1–3 % of the mass of a typical cloud has this fate—a fraction called the star formation efficiency. Once the cloud has formed its first small handful of stars, and once nuclear fusion has begun in the cores of these stars, they begin to produce not only a great deal of light but also strong stellar winds akin to our own Sun’s solar wind. In other words, a steady flow of energetic particles begins to be emitted from

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the surface of each newly-formed star. This means that much of the material in the outer layers of its parent globule is heated sufficiently that it is vented to interstellar space. In addition, as we have seen, the light of a young star may itself be sufficient to gently heat any other globules which happen to be nearby—as is happening to the Pillars of Creation—and may be enough to prevent them from forming into stars at all if they evaporate sufficiently quickly.

Of more interest is the material which is not quite close enough to any of the dense cores that form within a globule to be absorbed into any of the forming stars, but which nonetheless is tightly gravitationally bound in orbit around one of them. This is the material which may form into a system of planets around that star. In time, it may form into what is known as a protoplanetary disk—a flat disk of gas and dust circulating around the young star, in which solid dust grains may begin sticking together to form ever-larger bodies, until eventually planet-sized objects have been built. But there are some intermediate steps. How does a loosely-bound mass of material become transformed into a DVD-shaped thin disk out of which planets can be built?

Disk Formation

This transformation of a spherical globule into a thin planet-forming disk of mate-rial comes about because of the particular way in which the gas and dust swirls around the central star. It is not supported by pressure from within—if it were touching the star’s surface it would be part of the star—but is instead in orbit around it. Just like the planets of the solar system, it avoids falling onto the star’s surface by circling around it at high speed. Whereas the planets all circle around the Sun in the same plane, around a young star different gas particles begin by all circling around it on different orbits. They form a chaotic swirling mass. But this is not a stable state of affairs. If the gas has any viscosity—a word used by physicists to describe materials like treacle or honey that are thick rather than runny—particles on different orbits will collide and rub against one another and lose energy through friction. Even though hydrogen gas is much less viscous than treacle, it is still not perfectly runny.

As an example which demonstrates the long-term effect that such friction can have, suppose that a cloud were composed of two halves, each rotating around a central star, but flowing past one another in exact opposite directions. Exactly half of the gas would be rotating clockwise, on top of the other half, that would be trying to rotate past it in the same plane but in the opposite direction. The two halves would rub against one another until they lost all of their orbital speed to friction, came to a standstill, and eventually fell inward onto the surface of the star.

In any real protoplanetary nebula, the situation is more complex. Individual gas particles follow orbits in all sorts of different orientations in three-dimensional space. However, even in a more complicated three-dimensional swirling mass, energy is nonetheless lost to friction over tens of thousands of years as particles

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collide with one another. Slowly, the gas loses some of its orbital energy and creeps inwards towards the central star. As the process proceeds, it accelerates: there is less space at smaller distances from the star—just as the circumference of Mercury’s orbit is physically shorter than that of Jupiter’s orbit—and so the gas particles find themselves packed closer together. In other words, the gas becomes compressed to a higher density, and gas molecules collide more often.

When does this process stop? Extending the example above: if half the gas were rotating clockwise and the other half counterclockwise in the same plane, the two halves would have exactly the same amount of rotational inertia. Over time, their two motions would exactly cancel out, bringing both halves to a dead halt. In nature, however, things are very rarely exactly balanced, and it is very likely that there will be ever-so-slightly more gas rotating one way than the other. As before, the rotational motion of the two halves will mostly cancel out, but this time the cloud will be left with a tiny residual rotation at the end of the process. Once this rotational motion is shared equally among all of the gas particles, they all circle the central star in a common direction and there is little viscous friction between them.

The same process can work among gas particles that are swirling as a three- dimensional spherical cloud around a star. Initially, they follow orbits in all sorts of different orientations. Statistically, after all the other rotational motions have can-celled out through friction with other gas masses that are moving in different direc-tions, it will be found that there was slightly more gas rotating in one particular way than in any other. At this point, most of the cloud’s rotational motion will have been lost to friction. Having lost much of its orbital energy, it will have descended a long way inwards towards the central star. But finally, all parts of the cloud will be turn-ing in a common direction.

At this point, the cloud must have flattened into a plane, in order for its material to all be turning in a common direction. The massive central star must lie at the center of the orbit of every particle in the disk, since it is the force of its gravity that keeps each molecule and dust grain in the disk turning in orbit. Any given orbit has a plane associated with it, and if all of the particles at any given place in the cloud are flowing smoothly in a common direction, they must all be orbiting in the central star in same plane. In the process of losing most of its rotational energy to friction, the cloud must have flattened into a thin DVD-like disk of material.

This explains one of the most fundamental features of our solar system: that all of the planets orbit the Sun in almost exactly the same plane. It also explains why the scale of the solar system is so much smaller than the average distances that separate stars—because the planet-forming disk collapses inwards so far in the process of loosing most of its rotational motion to friction as it flattens out.

But it also explains much else besides: the process just described acts on all sorts of structures, large and small. Many astronomical objects are pancake-shaped, because disk flattening is a process that recurs again and again in astrophysics. For example, a large fraction of galaxies, including our own Milky Way, are also flat disk-like structures. When gas gravitates towards black holes it tends to collect into a thin swirling disk called an accretion disk as it spirals inward towards its ultimate fate. Many of the moons of Saturn share a common orbital plane—a plane that they

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also share with its rings. What these objects all have in common is that they all formed from the gravitational collapse of a swirling mass of material, where fric-tion acted to dissipate most of the material’s rotational energy until it was all flow-ing smoothly in a common direction, and a common plane.

Around the Earth, this process has taken place on two vastly different length scales. Within our local few light-hours, it has taken place in the formation of the solar system. But on scales of tens of thousands of light-years around the Earth, it has also taken place in the formation of the Milky Way. Since these two structures formed—one inside the other—by separate processes, they have flattened into dif-ferent planes, each of which was determined by the rotation of the particular gas cloud from which it formed (see Figs. 3.3 and 3.4 ).

Of course, not all galaxies are like the Milky Way. In the most simplistic catego-rization, some galaxies are flat spirals while others are bulbous ellipticals. Why do some galaxies follow the solar system’s example in collapsing down to thin disks, while others do not? It is now believed that the key to this puzzle lies not in how these galaxies formed, but in their subsequent evolution. Left to their own devices, individual galaxies each have their own individual rotational motions, and flatten into their own individual planes, entirely independent from those of their neighbors. But from time to time, galaxies crash into one another and merge together. When this happens to two similarly-sized galaxies—collisions which astrophysicists refer to as major mergers—the resulting merged galaxy appears as a messy, lumpy struc-ture. Once again, material finds itself swirling around on a wide variety of different orbits around the galaxy’s center. Over time, friction may smooth the material out

Fig. 3.3 The Sun lies around two-thirds of the way out from the center of the Milky Way, and the planets of the solar system orbit it in a plane that is tipped up at 63°—almost perpendicular—to the plane of the galaxy. In this artist’s impression, the scale of the solar system is vastly exaggerated to make it visible, and the nearby edge-on spiral galaxy NGC 634 is used to give some impression of what the Milky Way might look like from afar. Background image. Credit : NASA/HST

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into a steadily-rotating disk, but this may take billions of years, or even longer in galaxies where there is little interstellar gas remaining between the stars to provide any frictional drag.

For the time being, our own galaxy is of the flat variety, as is our close neighbor Andromeda (M31) at a distance of 2.5 million light-years. But the Milky Way and M31 are on a collision course which will bring them into a side-on collision in around 5 billion years’ time. As the material from the two galaxies conglomerates together, we can expect that it will form a messy remnant that looks much more like an elliptical galaxy than the flat spiral structure that we see today.

From Dust to Planets

Returning to the story of how the planets formed around the Sun, recall that the youthful Sun was surrounded by a disk of material, all rotating in a common direc-tion. This disk is made up of the same mixture of gas and dust from which the larger molecular cloud around it is composed, and it includes a significant mass of dust—a term used by astrophysicists for solid gritty grains of silicate rock and soot that measure up to a few micrometers across and litter interstellar space. As these solid

Fig. 3.4 The galactic plane and the ecliptic are shown here as they would be drawn onto the surface of a star globe, looking at the celestial sphere from the outside. A grid of right ascension and declination is also marked onto the globe, with the north celestial pole at the top

Equator

Ecliptic

GalacticPlane

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grains swirl around in a protoplanetary disk they can sometimes collide with one another and stick together. The traditional picture of how planets form is quite simple: dust grains stick together to form larger dust grains; larger dust grains stick together to form grains of sand; these in turn stick together to form pebbles; and so the process repeats itself until large rocks eventually come together to form plane-tesimals which measure a few kilometers across. At this point, the planetesimals—now around the size of an asteroid—have appreciable gravitational fields of their own and are able to start drawing in any small rocky fragments that pass nearby.

Some of the most massive rocky objects become large enough that their gravita-tional fields draw in not only rocky fragments, but also all the gas from the sur-rounding parts of the disk. In our solar system this led to the formation of the gas giant planets, most of whose mass is made up of gas rather than solid material. The inner terrestrial planets, on the other hand, only ever acquired a gravitational field that was strong enough to draw in a sprinkling of leftover rocky crumbs. Nonetheless some of the dust in the Sun’s protoplanetary disk was never incorpo-rated into rocky bodies, and remains visible today in the form of the zodiacal light—sunlight scattered from dust particles in the ecliptic plane (see Fig. 3.5 ).

Fig. 3.5 Long exposure photographs taken from very dark locations can reveal two lines across the sky which faintly glow. The fi rst of these is well known—the plane of the Milky Way—whose glow stems from the light of its countless sea of distant stars. The second glowing line—called the zodiacal light—follows the plane of the ecliptic, and arises from fi ne grains of grit and dust that litter the solar system and scatter the Sun’s light. In this photograph by Yuri Beletsky (ESO), the ecliptic crosses the Milky Way on the horizon, and from there sweeps up and to the left. Credit : Yuri Beletsky (ESO)

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Similarly, some of the rocky bodies were never incorporated into planets. In the large gap between the orbits of Mars and Jupiter, for example, planetesimals are believed to have been prevented from coalescing into larger bodies by the gravita-tional interference of the nearby massive planet Jupiter, and so the asteroid belt remains littered to this day with millions of rocky fragments of varying sizes.

This simple picture, attractive though it is, has some major problems. Most obvi-ous among these is a rather simple experimental result, obtained by any child who has ever tried throwing stones at one another at the beach. Time after time, rocks colliding at speeds of a few meters per second bounce off one other rather than sticking. Worse still, applying a little more violence in frustration at the obstinate refusal of the rocks to stick together—perhaps by taking hold of a larger rock and throwing it harder than before—the same child will merely find that instead of bouncing, the rocks eventually shatter into smaller fragments. Explaining why pebbles into protoplanetary disks appear to behave differently is not a problem eas-ily solved, just by turning powerful telescopes to nearby young stars with planet- forming disks and carefully observing what happens. Telescopes do exist that can take images of planet-forming disks—the most powerful among them being the Atacama Large Millimeter Array (ALMA) in the Chilean Andes—but even to such telescopes, the light of rocks that measure only a few centimeters across is entirely invisible amongst the haze of the millions of miles of surrounding dusty gas.

This embarrassingly simple problem, often referred to as the meter-barrier in allusion to the approximate size of the rocks most badly affected by it, remains an area of active research. A number of potential solutions have been put forward. One suggestion is that planet-forming disks, even if they start out smooth, might have a tendency to quickly develop so-called bumps —areas where there are higher con-centrations of dust particles. These dense dusty bumps might produce gravitational fields that are strong enough to sweep surrounding dust particles up directly into conglomerates, already massive enough to be bound together directly by gravity, without any requirement that the particles making them up must first become physi-cally stuck together. Another suggestion is that, as particles migrate between hotter and cooler regions of the disk, water ice may condense on their surfaces and bring additional mass and glue.

What we can say with certainty is that the very existence of the solar system demonstrates that nature must have found some way to build planets, even if scien-tific understanding of that process remains rather hazy. Moreover, in recent years we have learned that many—perhaps most—of the Sun’s neighboring stars also seem to have planetary systems around them (see Chap. 10 ). Simple models of how planets form are good enough to hint at explanations of why our solar system has some of the particular characteristics that it does, including why all of the planets orbit almost the same plane, why there is an asteroid belt between the orbits of Mars and Jupiter, and why the gas giants formed in the outer solar system while the ter-restrial planets formed further in. Nonetheless, the attempt to devise better answers to the most basic question—how did the Earth form?—remains one of the most active areas of present-day astrophysical research.

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Measuring Time

The Earth is a piece of rock that spins on its axis once every 24 h, and that circles the Sun once every 365.25 days. These two cycles give us our two most basic units of time: the day and the year. Through these two units, the way we define the prog-ress of time has, until very recently, been linked directly to the motion of our planet through the solar system. As a result, telling the time as accurately as possible has historically been one of the most important practical applications of astronomy. Astronomers have not only provided stable time standards to other people, but have also needed them for their own use. One of the most important prerequisites for any observation of the rate of progress of the planets across the sky is a clock that ticks at a steady rate.

In recent times, it has proven unsatisfactory to use the Earth’s rotation to define the progress of time. Specifically, doing so means that the basic units of time are susceptible to change if the Earth’s rotation rate were ever to change. There is a conflict between the need of scientists to have steady and predictable ways to pre-cisely measure long time intervals, and the need of the rest of society to have a simple system of timekeeping in which the Sun should always be highest in the sky at around midday. The present chapter is about this, and other problems that the Earth’s motion poses to calendar makers.

Leap Years

Perhaps the best known problem that the Earth’s orbit has historically presented to calendar makers is that each year does not contain an integer number of days. The Earth’s seasons repeat once every 365.2422 days, but simplicity demands that inte-ger numbers of whole days be grouped together into years. Even though historical

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civilizations have devised many varied calendars, none has ever found it acceptable to allow the year to change at different times of day from one year to the next.

In the long term, if years are defined to contain fixed numbers of either 365 or 366 days, the seasons drift through the year by either a quarter or three-quarters of a day per year. Within a few centuries, the seasons would completely reverse the months in which they came around. In Roman times, whole months of additional days were arbitrarily added into the calendar every few years—though not always very consistently—to compensate for this drift. It was in response to this chaotic and unpredictable calendar, in 45 bc , that Julius Caesar introduced the modern system of 365-day years, with a predictable pattern of leap days added in every 4th year. In his honor, this calendar has been known ever since as the Julian calendar.

Even the Julian calendar does not get the average length of each year quite right: an average Julian year lasts 365.25 days, whereas the seasons repeat every 365.2422 days. In other words, midsummer and midwinter drift earlier in the year by an average of one day every 128 years. This rate of drift was not corrected until the modern Gregorian calendar was devised by Aloysius Lilius (ca. 1510–1576) and Christopher Clavius (1538–1612), and later adopted in the Catholic world in 1582 with the support of Pope Gregory XIII. In the Gregorian reform, the Julian calendar was modified to remove three leap years from every 400 years, achieved by specifying that any years divisible by 100—for example 1800 and 1900—should not be leap years, unless also divisible by 400, as was the year 2000.

Even after this reform, the average length of each year remains some 26 s too long, at 365.2425 days. Some have proposed that the solution to this problem is a more complicated pattern of leap years still—among them, Sir John Herschel made such a proposal in the nineteenth century. However, the drift is small enough that it takes over 3,000 years for the seasons to drift by even a single day. As we shall see later in this chapter, irregularities in the precise length of each 24-h day, due to the fact that the Earth’s rotation is gradually slowing down, are likely to trigger need for much more substantial calendar reform long before this over-abundance of leap years will become a pressing problem.

Easter and Christmas

The problem of devising a pattern of leap years that leads to a satisfactory average length for each year has now been solved, but the historical confusion of the Julian calendar is still apparent in the date of Christmas. Today, the northern spring equi-nox is usually reckoned to occur on March 21, and the northern winter solstice on December 21. Astronomically, the exact moment when the Sun’s center appears to reach the tropics or cross the equator can occur up to 30 h before or after these canonical dates, which were chosen when the modern Gregorian calendar was introduced to satisfy long-standing religious traditions. Specifically, in the western world Easter is celebrated on the first Sunday after the first full Moon on or after the March equinox. This custom dates back to the Council of Nicaea ( ad 325), at which time the equinox happened to fall on the present canonical date of March 21.

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By the time of the Gregorian reform in 1582, the spring equinox had slipped forward to March 11, and so 10 days had to be removed from the calendar to restore the spring equinox to its former date. In Britain and the US, the Gregorian reforms were not adopted until 1752, by which time it was necessary to remove 11 days, to correct for the additional leap day which had been added in the year 1700.

The origin of the date of December 25 for Christmas is not known with certainty, but the most plausible explanation for its choice is that it was chosen to coincide with the traditional date of midwinter. Prior to 325, the winter solstice occurred later than December 21, and would have fallen on December 25 in around 200 bc . After Julius Caesar’s reform of the calendar, December 25 was widely taken to be the date of the solstice, and the date of Christmas has remained fixed since around the fourth century.

Similar confusion exists around the date of the June solstice. While customs vary greatly around the world, Britain traditionally celebrates midsummer on June 24, some 2–4 days after the astronomical solstice.

Defining the Year

So far in this chapter, the length of the year has been defined to be the period of time over which the Earth’s seasons repeat themselves—365.2422 days. More pre-cisely, this is the tropical year—the time taken for the Sun to travel from one sum-mer solstice to the next, or one winter solstice to the next.

A definition of the length of each year that is more often quoted is the length of time taken for the Earth to complete a single orbit around the Sun. Does it matter which definition is used? In fact, there is a slight difference—the period of the Earth’s orbit around the Sun is technically called a sidereal year, and at 365.2564 days, it is some 20 min longer than a tropical year. As seen from the Earth, it is the length of time it takes the Sun to complete one journey along the ecliptic to return to its starting point, and the period over which the constellations visible in the midnight sky each night repeat themselves after a full annual cycle.

Of course, it is the seasons that define the year for most people, since they deter-mine what the weather is like and when crops should be planted. It is probably only for a few astronomers that the most important thing about December is not the weather, but rather that the constellations Orion and Taurus are high in the midnight sky, and so the tropical year is the one more commonly used. But if the Earth’s seasons change as a result of its orbit about the Sun, why does the sidereal year differ from the tropical year? By the year 15000, that 20-min difference between the lengths of the two types of year will have accumulated to a 6-month offset between them. Does that mean that Orion and Taurus will have become constella-tions of the northern summer, while Sagittarius and Ophiuchus will have become January constellations? In fact, yes: the summer and winter constellations do indeed rotate gradually, so as to swap places every 13,000 years.

The clue to this difference is in the period of this rotation: the summer and win-ter constellations come back to their original places every 26,000 years. This is a

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period of time encountered before, at the end of Chap. 2 , and it is the length of time that it takes the positions of the two equinoxes to precess in a complete circuit around the ecliptic. As the Sun moves along the ecliptic—traveling from right-to- left across Fig. 2.16—the two points where the celestial equator cross its path move gradually to the right across this plot. One year after a March equinox, the next one comes momentarily before the Sun has completed a full circuit along the ecliptic. To be precise, it comes 20 min beforehand. It is these 20-min offsets that add up to mean that the time of year when any given constellation appears highest in the sky rotates gradually through the year.

How Long Is the Day?

Just as the number of days in each year has troubled calendar makers over past centuries, in more recent times it has been the length of each day that has been found to be more complicated then previously thought. Most people know that each day on Earth lasts for 24 h. The explanation often given for this is that the Earth rotates about its polar axis once every 24 h, and that as it does so, the Sun appears to complete a circuit around the heavens. At midday, the Sun is highest in the sky, and at midnight it is lowest in the sky—usually some distance below the horizon. As is often the case, however, the truth is a little more complicated.

The first inaccuracy in this simple picture is that the Earth doesn’t rotate on its axis once every 24 h, but a little faster than that—turning once every 23 h and 56 min. This is the period with which stars of the night sky appear to revolve around the celestial poles, called the sidereal day. Any given star will rise at exactly the same point on an observer’s horizon every 23 h and 56 min.

The time of day, however, is defined not by the positions of stars in the sky, but specifically by the position of the Sun. A simple definition of the midpoint of the day is the moment when the Sun is highest in the sky—when it transits—though we shall see shortly why this definition is nowadays only rather vaguely used. The moment of the Sun’s transit is called noon—as distinct from 12:00, midday.

Unlike the stars, the Sun moves appreciably across the celestial sphere from one day to the next—by around a degree, or twice its diameter. Since this motion is in the opposite direction to the sky’s apparent daily rotation, after each complete revo-lution the Sun is a full two Sun-widths behind where it appeared relative to any background stars the previous day. It takes the sky’s rotation just under 4 min to travel this extra distance, and so while astronomical objects transit once every 23 h and 56 min, the Sun does so once every 24 h (see Fig. 4.1 ).

This means that, as measured using the 24-h system of time, any given star rises, culminates, and then sets again 4 min earlier each day—or 2 h earlier each month. After 12 months, it rises 24 h earlier, at exactly the same time of day. In the inter-vening time, 365.25 days have passed, but the Earth rotated on its axis 366.25 times, and this is the number of times that the night sky appears to have revolved on its axis.

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Mean Time

In practice, things are more complicated still. The 4 min difference between the sidereal day and the solar day is not the same every day. The easiest way to understand why is to look at the Sun’s path across the night sky, which was pro-jected onto a rectangular grid of right ascension and declination in Fig. 2.11. Any star that stays fixed at the same spot on Fig. 2.11 culminates once every sidereal day. The Sun, however, moves leftward across the map by an average of 4 min in right ascension each day. But the Sun’s path across Fig. 2.11 it not a straight line. The ecliptic is a circle around the sky, but it is tipped up relative to the celestial equator. Although the Sun moves along the ecliptic at a fairly steady rate of around a degree each day, this causes the Sun’s position to vary not only in right ascension, but also in declination. As seen in Chap. 2 , this is what gives the Earth its seasons.

At the solstices, the Sun’s movement in declination comes to a standstill at the tropics—this is where the tropics are defined to be. But as the Sun passes the celes-tial equator at the equinoxes, its movement in declination is at its greatest. There is a corresponding change in the Sun’s rate of movement in right ascension: at the equinoxes, when the Sun traces a diagonal line across Fig. 2.11 rather than a hori-zontal line, it moves comparatively slowly in right ascension. Conversely, when the Sun moves along a horizontal line across Fig. 2.11 at the solstices, its right ascen-sion changes comparatively quickly. In short, a move of one degree along the ecliptic does not correspond to the same change in right ascension at all times of year. The obliquity of the ecliptic makes days longer around the solstices and shorter around the equinoxes.

There is an additional complication. The Earth’s orbit is not strictly circular, but slightly elliptical. It makes its closest approach to the Sun (perihelion) around

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Fig. 4.1 The Earth turns on its axis once every 23 h and 56 min, but the Sun appears to rise and set once every 24 h. This is because the Earth moves by around one degree along its orbit each day, changing the direction from which the Sun illuminates it (not shown to scale). Beginning at noon, an observer standing on the mountain shown, being carried round by the Earth’s rota-tion, needs to complete a little over one complete revolution around the Earth before the Sun appears directly overhead again

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January 3, and is furthest from the Sun (at aphelion) around July 4. According to Kepler’s Laws of planetary motion, any planet moves more quickly when it is closer to the Sun, and more slowly when it is further from the Sun. The Earth is no exception, and this means conversely that the Sun’s apparent rate of motion along the ecliptic is not completely steady over the course of the year. It is at its fastest in January, and at its slowest in July.

Both of these effects cause the length of the day to vary by up to 20 s through the year. Remarkably, the first of these effects had already been identified by the Babylonians as early as the second millennium bc ; they were aware that the rate of motion of the Sun in right ascension varies through the year. They even devised simple algebraic tools to work out the Sun’s position given this variable rate of motion. Nonetheless, before the widespread use of accurate clocks, this detail was largely academic. The Sun’s position was used to tell the time, and it was not a problem that days varied in length by a few seconds depending upon the time of year. For example, sundials work by measuring the east–west position of the Sun in the sky, and measure what is termed local solar time, a system in which midday is defined to be the moment when the Sun transits at noon.

However, with the advent of accurate mechanical clocks, it has become prefer-able to find a definition of the length of each day in which hours—defined to be a 24th of a day—and seconds have a constant length throughout the year. For clockmakers, this means their mechanisms do not need to run at different rates on different days of the year. For scientists, it means that experiments which involve making precise measurements of how long processes take do not suffer inaccura-cies due to the units of time themselves varying in length.

Mean time is just such a system. In such a system, the length of each 24-h period is constant throughout the year, defined to be the average (or mean) period of time it takes the Sun to move from noon on one day to noon on the following day over the course of the year. On any given day of the year, the length of the solar day may differ by up to 20 s from this, and since these errors accumulate day by day, the time at which noon occurs according to a clock showing mean time may drift at a rate of up to 10 min per month relative to solar time. However, the length of the mean day is chosen such that there is an exact balance between the times of year when noon drifts earlier in the day, and those when it drifts later in the day. After one whole year has elapsed, noon has returned to exactly the same mean time.

In a mean time system, the time interval between noon and midday is called the equation of time, where the word equation is used in a historical sense, not to mean an algebraic expression but rather a correction. Although the equation of time var-ies by up to 20 min through the course of the year (see Fig. 4.2 ), it repeats almost exactly the same pattern each year, since the Earth follows almost exactly the same path around the Sun from one year to the next. The equation of time is often repro-duced on modern sundials, whose readings of solar time must be corrected to give the mean time that is more conventionally used.

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Time Zones

A further complication stems from the use of local time zones which do not neces-sarily correspond to the observer’s exact longitude. For example, Ohio uses the same time zone as New York, and their clocks read midday at exactly the same moment—roughly the average time that noon might be observed from New York—even though noon occurs over half an hour later as seen from Ohio. A sundial in Ohio reading local solar time will consistently show a time that is half an hour earlier than that shown by an identical sundial placed in New York, resulting in a vertical offset to the equation of time shown in Fig. 4.2 .

Sunrise and Sunset

Another way to depict the equation of time is to plot the changing apparent position of the Sun in the sky at midday each day, as is done in Fig. 4.3 . Figure 4.3 represents what a northern-hemisphere observer would see, looking south, if he were to plot

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Fig. 4.2 The time difference between solar and mean time is called the equation of time. Over the course of the year it varies by up to 30 min, but following a pattern which repeats itself almost exactly from one year to the next. Thus, on any given day of any given month it has very nearly the same value every year. As discussed in the text, the annual variation of the equation of time arises from a combination of two mechanisms—the obliquity of the ecliptic and the eccentricity of the Earth’s orbit—whose individual contributions are shown above in red and blue respectively

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the position of the midday Sun on different days of the year. Vertically, the altitude of the Sun at midday cycles with the seasons, being highest around midsummer and lowest around midwinter. This is labeled as north–south in Fig. 4.3 , indicating the Sun’s changing declination. But the Sun’s apparent position also moves east and west relative to the meridian. On some days the Sun is still east of the meridian at midday, approaching transit, while on others it has already passed noon and is to the west of the meridian. This movement follows the equation of time. The result is a figure-of-eight pattern that the Sun traces out each year, called an analemma. Although Fig. 4.3 plots the analemma that would be recorded by a northern-hemi-sphere observer, the same pattern would also be seen in the southern hemisphere, viewed upside down and with the summer and winter solstices swapped.

The shape of the analemma is key to a question that is often asked about sunrise and sunset times. Through the spring, evenings draw out, until a date sometime around the summer solstice when the Sun sets later than on any other day of the year. By definition, the summer solstice is the longest day of the year, and so if sunset and sunrise grew later and earlier through the spring in exact mirror image, the summer solstice should also be the day of the latest sunset and the earliest sunrise.

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In fact, even a fairly casual observer can spot that this is not the case by taking note of the time of sunset each day. Figure 4.4 shows the sunrise and sunset times that might be recorded around the time of the summer and winter solstices. Exact times depend on the observer’s latitude; those plotted here are for a latitude of 50°N. It is apparent that the earliest sunrise occurs around a full week before the solstice, while the latest sunset occurs around a full week afterwards. Similarly, at midwinter, evenings begin to draw out a full week before the solstice is reached, while the mornings continue to draw in until over a week past the solstice. These patterns are identical in both northern and southern hemispheres.

These offsets occur because of the conversion between solar time and mean time. In solar time, sunrise and sunset times do follow a simple mirror-image pat-tern. In solar time, the solstice is simultaneously the longest day, the day of the earliest sunset, and the day of the latest sunrise. But to convert these times to mean time, the equation of time must be subtracted from them. Equivalently, looking at the analemma shown in Fig. 4.3 , at both solstices, midday Sun is moving eastward (to the left). This means that each day, the Sun transits a few seconds later than it did the day before, as measured using clocks that tell mean time. Even without any seasonal change in the length of the day, sunrise and sunset times would move a few seconds later each day in December and June, in step with the changing time of noon.

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Fig. 4.4 The times of sunrise ( bottom panel ), noon ( central panel ) and sunset ( top panel ) around the times of the summer and winter solstices. These charts are shown for a latitude of 50°N in 2016, but vary little from year to year

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In the weeks before the summer solstice, what is the effect of the daylight hours getting longer, while noon is simultaneously drifting a few seconds later each day? In solar time, the Sun rises a few seconds earlier each day. The number of seconds by which sunrise gets earlier is fewer each day, until eventually at the solstice, the time of sunrise comes to a standstill. When this is converted to mean time, the pattern changes. At the solstice itself, since there is no variation at all due to the changing length of the day, both sunrise and sunset get later in exact step with noon. At some point around a week before the solstice, the rate at which sunrise gets earlier in solar time is exactly counterbalanced by the rate at which noon is getting later. The two effects cancel out to bring sunrise to a standstill—the earliest sunrise of the year.

The effect is the same for both northern- and southern-hemisphere observers. Although the summer and winter solstices are swapped, on both occasions noon is moving later in the day at a rate of around 10–15 s per day, and so the effect acts in the same direction on both dates, albeit slightly more strongly in December than in June.

Atomic Time

Even in mean time, the length of each hour is still defined by a combination of the Earth’s rotation period and the time it takes to orbit the Sun. Specifically, each hour is a 24th of the length of a typical solar day, once seasonal variations are averaged out. This means that if the Earth’s rate of rotation were ever to change, the defined length of the hour would change, potentially causing problems for scientists whose work relies on timing events very accurately. Astronomers are just such a group, since modeling the motion of any planet, asteroid or comet involves making obser-vations of its position at accurately specified times, and then fitting a trajectory through a number of observed positions.

Until the twentieth century, no such experiment had data of sufficient accuracy to be troubled by any variation in the defined length of the hour. By the late 1920s, however, anomalies were beginning to be apparent in the observed orbits of Mercury, Venus and the Moon. These were particularly apparent in the Moon’s orbit, because the Moon travels such a significant distance across the celestial sphere each day—12°—and because the Moon is large enough that it often occults bright stars. The moment at which a star disappears behind the Moon can be timed with at least second accuracy, providing a very precise momentary fix on the Moon’s posi-tion. The Moon did not appear to be moving along its orbit at a perfectly steady rate, and there was no easy way to explain why. Moreover, simultaneous and identical anomalies were soon identified in the positions of Mercury and Venus. All three celestial bodies were speeding up and slowing down in unexpected ways—and all three were doing so in perfect synchrony. This provided a strong hint that the prob-lem lay not with the Moon’s orbit, but with the measurement of time itself. It appeared that the Earth was not rotating at a constant speed.

It is now understood that this is due to a variety of mechanisms. As will be elaborated on in Chap. 5 , the Earth’s ocean tides mean that its rotation is gradually slowing down and its days lengthening as it slowly transfers its rotational energy to

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the Moon. Moreover, on short timescales, events such as ocean currents and earth-quakes can trigger small short-term changes in the Earth’s rotation.

In 1952, a first attempt was made to fix the problems this posed to timekeepers. Instead of using the Earth’s spin, the Earth’s motion around the Sun was to be used to keep track of time. This was assumed—rightly—to be stable over much longer time periods than the Earth’s own rotation, and could be measured easily by observ-ing the Sun’s progress along the ecliptic relative to any background stars that it passed in front of. In the new system, the length of each hour was arbitrarily chosen to be a 24th of the length that January 1, 1900 had had in mean time, and the new hours were counted from midnight on that day. This system was named ephemeris time (ET), since it was used primarily by astronomers, who needed such a stable time standard to calculate planetary ephemerides in which the planets didn’t seem to waver in their speeds.

Within a very few years, technology provided a more workable solution. In 1955, the first accurate atomic clock was built by the National Physical Laboratory (NPL) in the UK, using the fact that atoms produce light waves of very well defined frequen-cies (i.e. colors) when electrically excited. Specifically, the 1955 clock worked by counting the cycles of microwave emission produced by caesium-133 atoms, which when kept in very well controlled conditions radiate at a very well- defined frequency of around 9.2 GHz, equivalent to a microwave wavelength of 32.6 mm. Modern atomic clocks—which still often use caesium-133 atoms—can now keep time with accuracy better than 1 s in a few tens of millions of years. In contrast to astronomical observatories that are equipped to make high precision measurements of the Sun’s position, they have the advantage that they can be built to order for anyone who needs a very accurate time standard, albeit at a cost of tens of thousands of US dollars.

Since 1972, ephemeris time has been superseded by international atomic time (TAI), defined such that each second is exactly the time taken for a caesium-133 atom to produce 9,192,631,770 cycles of microwave radiation. This definition was chosen so that TAI clocks read the same time, and used the same length of second, at the moment of the transition from ET. The process of refinement has continued ever since. Atomic clocks are now accurate enough to detect that higher altitude clocks run faster than low altitude clocks, due to an effect called gravitational time dilation predicted by Einstein’s General Theory of Relativity. The Earth’s gravita-tional field causes time itself to run fractionally slower at sea level than at any altitude above it, such that a high-altitude clock will drift ahead of one at sea level. It has become necessary to define the altitude at which TAI clocks should be situ-ated—the Earth’s average sea-level—and for clocks situated above sea level to be corrected for the fact that they run fast.

Leap Seconds

While the fixed pulse of atomic time is a great convenience for scientists, separating the definition of the length of each hour from the rate of the Earth’s rotation intro-duces the prospect that the times when the Sun appears in the sky may gradually

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drift out of alignment with the times of day read by clocks following TAI. Furthermore, the Earth’s rotation rate is gradually slowing down and days getting longer, while each 24-h period in TAI is defined to (roughly) match the historical length of January 1, 1900. It is inevitable, then, that such drift will eventually hap-pen. In a few thousand years’ time, the length of each day as reckoned by the progress of the Sun across the sky will be 1 s longer than 24 h of atomic time, lead-ing to an accumulated drift of over 6 min (360 s) per year in sunrise and sunset times (see Chap. 5 ).

To avoid this problem, since 1972 civil time has been defined using a system called coordinated universal time (UTC), which is distinct from atomic time. The two systems run at the same rate, but whenever UTC is found to disagree with the observed position of the Sun in the sky by more than half a second, a second is either inserted into or subtracted from UTC, causing a particular minute to have either 59 or 61 s. At present, the task of monitoring the Earth’s rotation is managed by the International Earth Rotation and Reference Systems Service (IERS), which ultimately decides when such leap seconds should be added. To date, the Earth has always been found to have been rotating more slowly than it was in 1900, and so seconds have been added rather than taken away, at a rate of roughly one every 2 years. By custom, such seconds are added at midnight, Greenwich time, on either January 1st or July 1st.

The offset between atomic time and universal time is recorded by a quantity called ΔT, though for historical reasons ΔT actually equals this time offset plus an additional 32.184 s. Strictly speaking, ΔT records the offset between another time standard, terrestrial time, and universal time, where terrestrial time lags atomic time by exactly 32.184 s.

The historical offset between universal time and atomic time provides an insight into the historical rate of the Earth’s rotation, and remarkably, historical records exist which allow it to be estimated many centuries in the past. For example, observers in past centuries have often noted the exact times at which they were able to make observations of lunar occultations and eclipses. Modern computer models of the Moon’s orbit allow the timing of its passage through the solar system to be traced with sub-second accuracy, even thousands of years in the past. Eyewitnesses from past centuries can tell us the exact time of day, using the solar time of the day, at which these events took place. Simulations, meanwhile, can tell us the exact atomic time at which they actually occurred. With suitable correction, the differ-ence between the two is a measure of the historical value of ΔT.

Since the invention of the telescope in 1609, occultations of stars by the Moon have provided the most frequent stream of events whose times it was technically feasible to observe and record with high precision. Before 1609, eclipses are the only events which provide occasional points of reference, and Durham University’s emeritus professor of applied historical astronomy Richard Stephenson (1941–) has pioneered the study of them in recent years. For present-day measurements of ΔT, it has become possible since the advent of radio astronomy after World War II to directly measure sidereal time with sufficient accuracy that it can be directly compared with atomic clocks to determine the Earth’s rotation rate. This is done

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using very distant quasars, which are so distant—typically billions of light-years away—that their positions in the night sky can be assumed constant and any tiny irregularity in their daily rotation can be attributed entirely to the Earth’s rotation.

Reconstructing historical values of ΔT from all of these data reveals a chaotic variability (see Fig. 4.5 ) over the past 400 years. If the Earth’s rotation were slow-ing at a constant rate, ΔT would be expected to follow the smooth dotted curve, with shorter days in the past and longer days in the future. The deviation of the two lines is due to short-term phenomena such as earthquakes and ocean currents, which even on century-long timescales overwhelm the long-term slowing of the Earth’s rotation.

Looking back further using historical eclipse observations, Richard Stephenson has been able to estimate the historical length of days over the past 3,000 years. A particularly clear-cut demonstration that days have grown longer is a set of obser-vations of the total solar eclipse of April 15, 136 bc , which was observed from Babylon. Modern computations of the Moon’s orbit, combined with a naive assumption that the Earth has been rotating at a constant rate over the intervening years, find that the Moon was indeed aligned to produce a total solar eclipse on that day, but that its shadow didn’t pass anywhere near Babylon. Instead, it passed along the west coast of Africa, some 50° in longitude (3 h) to Babylon’s west. The Earth’s rate of rotation has no effect on the alignment of the Sun and Moon that

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Fig. 4.5 The offset between terrestrial time (TT) and universal time (UT) is called ΔT. Here, estimated historical values of ΔT are compared ( solid line ) against the trend that would have been expected if the Earth were slowing at a steady rate ( dotted line ). Terrestrial time, for his-torical reasons, runs in step with international atomic time, but 32.184 s ahead

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produced the eclipse, but it did affect which landmass lay beneath the Moon’s shadow at this particular moment in 136 bc . The Earth’s faster rate of rotation in past centuries has added up to produce a full 50° additional rotation over the inter-vening 2,200 years. Based on data such as this, Fig. 4.6 shows Stephenson’s best estimate of the historical lengths of days over the past 3,000 years, expressed as an offset in milliseconds from their present length of 86,400 modern seconds. Extending the data back further still, it is likely that days lasted only 22 h at the time of the dinosaurs, 65 million years ago.

The Future of Leap Seconds

In recent years, there has been growing debate about the future of leap seconds, especially in those years where leap seconds have been added. Essentially, the argu-ment for abolishing leap seconds is that they make our calendar excessively com-plicated. For example, two observations of Mars, made at exactly 11 p.m. on June 30, 2012 and 1 a.m. on July 1, 2012, are separated by 2 h and 1 s, but this is only apparent if the person doing the calculation happens to have an up-to-date list of leap seconds available to hand. Care must be taken when doing arithmetic with times written in civil time when wanting to calculate how long processes have

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taken. Scientists making very precise timings of long-running events often use atomic time to ensure that no leap seconds are missed in their arithmetic, but it is an easy mistake to slip into. Furthermore, it is completely impossible to do such arithmetic with future dates—to ask when a 30-s process will finish, if started at 23:59:50 on December 31, 2100—as leap seconds are usually only announced 6 months in advance. This is an especial problem for computer software, and on June 30, 2012, there were several reported cases of computer systems crashing when their clocks appeared to stand still for a second.

In the near term, the benefit from having leap seconds is arguably quite small, since few people would notice if noon were to systematically drift by a few seconds later in the day. Over coming centuries, however, if the Earth’s rotation continues to slows down at the average rate that it has done over past centuries, leap seconds will have to be added at an ever-increasing rate. By 2250, leap seconds may be needed every year, and by 3000, three may be needed each year. Arguably, it may make more sense by then to redefine the length of each day to be a little longer, rather than to make such frequent adjustments to our clocks. In the near term, the future of leap seconds will next be discussed at the International Radio Conference in 2015, and they may then be abolished. In the longer term, we will have plenty of time to consider how to deal with the growing length of days.

The Future of Leap Seconds

77D. Ford, The Observer’s Guide to Planetary Motion: Explaining the Cycles of the Night Sky,The Patrick Moore Practical Astronomy Series, DOI 10.1007/978-1-4939-0629-1_5,© Springer Science+Business Media, LLC 2014

The Moon

The Moon is uniquely spectacular among astronomical objects—the only one bright enough to be visible in broad daylight, and which provides enough light to work by at night. Sometimes amateur astronomers challenge one another to see if they can take photographs of shadows cast by the light of Venus, which can just about be done from an incredibly dark site. By contrast, shadows cast by moonlight are so easily apparent that they can even be seen by the unaided eye in a light- polluted town.

Friend or Foe?

In fact, the Moon is so bright that the whole sky glows faintly whenever it is above the horizon. Just as the Sun’s light is scattered by particles in the Earth’s atmo-sphere to make the sky appear blue during the day, moonlight creates a similar, albeit much more faint, glow at night. At around the time of new moon, when the Moon is safely below the horizon all night, it is often possible to photograph stars down to at least eighth magnitude, even from a small town, simply by mounting a camera on a tripod and opening its shutter for 30 s. The result of trying to do the same when the Moon is close to full is invariably a disappointment. Photographs of the sky come out looking remarkably as if they had been taken during the day, with the Moon taking the place of the midday Sun and only a few of the brightest stars piercing through the sky’s blue glow.

In this way, the Moon can be rather a nuisance. It is surely the only astronomical object about which the letters columns of astronomy magazines can contain argu-ments between planetary and deep sky observers, debating whether it might

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legitimately be called a source of light pollution. The target of one person’s observing can be to another person a blinding white light (Fig. 5.1 ) .

However, for all the annoyance its bright light may sometimes cause, the Moon has a singular ability to inspire new generations of people into astronomy. It is vis-ible from light-polluted cities and dark woodlands alike, and its exceptional appear-ance is not just a matter of its being bright. At a distance of only 380,000 km (0.00254 AU), it has almost exactly the same angular size as the Sun—roughly half a degree—and is the only heavenly body on which surface features can be resolved by the unaided eye. Its mottled pattern of light and dark areas represent two distinct types of terrain. The dark areas are called maria —originally so named because they were thought to be oceans of water, they are now known to be vast flat volcanic planes. Between the maria, the lighter colored terrain is considerably rougher and more mountainous—the lunar highlands .

To bring the Moon’s heavily cratered surface into view, nothing more expensive than a cheap pair of binoculars is needed. This sight—which can be improved by using a modest telescope—is the only such detailed glimpse that any ground-based

Fig. 5.1 The First Quarter Moon. Image credit : NASA Goddard Space Flight Center

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observer can ever get of the surface of an alien world without flying into space. With a moon map to hand, it is easy to pick out dozens of named features.

The Moon is often the place where beginners in amateur astronomy turn their telescopes first. It is an object that anybody can find, and whose surface has plenty to offer even when viewed through the cheapest instrument. This role as a training ground goes back a long way. Historically, it was one of the obvious places for the pioneers of telescopic astronomy to try pointing their first rather crude instruments in order to cut their teeth. Even earlier still, before the invention of the telescope, the maria had already been coarsely mapped out with the naked eye. For example, an exceptional pre-telescopic map was made by the English physicist William Gilbert (1544–1603) in around 1603. Curiously, no such maps survive from ancient times, even though earlier generations would have been at little disadvantage in terms of the instrumentation available to them. Nonetheless, even if documentary evidence is lacking, it seems unlikely that the ancient world was entirely devoid of lunar observers, not least because references to the mythical ‘man in the Moon’, whose figure is made up from the pattern of dark maria on the Moon’s face, date back at least as far as Plutarch (second century AD ).

Within a few months of the invention of the telescope in 1609, several observers had produced detailed maps, including Galileo and Thomas Harriot. Many of the names that we now associate with the most prominent of the Moon’s craters were assigned by the Jesuit priest Giovanni Riccioli (1598–1671) and first published in 1651.

The Formation of the Moon

The Earth is unusual among the solar system’s planets in having a moon that is comparable in size to itself. Even though the Moon is considerably smaller than the Earth—it measures a little over a quarter of an Earth-diameter across and has less than an 80th of the Earth’s mass—this relative size is large in comparison to the moons of the other planets. Among the other terrestrial planets, Mercury and Venus have no known moons at all, and though Mars has two companions, Phobos and Deimos, their masses are both less than a millionth that of their parent.

By contrast, the gas giants each have dozens of moons. Four of these are even larger than our own moon—in decreasing order of size, Ganymede (Jupiter), Titan (Saturn), Callisto (Jupiter) and Io (Jupiter). However, the gas giants are much larger than the Earth: Jupiter and Saturn have masses of 320 and 95 times the mass of the Earth respectively. In terms of relative size, even if these moons are larger than our own, they are tiny in comparison to their parents.

How did the Earth come to have such an unusual Moon? As well as its large size, any theory of how the Moon formed must also explain another puzzle: the fact that it has a composition that is remarkably similar to that of the Earth. Each chemical element can exist in multiple variant forms known as isotopes, each of which are chemically identical but weigh slightly different amounts. For example,

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the nuclei of titanium atoms all contain 22 protons, but can contain either 25 or 28 neutrons. Any given piece of titanium contains a mixture of these two types of atom, and the two can only be distinguished by their slightly differing weights. Titanium- containing rocks found on each of the terrestrial planets have different relative fractions of these two isotopes, but the fractions are quite consistent among different individual rocks found on the same planet. The same is true for other atoms which come in multiple isotopic varieties. Putting all of this informa-tion together for any given piece of space rock, it is possible to make a reasonable guess of which planet it originated from, based on a detailed analysis of its composition.

It is likely that these distinct isotopic fingerprints date back to the solar system’s early history. In the Sun’s original protoplanetary disk, the relative abundances of heavier and lighter isotopes would have varied with distance from the center; denser isotopes would have gravitated more strongly towards the Sun, while lighter isotopes would have floated buoyantly out to its outskirts. Hence the inner planets formed from material that was richer in heavier isotopes than the outer planets.

In contrast to rocks studied on other planets, those returned by the Apollo mis-sions from the Moon have shown very similar isotopic fingerprints to rocks found on the Earth. This is not only suggestive that the Earth and Moon formed in very close proximity, but even implies that they were once part of the same body. The evidence for this claim comes from one of the most abundant elements in the Universe: iron. Even though there is enough iron ore in mines for most human needs, by the standards of other bodies, the Earth’s surface has less iron than might be expected. This deficit can be easily explained: iron is heavy, and in all probabil-ity, most of the Earth’s iron sank to its core early in its history. We know from the Earth’s strong magnetic field that its core is indeed very rich in iron. But the Moon’s surface is also deficient in iron, by about the same amount as the Earth’s surface, and this is despite its having no magnetic field or any other evidence for an accumulation of iron at its core.

The Giant Impact Hypothesis

The now widely accepted theory of the Moon’s formation is known as the giant impact hypothesis, proposed by William Hartmann and Donald Davis in 1975. According to the theory, the Earth collided with a large protoplanet early in its history, similar in size to Mars and called Theia. This happened only around 100,000 years after the Earth’s own formation—around 4.5 billion years ago—but sufficiently long afterwards that the Earth’s iron had already sunk to form a heavy metallic core, which as today was surrounded by a less dense rocky mantle. The collision had two effects: it melted much of the Earth’s crust and mantle, and it placed a sizeable cloud of debris into orbit around the Earth. It was this debris, largely material from the Earth’s own mantle, that later conglomerated to form the Moon.

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This model not only explains the similarities between the Earth and Moon, but also some of their differences. The Moon has little magnetic field and is less dense than the Earth, which suggests that it has little or no iron core. This matches the predictions of the Hartmann & Davis model, in which only material from the Earth’s outer mantle would have been present in the post-collision debris cloud.

Nonetheless, the model leaves some unanswered questions which still trouble theorists today. In particular, the debris resulting from such a collision would have included a sizeable fraction of material from Theia itself, which we must presume to have had a different composition from the Earth. But in fact, the closeness of the Moon’s composition to the Earth’s mantle suggests very little pollution with mate-rial from another body.

Moreover, the Moon’s surface can be divided into two halves which are charac-terized by substantially different types of terrain. The near side, which is always turned towards the Earth, is almost one-third covered by dark flat maria, with the remaining two-thirds being brighter and more mountainous. If we could see the far side, were it not perpetually turned away from the Earth, it would appear quite dif-ferent from the near side, even to the unaided eye. It is considerably more moun-tainous, and less than 2 % of its area is covered by flat planes. This division of the Moon’s surface into two halves goes well beyond what might have arisen by chance alone, and suggests that some additional mechanical process has been at work on one side of the Moon. In 2011, a revised version of the Hartmann & Davis model was proposed by Martin Jutzi and Erik Asphaug, in which debris from an interplan-etary collision with Theia conglomerated into not one, but two separate moons, 130 times larger than the other. Jutzi & Asphaug argue that these could have remained in stable orbits around the Earth for tens of millions of years, before eventually colliding at low speed. If the resulting collision were too slow to trigger substantial melting of the larger body’s crust, the material from the smaller moon would have formed a mountainous rubble pile on one side of the larger body, resembling the lunar far side.

The Geology of the Moon

Geologists refer to the lunar highlands and maria as primary and secondary crust, reflecting their formation in two distinct phases of the Moon’s history. As the Moon cooled after its violent formation event, different materials within it solidified at different times, depending on their freezing points. Silicate rocks solidified first and rose buoyantly to the surface, floating on the sea of magma below. These silicate rocks formed the Moon’s initial primary surface, now the lunar highlands, which originally covered its whole surface. At later times, the molten rock which remained beneath this primary surface broke through from time to time in volcanic eruptions, flooding areas with lakes of basalt to form the flat lunar maria—the Moon’s sec-ondary crust.

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On the Earth, volcanism continues to this day. Magma beneath its surface remains molten, and the continents continue to drift in their positions as a result of plate tectonics. The Earth’s larger size and longer cooling time, together with radio-active elements in its core which act as a nuclear heat source, mean that its mantle remains hot enough to be fluid. Floating as a solid skin on top of this flowing rock, the continents shift by up to a few centimeters each year. For example, the distance between Europe and North America widens by an average of 1–4 cm each year, while some parts of the sea bed around South America move by up to 12 cm in a typical year.

By contrast, the Moon is believed to be geologically dead. Its rock has long since frozen solid all the way through and volcanic eruptions no longer occur. Its surface is almost entirely unchanging—especially so since there is no lunar atmosphere to produce weathering or erosional processes on its surface. Meteorite impacts are the only ongoing process that can occasionally create new features. Small meteoroids regularly collide with the Moon, and at the heights of major meteor showers such as the Leonids it is possible given a large telescope and plenty of patience to detect a handful of flashes from the unilluminated part of the Moon’s disk when these meteoritic particles strike it. Such meteoroids may leave craters a few meters in diameter, and the flashes from their impacts can vary between fourth and eighth magnitude as seen from Earth. However, cratering events of the kinds that created the named craters that are shown on maps of the Moon’s surface are now believed to be very rare.

The Apollo missions took samples of material from around a number of large craters, and these have been analyzed to try to find out how long ago these craters formed. The resulting estimates suggest that they all formed at a very similar time, around 4 billion years ago. This not only implies that the Moon’s craters are very ancient structures, but also that many of them formed in a short but intense burst of impacts which has now become known as the late heavy bombardment. Speculation continues as to what might have triggered this violent episode is the solar system’s history, and what effect it might have had on the Earth itself. One idea is that a sud-den instability in the orbits of a sizeable group of asteroids may have caused them to simultaneously career into the inner solar system.

Today, however, cratering events seem to be so rare that the footprints left by the Apollo astronauts are likely to remain intact for at least several tens of millions of years, and perhaps much longer still. By contrast, the six US flags left behind at each of the Apollo landing sites are likely to last only decades. They will already appear heavily faded, after decades of exposure to the Sun’s ultraviolet radiation, and they may already have disintegrated entirely. Images taken by the Lunar Reconnaissance Orbiter (LRO) in 2012 had high enough resolution to be able to identify shadows cast by five of them, suggesting that they remain intact for the time being, however. The sixth, that left behind by Apollo 11, is believed to have blown over when the astronauts departed the surface.

Seismometers planted at the Apollo landing sites returned data for several years after the Moon landings, detecting not only shock waves from meteoroid impacts, but also, rather surprisingly, some moderate earthquakes beneath the Moon’s

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surface. How earthquakes can arise on a body that has not had any volcanic eruptions or continental drift for billions of years remains poorly understood, but one suggestion is that they stem from the slumping of large crater walls.

The Moon’s Phases

Without doubt the most conspicuous changes in the Moon’s visual appearance are its monthly cycle of phases. At new moon—taken to be the beginning of each cycle—it is entirely unobservable, both because it presents an almost entirely unilluminated disk and also because it lies so close to the Sun in the sky. Over the following 29.5 days, the Moon drifts gradually eastward relative to the Sun, rising and setting around an hour later each day. Eventually, having made a complete circuit around the celestial sphere, it comes back to meet the Sun again at the next new moon.

Over the first 2 weeks of this cycle, its waxing phases, the Moon is visible in broad daylight in the afternoon, and remains visible for gradually longer periods each day in the post-sunset evening sky. It grows from an initially thin crescent, through half phase on the seventh day—at first quarter—to become gibbous, even-tually reaching full moon on the 14th day. Seen from the northern hemisphere, the Moon’s disk appears to become illuminated from right-to-left, while the opposite is seen from the southern hemisphere. Observers near the equator see the Moon’s phases in an almost vertical orientation.

When full, the Moon lies almost directly opposite to the Sun in the sky, rising as the Sun sets and setting as the Sun rises, so as to be visible for almost the whole night. Over the following 2 weeks the Moon continues its eastward jour-ney, now getting closer to the Sun again and approaching it from the west. As it does so, it rises an hour later in the evening each day, until eventually it is only visible in the early morning and pre-dawn sky. At this time it is also visible in broad daylight in the morning sky. Each day, a smaller portion of the Moon’s disk is illuminated, returning to half phase at last quarter and then becoming an ever-narrowing crescent for the cycle’s final week. Darkness spreads across the Moon’s disk in the same direction that light had spread across it in the first half of the cycle; from right-to-left in the northern hemisphere, and vice versa in the southern hemisphere.

Although the Moon is brightest when it is full, in many ways this is not the best time to observe its surface. The line that divides the Moon’s illuminated and unil-luminated portions is called the terminator, and it is along this line that the Moon’s terrain is visible in the sharpest contrast. A hypothetical observer standing on this line on the Moon’s surface would see the Sun either rising or setting on the horizon, at the beginning or end of lunar days which come and go every 29.5 Earth days. As the Sun’s rays illuminate the lunar surface at a very low angle at these times, long shadows are cast—just as at sunset on the Earth—and the slightest undulation in the Moon’s surface becomes readily apparent. Thus, the best day to observe any individual feature on the Moon’s surface is usually reckoned to be the day when the terminator passes over it, and so depends on its location.

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The Moon’s Orbit

Each repetition of the Moon’s cycle of phases is called a lunation. The Moon’s changing appearance over the course of each cycle stems from its monthly orbit around the Earth, which shares almost exactly the same plane as the Earth’s orbit around the Sun (see Fig. 5.2 ). The two are inclined relative to each other by a mere 5.1°. At all times in its cycle, the half of the Moon which is turned to face the Sun is illuminated. But as the Moon circles around the Earth, it is seen from different angles from the Earth.

At new moon, the Sun, Moon and Earth lie in a line which is almost exactly straight, with the Moon in the middle. The illuminated side of the Moon is almost the exact opposite to that which faces the Earth, meaning that the Moon’s disk appears almost entirely unilluminated from the Earth. Conversely, at full moon the three bodies form a line once again, but this time with the Earth in the middle. The Sun’s rays illuminate the Moon from almost directly behind the Earth, lighting almost exactly the same half of the Moon’s surface as is turned towards the Earth.

However, the period of the Moon’s cycle of phases does not quite match the period of its orbit around the Earth. The Moon circles the Earth once every 27.3 days—once each sidereal month—but its phases repeat every 29.5 days—once each synodic month. In a month, the Earth moves by around 30° along its orbit around the Sun, and conversely the Sun appears from the Earth to have moved by 30° along the ecliptic (see Fig. 5.3 ). This means that it is not quite sufficient for the

N

S

Earth Sunlight

Last Quarter

First Quarter

NewMoon

FullMoon

Fig. 5.2 At any moment in time, exactly half of the Moon’s surface is illuminated by the Sun—the half which is directed towards the Sun—always on its right-hand side as drawn here. The phase of the Moon depends how the side of the Moon which is directed towards the Earth is orientated with respect to its illuminated and unilluminated halves. This changes over the course of its monthly orbit around the Earth. See the text for details

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Moon to just complete one full revolution around the celestial sphere after each new moon in order to come back and meet the Sun again. It takes the Moon an addi-tional two days to travel the extra 30° that it needs to cover to catch up with the distance that the Sun has moved in the intervening month. This effect is directly analogous to the length of each 24-h day on Earth being 4 min longer than the Earth’s rotation period (see Chap. 4 ).

Table 5.1 lists the dates of all of the new moons between 2010 and 2051. To work out the age of the moon on any given day, find the last new moon which occurs before that date. The age of the moon is the number of days which have elapsed since that new moon. Where new moons are marked in the table with dag-gers, they coincide with solar eclipses, and where they are marked with stars, they are followed by a lunar eclipse at the next full moon, 2 weeks after the date shown.

Naming Full Moons

Because of the Moon’s brightness, it has always held a wider cultural significance beyond the interest of astronomers alone. Before the widespread availability of artificial light, the evenings around full moon were the only times when it was eas-ily possible to carry on working for much more than an hour after sunset. In past times, the months of the year were often associated with particular agricultural activities, and so the sequence of full moons through the year often acquired popu-lar names which were connected with these activities. In many cases, the names used were highly specific to individual communities and localities, but Table 5.2 lists the modern names that are still used by the Farmers’ Almanac in the US.

By historical tradition, these names usually run in series through each of the seasons. The astronomical definitions of the seasons are used here—summer and winter are defined to start on the days of their respective solstices, while spring and fall start of the days of the two equinoxes. For example, the first full moon after the autumnal equinox is the harvest moon—when the additional hours of work that are

SunlightEarth’sOrbit

NewMoon

FirstQuarter Full

Moon

LastQuarter

NewMoon

Fig. 5.3 New moons occur at intervals of 29.5 days, even though the Moon orbits the Earth in only 27.3 days. However, in a month the Sun moves a full 30° along the ecliptic, and it takes the Moon over 2 days to cover this additional distance before once again reaching solar conjunction

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Table 5.1 List of new moons, 2010–2051

Year

2010 01/15 † 02/14 03/15 04/14 05/14 06/12* 07/11 † 08/10 09/08 10/07 11/06 12/05*

2011 01/04 † 02/03 03/04 04/03 05/03 06/01* † 07/01 † 07/30 08/29 09/27 10/26 11/25* † 12/24

2012 01/23 02/21 03/22 04/21 05/20* † 06/19 07/19 08/17 09/16 10/15 11/13* † 12/13

2013 01/11 02/10 03/11 04/10* 05/10* † 06/08 07/08 08/06 09/05 10/05* 11/03 † 12/03

2014 01/01 01/30 03/01 03/30* 04/29 † 05/28 06/27 07/26 08/25 09/24* 10/23 † 11/22 12/22

2015 01/20 02/18 03/20* † 04/18 05/18 06/16 07/16 08/14 09/13* † 10/13 11/11 12/11

2016 01/10 02/08 03/09* † 04/07 05/06 06/05 07/04 08/02 09/01* † 10/01 10/30 11/29 12/29

2017 01/28* 02/26 † 03/28 04/26 05/25 06/24 07/23* 08/21 † 09/20 10/19 11/18 12/18

2018 01/17* 02/15 † 03/17 04/16 05/15 06/13 07/13* † 08/11 † 09/09 10/09 11/07 12/07

2019 01/06* † 02/04 03/06 04/05 05/04 06/03 07/02* † 08/01 08/30 09/28 10/28 11/26 12/26* †

2020 01/24 02/23 03/24 04/23 05/22* 06/21* † 07/20 08/19 09/17 10/16 11/15* 12/14 †

2021 01/13 02/11 03/13 04/12 05/11* 06/10 † 07/10 08/08 09/07 10/06 11/04* 12/04 †

2022 01/02 02/01 03/02 04/01 04/30* † 05/30 06/29 07/28 08/27 09/25 10/25* † 11/23 12/23

2023 01/21 02/20 03/21 04/20* † 05/19 06/18 07/17 08/16 09/15 10/14* † 11/13 12/12

2024 01/11 02/09 03/10* 04/08 † 05/08 06/06 07/05 08/04 09/03* 10/02 † 11/01 12/01 12/30

2025 01/29 02/28* 03/29 † 04/27 05/27 06/25 07/24 08/23* 09/21 † 10/21 11/20 12/20

2026 01/18 02/17* † 03/19 04/17 05/16 06/15 07/14 08/12* † 09/11 10/10 11/09 12/09

2027 01/07 02/06* † 03/08 04/06 05/06 06/04 07/04* 08/02* † 08/31 09/30 10/29 11/28 12/27*

2028 01/26 † 02/25 03/26 04/24 05/24 06/22* 07/22 † 08/20 09/18 10/18 11/16 12/16*

2029 01/14 † 02/13 03/15 04/13 05/13 06/12* † 07/11 † 08/10 09/08 10/07 11/06 12/05* †

2030 01/04 02/02 03/04 04/02 05/02 06/01* † 06/30 07/30 08/28 09/27 10/26 11/25* † 12/24

2031 01/23 02/21 03/23 04/21* 05/21* † 06/19 07/19 08/18 09/16 10/16* 11/14 † 12/14

(continued)

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Table 5.1 (continued)

Year

2032 01/12 02/11 03/11 04/10* 05/09 † 06/08 07/07 08/06 09/04 10/04* 11/03 † 12/02

2033 01/01 01/30 03/01 03/30* † 04/29 05/28 06/26 07/26 08/24 09/23* † 10/23 11/22 12/21

2034 01/20 02/18 03/20* † 04/18 05/18 06/16 07/15 08/14 09/12* † 10/12 11/11 12/10

2035 01/09 02/08* 03/09 † 04/08 05/07 06/06 07/05 08/03* 09/02 † 10/01 10/31 11/29 12/29

2036 01/28* 02/27 † 03/27 04/26 05/25 06/24 07/23* † 08/21 † 09/20 10/19 11/18 12/17

2037 01/16* † 02/15 03/16 04/15 05/15 06/13 07/13* † 08/11 09/09 10/09 11/07 12/06

2038 01/05* † 02/04 03/05 04/04 05/04 06/03* 07/02* † 08/01 08/30 09/28 10/28 11/26* 12/26 †

2039 01/24 02/23 03/24 04/23 05/23* 06/21 † 07/21 08/19 09/18 10/17 11/16* 12/15 †

2040 01/14 02/12 03/13 04/11 05/11* † 06/09 07/09 08/08 09/06 10/06 11/04* † 12/04

2041 01/02 02/01 03/02 04/01 04/30* † 05/29 06/28 07/28 08/26 09/25 10/25* † 11/23 12/23

2042 01/21 02/20 03/21* 04/20 † 05/19 06/17 07/17 08/15 09/14* 10/14 † 11/12 12/12

2043 01/11 02/09 03/11* 04/09 † 05/09 06/07 07/06 08/05 09/03* 10/03 † 11/01 12/01 12/31

2044 01/30 02/28* † 03/29 04/27 05/27 06/25 07/24 08/23* † 09/21 10/20 11/19 12/19

2045 01/18 02/16* † 03/18 04/17 05/16 06/15 07/14 08/12* † 09/11 10/10 11/08 12/08

2046 01/07* 02/05 † 03/07 04/06 05/06 06/04 07/04* 08/02 † 08/31 09/30 10/29 11/27 12/27*

2047 01/26 † 02/24 03/26 04/25 05/24 06/23* † 07/22 † 08/21 09/19 10/19 11/17 12/16* †

2048 01/15 02/14 03/14 04/13 05/12 06/11* † 07/11 08/09 09/08 10/07 11/06 12/05* †

2049 01/04 02/02 03/04 04/02 05/02* 05/31* † 06/30 07/29 08/28 09/27 10/26* 11/25 † 12/24

2050 01/23 02/21 03/23 04/21* 05/20 † 06/19 07/18 08/17 09/16 10/15* 11/14 † 12/14

The new moons that fall in each year are listed in month/day format. Daggers indicate those new moons that coincide with solar eclipses, while stars mark those new moons which are followed by a lunar eclipse at the following full moon. Source : DE405

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made possible by the light of the Moon help farmers to bring the harvest in. However, not all of the names stem from agriculture—the third full moon of winter is called the lenten moon, since by definition it always falls during lent.

Blue Moons

It can sometimes happen that four full moons fall within a single season. Each of the Earth’s seasons lasts for an average of a quarter of a year—91.31 days—and full moons occur at 29.53-day intervals. Dividing these two numbers reveals that there are an average of 3.1 lunar cycles in each season. If a full moon falls within the first 65 h of a season, the full moon three lunations later will also sneak in just before the end of that season. This happens roughly once every 2–3 years, and causes a problem for the traditional naming schemes which list only three names, for the first three full moons in each season. What should this fourth full moon be called? For want of another name, such moons are called blue moons, even though any observer will confirm that the Moon appears just the same color on these occasions as at any other.

In recent times, however, as the traditional names of the full moons have become less widely used, it has become increasingly common for an alternative definition of the term blue moon to be used. This definition is modern, and stems from what was originally a factual error printed in Sky & Telescope magazine in 1946, but which has now become widespread. According to this definition, a blue moon is any full moon that falls within the same calendar month as its predecessor. For example, any full moon that occurs on the 31st day of a month is guaranteed to be a blue moon, as its predecessor will have fallen on the 1st or 2nd day of the same month.

Remarkably, although the traditional and new definitions lead to different full moons being deemed to be blue moons, such events occur with exactly the same frequency regardless of which definition is used. According to both, a blue moon happens whenever 13 full moons fall some within a particular choice of year-long period.

However, looking back in history still further, there is more confusion still as to when blue moons actually occur, and this still-older confusion may give some clue

Table 5.2 The traditional names of the moons in each season, as used by the Farmers’ Almanac

Season First Second Third

Winter Old Wolf Lenten Spring Egg Milk Flower Summer Hay Grain Fruit Autumn Harvest Hunter’s Oak

Many other systems of names are used elsewhere

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as to the original etymology of the term blue moon. As we have seen, blue moons are calendrical anomalies rather than occasions when the Moon changes color. So why should they be called blue?

By a third definition, blue moons occur, as before, whenever four full moons fall within a single season. But this time, the blue moon isn’t the last of these four full moons, but the penultimate of them. The last full moon of the season takes the same traditional name that is usually assigned to it, while the one before it is deemed to be the blue moon. In spring, a blue moon would come between the milk moon and the flower moon.

Why does this matter? The significance comes in the definition of the lenten moon—the last full moon of winter. Easter Day is the first Sunday after the first full moon of spring. The last full moon of winter is the one that immediately precedes this, 30–37 days before Easter, and always falls within lent. Hence its name, the lenten moon. The problem is, if there are four full moons in a particular winter, the last of these is only a few hours before the spring equinox, and Easter falls nearly a full month or more after the beginning of Spring. The third full moon of winter falls 60 days or more before Easter, and so it could not reasonably be called the lenten moon.

It is this particular case that may explain the origin of the term blue moon—per-haps a corruption of an earlier term, betrayer moon, which was used in the past to describe the third full moon of winter when it did not fall within the 40 days of lent.

Lunar Calendars

The calendar that is used in the western world today is a solar calendar—it depends only on the Sun’s movement across the sky. Each day is defined by the Sun’s daily rising and setting, while each year is defined by the Sun’s movement through the constellations (see Chap. 4 ). Although we still divide the year into months, these have no relation to the Moon’s phases.

In the past, however, the Moon’s 29.5-day cycle of phases has often been seen as a convenient division of the year into 4-week blocks, and this custom lives on in the modern system of months. A calendar which is based entirely on the Moon’s motion is called a lunar calendar—of which the Muslim calendar is an example. In the Muslim calendar, each year lasts precisely as long as 12 lunations—either 354 or 355 days—and so the Muslim year drifts with respect to the seasons by more than 10 days each year. Other cultures have adopted calendars which use both lunar months and solar years; these are called a lunisolar calendar, and the Jewish calen-dar is an example.

Devising a lunisolar calendar, in which the months remain synchronized with the Moon’s phases, is difficult for two reasons. Firstly, there are not an integer number of days in a 29.5-day month. Secondly, there are not an integer number of lunations in a year. It is not possible to devise a system in which all months have the same number of days, or in which a constant number of months are assigned to each year.

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Since the Moon’s phases cycle 12.37 times each year, roughly 1 year in three must have an additional thirteenth month to keep in step with the seasons, just as 1 year in three has an additional blue moon today.

Various systems have been tried. In the fifth century BC , the Greek astronomer Meton of Athens observed that the pattern of full moons through the year almost exactly repeats itself every 19 years. The Moon’s phases cycle 235 times in 6,939.69 days, while the duration of 19 tropical years is 2 h longer, at 6,939.79 days. This is the Metonic cycle, and means that over short periods, at least, an irregular assignment of either 12 or 13 lunar cycles to each year can be repeated predictably every 19 years. More recently it has been used to devise simple repeating formulae for working out the date of Easter.

More generally, this demonstrates a technique that is commonly used when mak-ing calculations of phenomena that depend on two different cycles that have differ-ent periods. Intervals of time that are close to being multiples of both periods are of interest because they are intervals after which sequences of events often repeat themselves. As we shall see shortly, just as lunisolar calendars come very close to repeating themselves every 19 years, sequences of eclipses commonly repeat every 18 years and 11 days (the Saros cycle), while transits of Venus occur in pairs sepa-rated by 8 years.

Some lunisolar calendars remain in use—the Jewish traditional calendar follows the Metonic cycle, and each 19-year period has 12 years of 12 months, and 7 years which have an additional thirteenth intercalary month. The Islamic traditional cal-endar is tied more closely still to the Moon’s phases—each month can start only when the new moon has been officially observed, making it impossible to know with certainty which day will be the first of any given month. More usually, alma-nacs of the times of new moon are used for practical purposes. Each year lasts for exactly 12 months—on average, 354.4 days—since the Koran specifically prohibits the addition of intercalary months to the calendar. The result is a calendar which drifts by almost 2 weeks each year relative to the seasons.

The Exact Moment of Full Moon

Computer models now exist that can trace the hour-by-hour movement of the Sun and Moon across the sky, making it possible to pinpoint the exact dates and times of the moments when the Moon will make closest approach to the antisolar point—the point opposite to the Sun in the sky. With this information, the exact moment can be identified when any given full moon occurs, to within the nearest second. However, does full moon occur at exactly the same moment, everywhere on Earth?

To a rough approximation it does. The dates of the new moons listed in Table 5.1 are good for any location in the world. As we have seen, a full moon happens when there is a particular spatial alignment of three celestial bodies in their orbits around one another, and whether those bodies are aligned in three-dimensional space is a question independent of where on the Earth’s surface somebody might be observing them from.

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However, in Chap. 2 , we saw that any given observer sees the Moon wobbles back-and-forth by up to 2°—four times its diameter—each day due to the Earth’s rotation. The Moon is sufficiently close to the Earth that it has parallax. Observers in Europe and America, making simultaneous observations, will disagree as to its position relative to background stars. As those observers are carried around by the Earth’s daily rotation, their perspectives change and the Moon rocks from side to side. If they make measurements of when the Moon passes opposite to the Sun in the sky, they will disagree, by up to an hour.

In terms of the three-dimensional geometry of the Moon’s orbit at full moon, our error has been in assuming that it is the center of the Earth that has to be aligned with the centers of the Moon and the Sun. For simplicity’s sake, almanacs listing the times when new moon and full moon occur generally pick the Earth’s center as a convenient point from which to calculate the Moon’s position in the sky. In prac-tice, however, the Earth measures 12,700 km across and observers are on its sur-face, not at its center. Calculating the alignments for specific points on the Earth’s surface may mean that full moon comes up to half-an-hour before or after the times circulated for the Earth’s center.

Of course, the matter is usually rather academic. It would defy any observer to notice the exact moment when the Moon’s phase reached full illumination, and at new moon, the Moon is close enough to the Sun to make it impossible to observe. However, it is a different matter for solar eclipses, which occur at the exact moments of new moons. Any given total solar eclipse is visible from locations along a long thin eclipse track which the eclipse travels along. Although the eclipse is only visible for at most a few minutes at any given location, the eclipse takes up to an hour to traverse from one end of the track to the other, as a result of the Moon’s varying parallax along the track.

Eclipses

Eclipses are without doubt the most dramatic of all astronomical phenomena. At a total solar eclipse, the Earth is plunged into darkness for a few minutes, and even though lunar eclipses can hardly compete with that spectacle, they are nonetheless occasions when the light of the brightest object in the night sky is extinguished and may turn a deep red color.

When Christopher Columbus found himself beached and stranded in Jamaica in 1504, he is said to have used the total lunar eclipse of February 29 of that year in a desperate ploy to persuade the natives to give his crew food and supplies. On ship, he had a copy of astronomical tables which predicted the time and duration of the upcom-ing eclipse. He informed the leader of the natives that his god was angry and that the Moon would appear inflamed with wrath. Then, minutes before the end of totality, he sent word that the natives had been pardoned. Columbus’s son Ferdinand, then aged 15, recounted that ‘with great howling and lamentation they came running from every direction to the ships, laden with provisions, praying the Admiral to intercede by all means with God on their behalf; that he might not visit his wrath upon them.’

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Solar Eclipses

Solar eclipses occur when the Moon passes between the Sun and the Earth, such that it appears to pass in front of the Sun’s disk and block its light for a short time. Part of the wonderment they evoke is because they are rather rare. Even though two to five eclipses occur somewhere on the Earth each year, they are not visible every-where. At any particular location, a total solar eclipse will only be seen every few hundred years, or every few decades if the observer is willing to travel a few hun-dred miles.

Their rarity is down to the remarkable coincidence—which appears to be no more than pure chance—that the Sun and Moon appear to have almost exactly the same sizes in the sky. While the Sun is around 370 times larger then the Moon, it is also almost exactly 370 times further away, meaning that both measure around half-a-degree across. Because of this coincidence the Moon can completely cover the Sun’s disk when it passes in front of it, but only when their alignment is exactly correct. If the Moon were much larger, total solar eclipses would be much more common than they are, but if the Moon were even slightly further away they would never happen at all, since the Moon would not be big enough to entirely cover the Sun.

Solar eclipses occur because behind the Moon, there is a shadowed region of space in which the Sun’s light is blocked by it. Eclipses occur when the Earth passes through this region, whose geometry is shown in Fig. 5.4 . It divides into two portions called the umbra and the penumbra. In the umbra (red), the Sun’s entire disk appears hidden behind the Moon and there is complete darkness. In the pen-umbra (blue), only part of the Sun’s disk is obscured by the Moon, and whilst the Sun’s light is reduced, it is not entirely blocked. Total solar eclipses occur when the Earth passes through the Moon’s umbra, while partial solar eclipses occur when the Earth passes within the much larger volume of the Moon’s penumbra.

Sun UmbraAnnulareclipseseen

Penumbra

A

B

Fig. 5.4 The geometry of eclipses. Any solar system body casts a shadow over the region of space in which the Sun’s light is blocked by it. In the red region shown above, the umbra , the Sun’s light is entirely blocked; observers here would see a total solar eclipse. In the blue region shown above, the penumbra , the Sun’s disk is partially obscured; observers here would see a partial solar eclipse. In the green region , the antumbra , an annular solar eclipse is seen (see the text)

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The umbra extends only to a finite distance behind the Moon, and one way to see why this is so is to consider what would be seen by a hypothetical observer traveling away from the Moon. As this observer moves further away from the Moon, its disk appears to get smaller as it recedes into the distance. At a certain distance, the Moon’s disk has exactly the same size as the Sun’s, and can only cover the Sun’s disk when it is exactly aligned over the top of it. Coincidentally, this is the distance of the Earth from the Moon. Beyond this distance, the Moon’s disk becomes too small to ever entirely obscure the Sun. While an observer traveling along line A in Fig. 5.4 would see a total solar eclipse as they passed through the Moon’s umbra, an observer traveling along line B would briefly see the Sun’s light appear to form a complete ring—or annulus—around the Moon as they passed behind the back of the Moon’s umbra, through a region of space sometimes called the antumbra.

Such events are called annular eclipses, and commonly occur. The Moon’s dis-tance from the Earth varies by about 10 %, since it is in a slightly elliptical orbit, and its apparent diameter in the sky varies by the same amount. When the Moon is at its furthest from the Earth, it appears fractionally smaller than the Sun, such that the Earth can at best pass behind the end of its umbra along a path similar to that labeled B.

Figure 5.4 is, of course, not drawn to scale: the size of the Sun and Moon are vastly exaggerated to demonstrate the geometry of umbra and penumbra. However, even though the separation between the Earth and Moon is actually much greater than either of their diameters, it is just about possible to represent the geometry of the Moon’s umbra to scale without it being invisibly small, and this is done in Fig. 5.5 . The Earth can remain a reasonable size and the Moon still fit on the page, since the Earth–Moon separation is only 60 Earth radii, but the Moon is smaller than a letter ‘o’. As before, the Moon’s penumbra is shown in blue, and its umbra, like a long needle, is shown in red. A cross marks the end of the umbra, and the Earth is drawn to scale to the side of the Moon’s shadow, at both its closest and furthest distances from the Moon.

In addition to the long thin needle-like shape of the Moon’s umbra, Fig. 5.5 also makes apparent that the Earth is large in comparison to the Moon’s shadow. When

Solar eclipse configurationEarthMoon

Lunar eclipse configurationEarth Moon

Fig. 5.5 A scale diagram of the geometry of solar and lunar eclipses. The penumbrae of the Earth and Moon are drawn in blue ; their umbrae are drawn in red

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the Earth passes through the Moon’s shadow, only certain locations on its surface will experience a total eclipse. At any particular moment during an eclipse, only an area measuring a few tens or at most a little over a 100 miles across can lie within the Moon’s umbra, though as the Earth travels through space this shadowed spot sweeps across its globe.

Another consequence of the Earth’s large size is that the distance of any Earth- bound observer from the Moon varies slightly with the time of day. When the Moon is on the horizon, the observer is standing on the left or right edge of the Earth as shown in Fig. 5.5 , and the Moon is nearly 2 % further away than when it appears directly overhead. When a solar eclipse is seen at around midday local time, the Sun and Moon are both high in the sky, and in Fig. 5.5 the observer is on the part of the Earth’s surface that is turned closest to the Moon. However, when such an eclipse is seen at around sunrise or sunset, the observer is up to a full Earth-radius more distant from the Moon.

For most total solar eclipses, this is not a major consideration: it only means that observers who watch from locations where the Sun is higher in the sky see the moment of totality last a few seconds longer than those watching from places where the Moon appears a little smaller. But when the Earth is very close to the end of the Moon’s umbra, any small change in the Moon’s size can make the difference between a total and an annular solar eclipse. The result can be what is termed a hybrid solar eclipse, in which the eclipse begins as an annular event, before becom-ing total as it passes over regions of the Earth’s spherical surface that are closer to the Moon, before reverting once again to an annular event before the eclipse’s conclusion.

Table 5.3 lists all of the solar eclipses that will occur between 2010 and 2050. The time of maximum eclipse is indicated in Universal Time (UTC), and the maxi-mum duration of totality or annularity is indicated in minutes and seconds where appropriate. The right-most two columns indicate the greatest percentage of the Sun’s disk that the Moon will cover, and the declination of the Sun at the moment of the eclipse.

Solar Eclipses as Seen from the Moon

What would a solar eclipse look like to a hypothetical observer on the Moon? Seen from the Moon, the Earth hangs in the sky and measures 2° across—a sight com-pared by NASA after the final Apollo 17 Moon landing to that of a ‘blue marble’. In the direction opposite to the Sun in the lunar sky, the regions of the Moon’s umbra and penumbra always stretch out behind it. Projecting them onto a hypo-thetical giant sheet of paper at the Earth’s average distance from the Moon, the umbra would appear as a tiny speck of darkness, measuring around an arcminute across, at the point in the sky directly opposite the Sun. The penumbra would appear closer to a degree across.

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Table 5.3 List of solar eclipses, 2010–2050

Date Duration Mag (%) Dec

2010 January 15 7:13 Annular solar eclipse 11:08 100 20S 2010 July 11 19:42 Total solar eclipse 5:20 100 21N 2011 January 4 9:04 Partial solar eclipse – 85 21S 2011 June 1 21:04 Partial solar eclipse – 60 23N 2011 July 1 8:55 Partial solar eclipse – 9 21N 2011 November 25 6:11 Partial solar eclipse – 90 21S 2012 May 20 23:48 Annular solar eclipse 5:46 100 20N 2012 November 13 22:09 Total solar eclipse 4:02 100 18S 2013 May 10 0:30 Annular solar eclipse 6:03 100 17N 2013 November 3 12:51 Hybrid solar eclipse – 100 14S 2014 April 29 6:16 Annular solar eclipse – 100 13N 2014 October 23 21:58 Partial solar eclipse – 81 10S 2015 March 20 9:37 Total solar eclipse 2:47 100 0N 2015 September 13 6:43 Partial solar eclipse – 78 3N 2016 March 9 1:56 Total solar eclipse 4:09 100 4S 2016 September 1 9:04 Annular solar eclipse 3:06 100 7N 2017 February 26 15:00 Annular solar eclipse 0:44 100 8S 2017 August 21 18:31 Total solar eclipse 2:40 100 12N 2018 February 15 21:07 Partial solar eclipse – 59 13S 2018 July 13 2:49 Partial solar eclipse – 33 20N 2018 August 11 9:59 Partial solar eclipse – 73 16N 2019 January 6 1:30 Partial solar eclipse – 71 21S 2019 July 2 19:18 Total solar eclipse 4:33 100 22N 2019 December 26 5:15 Annular solar eclipse 3:40 100 22S 2020 June 21 6:43 Annular solar eclipse 0:38 100 23N 2020 December 14 16:18 Total solar eclipse 2:10 100 23S 2021 June 10 10:54 Annular solar eclipse 3:51 100 23N 2021 December 4 7:44 Total solar eclipse 1:54 100 23S 2022 April 30 20:30 Partial solar eclipse – 63 13N 2022 October 25 10:50 Partial solar eclipse – 86 11S 2023 April 20 4:14 Hybrid solar eclipse – 100 10N 2023 October 14 17:57 Annular solar eclipse 5:17 100 7S 2024 April 8 18:22 Total solar eclipse 4:28 100 7N 2024 October 2 18:51 Annular solar eclipse 7:25 100 4S 2025 March 29 10:59 Partial solar eclipse – 93 4N 2025 September 21 19:56 Partial solar eclipse – 85 0S 2026 February 17 12:03 Annular solar eclipse 2:20 100 12S 2026 August 12 17:38 Total solar eclipse 2:18 100 15N 2027 February 6 15:58 Annular solar eclipse 7:51 100 15S 2027 August 2 10:07 Total solar eclipse 6:23 100 18N 2028 January 26 15:14 Annular solar eclipse 10:27 100 18S 2028 July 22 3:03 Total solar eclipse 5:10 100 19N 2029 January 14 17:26 Partial solar eclipse – 87 20S 2029 June 12 3:52 Partial solar eclipse – 45 24N 2029 July 11 15:52 Partial solar eclipse – 23 20N 2029 December 5 14:53 Partial solar eclipse – 89 23S 2030 June 1 6:23 Annular solar eclipse 5:21 100 22N

(continued)

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Date Duration Mag (%) Dec

2030 November 25 6:48 Total solar eclipse 3:44 100 21S 2031 May 21 7:19 Annular solar eclipse 5:26 100 19N 2031 November 14 21:11 Hybrid solar eclipse – 100 17S 2032 May 9 13:37 Annular solar eclipse 0:22 100 16N 2032 November 3 5:46 Partial solar eclipse – 85 14S 2033 March 30 17:53 Total solar eclipse 2:37 100 4N 2033 September 23 13:41 Partial solar eclipse – 68 1S 2034 March 20 10:16 Total solar eclipse 4:09 100 0N 2034 September 12 16:15 Annular solar eclipse 2:58 100 3N 2035 March 9 23:11 Annular solar eclipse 0:48 100 4S 2035 September 2 2:01 Total solar eclipse 2:54 100 8N 2036 February 27 5:01 Partial solar eclipse – 62 9S 2036 July 23 10:18 Partial solar eclipse – 19 18N 2036 August 21 17:37 Partial solar eclipse – 86 12N 2037 January 16 9:36 Partial solar eclipse – 70 19S 2037 July 13 2:33 Total solar eclipse 3:58 100 21N 2038 January 5 13:43 Annular solar eclipse 3:18 100 22S 2038 July 2 13:34 Annular solar eclipse 1:00 100 23N 2038 December 26 1:03 Total solar eclipse 2:18 100 23S 2039 June 21 17:23 Annular solar eclipse 4:04 100 24N 2039 December 15 16:33 Total solar eclipse 1:51 100 24S 2040 May 11 3:29 Partial solar eclipse – 53 16N 2040 November 4 18:57 Partial solar eclipse – 80 14S 2041 April 30 11:48 Total solar eclipse 1:51 100 14N 2041 October 25 1:32 Annular solar eclipse 6:07 100 11S 2042 April 20 2:21 Total solar eclipse 4:51 100 11N 2042 October 14 2:05 Annular solar eclipse 7:44 100 8S 2043 April 9 19:08 Total solar eclipse – 100 8N 2043 October 3 3:14 Annular solar eclipse – 100 4S 2044 February 28 20:14 Annular solar eclipse 2:27 100 8S 2044 August 23 1:07 Total solar eclipse 2:04 100 12N 2045 February 16 23:53 Annular solar eclipse 7:47 100 12S 2045 August 12 17:41 Total solar eclipse 6:06 100 15N 2046 February 5 23:11 Annular solar eclipse 9:42 100 15S 2046 August 2 10:27 Total solar eclipse 4:51 100 17N 2047 January 26 1:45 Partial solar eclipse – 89 17S 2047 June 23 10:37 Partial solar eclipse – 31 24N 2047 July 22 22:51 Partial solar eclipse – 36 19N 2047 December 16 23:40 Partial solar eclipse – 88 24S 2048 June 11 12:51 Annular solar eclipse 4:58 100 23N 2048 December 5 15:31 Total solar eclipse 3:28 100 22S 2049 May 31 14:02 Annular solar eclipse 4:45 100 21N 2049 November 25 5:37 Hybrid solar eclipse – 100 20S 2050 May 20 20:52 Hybrid solar eclipse – 100 19N 2050 November 14 13:43 Partial solar eclipse – 88 17S

Source : Five Millennium Canon of Solar Eclipses , NASA/TP-2006-214141

Table 5.3 (continued)

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Eclipses occur whenever the Earth happens to pass through that part of the sky, as seen from the Moon. Because the Earth’s globe appears with a diameter of 2°, while the Moon’s umbral shadow measures only an arcminute across, only a tiny pinpoint of darkness can ever be projected onto the Earth. In other words, only one specific location on the Earth’s surface can ever experience a total solar eclipse at any particular moment in time. However a sizeable fraction of the Earth’s surface can be covered by the Moon’s penumbral shadow at any given moment, experienc-ing a partial solar eclipse.

Perhaps one of the surprising features of Table 5.3 is that total and annular solar eclipses are not much more rare than partial solar eclipses. Given how rarely total solar eclipses occur in any particularly place, it is easy to forget that they happen somewhere in the world on average every year or two. However, looking at the eclipse geometry as seen from the Moon, it is easy to see why so many solar eclipses appear total somewhere in the world. Both the Moon’s umbra and its pen-umbra appear smaller than the Earth in the lunar sky. The umbra is only a tiny speck at the penumbra’s center, but if any part of the Earth’s large disk grazes the penum-bra to create any eclipse at all, it is quite likely that some part of the Earth will also cross its center, except in the very most grazing contacts.

Lunar Eclipses

The geometry of a lunar eclipse is similar to that of a solar eclipse, but now it is the Earth that casts a shadow onto the Moon, rather than vice versa. More generally, any eclipse involves two astronomical objects: one that casts a shadow, and the other that passes through that shadow. As has been seen, if a solar eclipse were viewed by a hypothetical observer on the Moon, it would appear very different from how it would appear on Earth. The difference is whether the eclipse is being viewed from the body which is casting the shadow, or that which is passing through it. In a lunar eclipse, these roles are reversed.

In a lunar eclipse, the Sun, Earth and Moon are once again aligned in a straight line. This time, however, the Earth is in the middle and casts its shadow onto the Moon (see Fig. 5.5 ). The region of shadow behind the Earth is much larger than that behind the Moon, since the Earth has four times the diameter of the Moon. As a result, whereas the Moon can do no more than cast a pinpoint of shadow onto the Earth’s surface, the whole Moon can comfortably fit within the Earth’s umbra with plenty of room to spare.

The appearance of a lunar eclipse as seen from the Earth is directly analogous to how a solar eclipse appears as seen from the Moon. In the direction pointing away from the Sun, the Earth’s umbra and penumbra taper out behind it. Once again, they can be projected onto a hypothetical piece of paper at the Moon’s average distance from the Sun, only this time they are much larger. There is perpetually a region of the celestial sphere, opposite to the Sun in the sky, where the Moon cannot pass without being eclipsed by the Earth’s shadow. Rather than being a pinpoint as

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before, this region measures 1.5° (three Moon widths) across. Around it, the Earth’s penumbra occupies a region of the sky 2.5° (five Moon widths) across.

As seen from the Moon, the Earth’s disk appears to pass in front of the Sun at a lunar eclipse. Because it is so large, it is rather easily able to cover it, since it mea-sures 2° across as compared to the Sun’s mere half-degree. It is rather curious to think that what we on Earth call a lunar eclipse might reasonably be called a solar eclipse by an inhabitant of the Moon. Likewise, what we call a solar eclipse on Earth might reasonably be called a terrestrial eclipse on the Moon. If our hypotheti-cal lunar inhabitant were to see a partial solar eclipse—the Earth’s disk partially covering the Sun—then the part of the Moon’s surface beneath his feet would lie within the Earth’s penumbra. However, if he were to see a total solar eclipse—the Earth entirely covering the Sun’s disk—then he would be standing within the Earth’s umbra.

As is clear from Fig. 5.5 , the Moon’s finite size means that it is quite possible for some parts of its surface to lie within the Earth’s umbra while at the same time others lie within its penumbra. From the point-of-view of our lunar inhabitant, this is equivalent to saying that the Earth has a sizeable parallax as seen from the Moon—that it appears in slightly different locations in the sky as seen from differ-ent places on the Moon’s surface. The Sun is far enough away from the Moon that it appears in much the same spot on the sky from anywhere on the lunar surface, but the same is not true of the Earth.

For total solar eclipses on Earth, a very exact alignment of Sun and Moon is needed, and it is the Moon’s parallax that means that this exact alignment can only ever be achieved in one very small locality at any given time. However, since the geometry required for the Earth to completely cover the Sun’s disk in the lunar sky is relatively inexact, it is quite common for the Earth to plunge the whole of the Moon’s surface into darkness—something that it is impossible for the Moon to do to the Earth.

Observing Lunar Eclipses

In contrast to solar eclipses, lunar eclipses appear the same to all observers, regard-less of where they are on the Earth. What matters is the light that is falling on the Moon’s surface to illuminate it, independent of where it is being viewed from. This is in contrast to the view from the Moon, where some parts of the lunar surface may experience a total eclipse of the Sun, while others experience only a partial eclipse. What is seen from the Earth is a global map of which areas are totally dark, and which are partially illuminated by the Sun—the projection of the Earth’s umbra onto the Moon’s disk.

When a lunar eclipse takes place, two things are easily apparent. The first is that the bite that the Earth appears to take out of the Moon is circular in shape. This may not seem very remarkable today, but the fact that the Earth’s umbra is circular

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provides one of the few readily-observable demonstrations that the Earth is spheri-cal rather than flat, a point that was well understood by the philosophers of Ancient Greece. By observing lunar eclipses, the Ancient Greeks had deduced that the Earth was spherical, 1,500 years before Christopher Columbus ‘discovered’ the New World.

The second is that the Moon very often appears to turn bright red when eclipsed. This happens because the Earth is not merely a lump of rock, but also has a transparent atmosphere around it that bends light, in much the same way that rays of light bend when they pass through a glass prism. Even when the Earth passes in front of the Sun, some light is still bent around its edges to illuminate the Moon behind, and the Earth preferentially bends red light in this way, rather than blue light.

The reason for this is exactly the same as the reason why the sky appears blue. Tiny particles in the Earth’s atmosphere—perhaps as small as individual mole-cules—scatter the Sun’s light by a process known as Rayleigh scattering. Short- wavelength blue light is much more susceptible to being scattered than red light, and so while red light is typically transmitted in almost straight lines through the atmosphere, blue light can be scattered in any direction. One result of this is that the Earth’s atmosphere appears to have a faint blue glow. The other, of relevance to lunar eclipses, is that any observer who is sitting behind the Earth, and seeing only the light which is able to penetrate all the way through the Earth’s atmosphere, sees primarily the red component of Sun’s light.

Table 5.4 lists all of the lunar eclipses that will occur between 2010 and 2050. The durations of their partial and total phases are listed in hours and minutes, together with the maximum percentage of the Moon’s disk that will enter the Earth’s umbra and the declination of the Moon at the time of the eclipse. The time indicated is the midpoint of each eclipse.

The Moon’s Nodes

If, over the course of each lunation, the Moon simply followed the same path as the Sun through the constellations, traveling along the line of the ecliptic, then it would pass through the Earth’s umbra at every full moon. Two weeks later, it would go on to cut across the Sun’s disk at every new moon.

In fact, of course, this does not happen. The Moon’s orbit is inclined by around 5.1° to the ecliptic, meaning that the Moon’s position in the sky can deviate by up to 5.1° away from the ecliptic to either side. Figure 5.6 shows how the Moon’s orbit is orientated relative to the ecliptic. The grid shows the plane of the Earth’s orbit around the Sun—that of the ecliptic. Every 27.3 days, the Moon circles around the Earth, and on each circuit it cuts through the plane of the ecliptic at two points, called its nodes.

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Table 5.4 List of lunar eclipses, 2010–2050

Date Partial Total Mag (%) Dec

2010 June 26 11:32 Partial lunar eclipse 2:42 – 53 24S 2010 December 21 8:15 Total lunar eclipse 3:28 1:12 100 23N 2011 June 15 20:15 Total lunar eclipse 3:39 1:40 100 23S 2011 December 10 14:38 Total lunar eclipse 3:32 0:51 100 22N 2012 June 4 11:13 Partial lunar eclipse 2:06 – 37 21S 2013 April 25 19:58 Partial lunar eclipse 0:27 – 1 14S 2014 April 15 7:44 Total lunar eclipse 3:34 1:17 100 9S 2014 October 8 10:52 Total lunar eclipse 3:19 0:58 100 6N 2015 April 4 12:07 Total lunar eclipse 3:29 0:04 100 5S 2015 September 28 2:52 Total lunar eclipse 3:19 1:11 100 1N 2017 August 7 18:12 Partial lunar eclipse 1:55 – 24 15S 2018 January 31 13:28 Total lunar eclipse 3:22 1:16 100 17N 2018 July 27 20:22 Total lunar eclipse 3:54 1:43 100 19S 2019 January 21 5:17 Total lunar eclipse 3:16 1:02 100 20N 2019 July 16 21:40 Partial lunar eclipse 2:57 – 65 21S 2021 May 26 11:15 Total lunar eclipse 3:07 0:14 100 20S 2021 November 19 8:59 Partial lunar eclipse 3:28 – 97 19N 2022 May 16 4:15 Total lunar eclipse 3:27 1:24 100 19S 2022 November 8 11:04 Total lunar eclipse 3:39 1:25 100 16N 2023 October 28 20:25 Partial lunar eclipse 1:17 – 12 14N 2024 September 18 2:36 Partial lunar eclipse 1:02 – 8 2S 2025 March 14 6:56 Total lunar eclipse 3:38 1:05 100 2N 2025 September 7 18:10 Total lunar eclipse 3:29 1:22 100 6S 2026 March 3 11:39 Total lunar eclipse 3:27 0:58 100 6N 2026 August 28 4:20 Partial lunar eclipse 3:18 – 92 9S 2028 January 12 4:04 Partial lunar eclipse 0:56 – 6 22N 2028 July 6 18:12 Partial lunar eclipse 2:21 – 38 23S 2028 December 31 16:50 Total lunar eclipse 3:28 1:11 100 23N 2029 June 26 3:24 Total lunar eclipse 3:39 1:41 100 23S 2029 December 20 22:48 Total lunar eclipse 3:33 0:53 100 23N 2030 June 15 18:42 Partial lunar eclipse 2:24 – 50 22S 2032 April 25 15:11 Total lunar eclipse 3:31 1:05 100 13S 2032 October 18 18:59 Total lunar eclipse 3:15 0:47 100 10N 2033 April 14 19:19 Total lunar eclipse 3:35 0:49 100 9S 2033 October 8 10:59 Total lunar eclipse 3:22 1:18 100 5N 2034 September 28 2:58 Partial lunar eclipse 0:26 – 1 0N 2035 August 19 1:02 Partial lunar eclipse 1:16 – 10 12S 2036 February 11 22:10 Total lunar eclipse 3:21 1:14 100 13N 2036 August 7 2:50 Total lunar eclipse 3:51 1:35 100 16S 2037 January 31 14:05 Total lunar eclipse 3:17 1:03 100 17N 2037 July 27 4:17 Partial lunar eclipse 3:12 – 80 19S 2039 June 6 18:49 Partial lunar eclipse 2:59 – 88 22S 2039 November 30 16:51 Partial lunar eclipse 3:26 – 94 21N 2040 May 26 11:48 Total lunar eclipse 3:30 1:32 100 21S 2040 November 18 19:08 Total lunar eclipse 3:40 1:27 100 19N

(continued)

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Date Partial Total Mag (%) Dec

2041 May 16 0:54 Partial lunar eclipse 0:58 – 6 19S 2041 November 8 4:45 Partial lunar eclipse 1:30 – 16 17N 2043 March 25 14:28 Total lunar eclipse 3:34 0:53 100 1S 2043 September 19 1:48 Total lunar eclipse 3:26 1:11 100 2S 2044 March 13 19:43 Total lunar eclipse 3:29 1:06 100 2N 2044 September 7 11:26 Total lunar eclipse 3:26 0:33 100 5S 2046 January 22 12:53 Partial lunar eclipse 0:50 – 5 20N 2046 July 18 0:57 Partial lunar eclipse 1:54 – 24 21S 2047 January 12 1:23 Total lunar eclipse 3:28 1:10 100 22N 2047 July 7 10:35 Total lunar eclipse 3:38 1:40 100 22S 2048 January 1 6:59 Total lunar eclipse 3:34 0:55 100 22N 2048 June 26 2:09 Partial lunar eclipse 2:39 – 63 22S 2050 May 6 22:28 Total lunar eclipse 3:26 0:43 100 16S 2050 October 30 3:17 Total lunar eclipse 3:12 0:34 100 14N

Source : Five Millennium Canon of Lunar Eclipses , NASA/TP–2009–214172

The moments when the Moon passes through its two nodes are the two times in its orbit when it is possible for eclipses to occur. If these moments happen to coin-cide with either a new moon or a full moon, then the alignment of the Earth, Sun and Moon will be close enough to a straight line for an eclipse to occur. At other times, the Moon lies above or below the plane of the ecliptic, and so the line that the three bodies form in space at new moon and full moon is sufficiently poorly aligned that eclipses cannot occur. At new moon, the Moon is seen to pass to one side of the Sun rather than cutting across its disk. At full moon, the Moon passes to the side of the Earth’s umbra.

Table 5.4 (continued)

The Earth’s orbit about the Sun

Earth

The Moon

Node

Fig. 5.6 The nodes of the Moon (see the text for details)

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As the year progresses, the orientation of the Moon’s orbit in space remains fixed, and the line through the Moon’s two nodes remains a fixed direction in space. However, the Sun appears to revolve around the ecliptic as seen from the Earth. In Fig. 5.6 , the Sun lies at a large distance, in the plane of the grid, and completes a circuit around the Earth once a year. Twice each year, it crosses the line of the Moon’s nodes, and these are the only two times of year when eclipses are possible.

In fact, the alignment does not need to be quite exact. For lunar eclipses, the Earth’s umbra measures nearly three moon-widths across, and the Moon can pass up to 2° to either side of the umbra’s center and still show at least a partial eclipse. In other words, around the time that the Moon passes through either of its nodes, there is a span of its orbit measuring roughly 20° in which any full moon will coin-cide with a partial or total lunar eclipse. In a month, the Sun moves by 30° along the ecliptic, and so in successive months, full moons occurs at 30° intervals around the circuit shown in Fig. 5.6 . There is a roughly two-thirds chance that on any given occasion when the Sun crosses the line of the Moon’s nodes, there will be a partial or total lunar eclipse.

For solar eclipses, the arithmetic works slightly differently. The Moon’s umbra is only a few miles across at the Earth’s distance from the Moon. However, as seen from the Moon, the Earth is a large blue marble that measures 2° across. If any part of the Earth’s disk crosses the antisolar point, a total or annular solar eclipse will be seen somewhere on Earth. Once again, on roughly two-thirds of occasions when the Sun crosses the line of the Moon’s nodes there will be a total or annular solar eclipse somewhere on the Earth.

Precession of the Moon’s Nodes

Over long periods, the line of the Moon’s nodes does not remain fixed in space. Just as the axis of the Earth’s rotation precesses every 26,000 years, the orientation of the Moon’s orbital axis turns like that of a gyroscope. As shown in Fig. 5.6 , it is tipped towards the reader, but over time the line through its two nodes rotates around the ecliptic plane (indicated by the grid). The Moon’s orbit always remains inclined at 5.1° to the ecliptic plane, but the direction in which it is tipped up changes (see Fig. 5.7 ).

The timescale over which this happens is much quicker than the precession of the Earth’s equinoxes. The Earth’s rotation axis precesses because of the slight imbalance in the gravitational pull that the Sun exerts on the two sides of its equato-rial bulge. The Moon’s orbit measures over 60 Earth-radii across, and the difference in the Sun’s gravity from one side of its orbit to the other is much more pronounced. As a result, the Moon’s nodes rotate once every 18.6 years. Thus, while eclipses occur in 2015 in March/April and September, by 2020 the Moon’s nodes will have rotated such that eclipses occur in June and December. By 2024, the Moon’s nodes will have completed a full half-revolution, swapping places, and eclipses will once again occur in April and September/October.

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Lunar Standstills

The precession of the Moon’s nodes also alters the way that the Moon’s position varies in declination. Figure 5.7 shows five snapshots of the rotating plane of the Moon’s orbit over an 18.6-year period. At the center of each snapshot it also shows the tilt of the Earth’s rotation axis, which is tipped up at an angle of 23.4° to the ecliptic, and as we saw in Chap. 2 , precesses much more slowly. Any objects that lie along the line of the Earth’s rotation axis appear at the celestial poles, while objects that lie in the plane perpendicular to its rotation axis appear around the celestial equator.

As the plane of the Moon’s orbit changes, the monthly variation in its declina-tion also changes. When the Moon’s orbit is tipped in the same direction as the Earth’s rotation axis, it comes closest to aligning with the celestial equator, varying in declination between 18°S and 18°N and never swinging very far into the northern or southern sky. Such a moment is called a minor standstill and will next occur in 2015.

However, at the opposite point in the cycle, when the Moon’s orbit is tipped in the opposite direction to the Earth’s rotation axis, it is significantly more steeply inclined to the celestial equator, and its declination swings each month between 28°S and 28°N. Such a moment is called major standstill.

It is rather remarkable that the cycle of minor and major standstills in the Moon’s motion appears to have been known even in the stone age, even though it can only be detected by comparing observations of the Moon made over a period of at least 18 years. In Britain, and especially Scotland, there are dozens of examples of stone circles which date from around 3000 BC and which include a large recumbent stone that is aligned towards a point on the horizon at a declination of either 28°S or 28°N. The significance of these directions is generally assumed to be that they are the most northerly and southerly points on the horizon where it is possible for the Moon to rise or set.

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Fig. 5.7 The precession of the lunar nodes (see the text for details)

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The Size of the Moon

As we have already seen, the Moon’s distance from the Earth is not constant, but varies between 363,000 and 405,000 km because the Moon’s orbit around the Earth is slightly elliptical. This means that not all full moons are exactly the same size. The angular size of the Moon can vary from 29′ to 33′, and the brightness of full moons can vary by more than 50 %, between those events that occur when the Moon is at its nearest to the Earth, and those that occur when the Moon is at its furthest from the Earth.

Just as the Moon’s nodes precess around its orbit, the points where it passes closest to and furthest from the Earth precess, albeit at twice the rate of its nodes, completing a full circuit around its orbit once every 9 years.

The Saros

Previously, we saw that the calculation of lunisolar calendars is simplified by the fact that the duration of 235 lunar months very nearly matches that of 19 tropical years. As a result, lunisolar calendars come very close to repeating themselves after 19 years—the Metonic cycle. The mathematics of eclipses is rather similar. They can only occur at full and new moons, which occur at 29.53-day intervals—once each synodic month—when the Moon is simultaneously passing through the eclip-tic plane at one of its two nodes. Because of the precession of the Moon’s nodes, these node crossing events happen with a period that is slightly shorter than a syn-odic month, once every 27.21 days—a period of time that is called a draconic month.

Just like lunisolar calendars, eclipses depend on the coincidence of events which happen at different intervals. Once again, a very simple way of predicting when they will occur is to identify some period of time after which both cycles repeat themselves—a period of time in which an integer number of both synodic and dra-conic months have taken place. For example, 223 synodic months last for 6,585.321 days, while 242 draconic months last for 6,585.357 days—some 52 min longer. What this means is that after 18 years and 11.3 days, both of the cycles of events that eclipses depend upon repeat themselves to within an alignment of 52 min. Whenever an eclipse occurs, it is very likely to be followed by another similar eclipse 18 years later. However, because it will happen a third-of-a-day later, it may not be observable in exactly the same part of the world.

The period of 6,585.3 days is known as a Saros, and sequences of eclipses that occur at 6,585.3-day intervals are known as a Saros series. The re-alignment of the Moon’s synodic and draconic cycles after one Saros is sufficiently exact that each Saros series runs for between 69 and 87 eclipses before the cycles drift sufficiently far out of alignment that the series comes to an end.

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The resulting periodic repetition of eclipses is sufficiently obvious that it has been known about for over 2,000 years, and allowed crude eclipse predictions to be made long before the world had models of the Moon’s motion across the sky which had anything like the precision that would be needed to predict eclipses directly from its orbital motion.

Tides

Eclipses may be dramatic, but they are also rather rare. By contrast, it is by generat-ing tides that the Moon has perhaps the greatest effect on everyday life—for seafar-ers at least. Having said that, dramatic though ocean tides are, it is not immediately obvious merely from observing them that they are astronomical in origin. Perhaps the only clue is that the times of high- and low-tide drift through the day with exactly the same period as the Moon’s phases. The oft-told explanation of how they come about is that the Moon’s gravitational pull on the Earth’s oceans causes them to rise and fall by a meter or more twice each day. This is in essence true, though as we shall see, the full story is a little more complicated than that.

That story begins with the Moon’s gravitational field, which exerts a small pull on everything on Earth. That pull is rather weak, for two reasons. First, the strength of the gravitational pull of any object is in proportion to its mass, and Moon is not very heavy—it has only around an eightieth of the Earth’s mass. Secondly, the gravi-tational pull of any body decreases with distance, and the Moon is much more dis-tant from us than the Earth beneath our feet. Far from being on the Moon’s surface, we are at a distance of 384,000 km away from it, and at this distance the Moon’s gravitational pull is reduced by a further factor of well over a 100,000 relative to what the Apollo astronauts felt. Because the Moon is not very heavy, even the gravi-tational pull that the they experienced when they were on its surface was no stronger than a sixth of what they were used to feeling back at home on the surface of the Earth. The strength of the pull that we Earth-dwellers feel towards the Moon is around one three millionth of the pull that we feel from the Earth’s own gravity. That is to say, the pull that a three tonne weight feels towards the Moon has roughly the same strength as the pull that a one-gram paperclip feels towards the Earth.

However, this does not mean that anybody standing on a bathroom scale will find that they weigh fractionally less when the Moon is overhead. When the Moon is overhead, common sense says that it exerts an upward pull on that person, and should make him appear to weigh less. The Moon does indeed exert just such an upward pull, but it doesn’t affect the reading of the bathroom scales.

This is for exactly the same reason that astronauts feel weightless aboard the International Space Station (ISS). At an altitude of only 370 km above the Earth’s surface, the ISS experiences a gravitational pull towards the Earth that is only 10 % weaker than that felt on the surface of the Earth. However, because there is nothing holding the ISS up, it is in perpetual free-fall towards the Earth. It is only because of the ISS’s very fast sideways motion, at around 7.7 km/s, that it stays in orbit rather than crashing to Earth.

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The astronauts aboard the ISS feel weightless because both they and the space station are falling freely towards the Earth at exactly the same rate. Similarly, those on Earth are oblivious to the Moon’s gravitational pull, because the Earth and Moon are in perpetual free-fall towards on another, circling around each other in orbit (see Fig. 5.8 ). If somebody stands on a bathroom scale when the Moon is overhead, the Moon does exert a weak upward force on them. But this force is exactly counterbalanced by the fact that the Moon also exerts a pull on the Earth, making the whole planet accelerate towards it. The person standing on the scales accelerates gently towards the Moon in response to its pull, but so too does the Earth beneath his feet. The upward acceleration of the ground beneath the scales towards the Moon makes the Earth push upwards on the bottom of scales, rather like the floor of an ascending elevator. One effect exactly counterbalances the other.

This being so, it might appear that the Moon’s gravity is entirely imperceptible to those who live on a planet that is in perpetual freefall towards it. However, the Moon’s gravity is not quite the same at all points on the Earth’s surface, and this is the origin of tides. As we have already seen, the Moon is close enough to the Earth that two observers on opposite sides of the globe may disagree as to its position in the night sky by up to 2°—four times the width of a full Moon. This means that the Moon’s pull on these two observers differs in direction by up to 2°. Moreover, as the pull of the Moon’s gravity decreases with distance, the side of the Earth closest to the Moon feels a slightly stronger pull than the side that is turned away from it.

This is illustrated in Fig. 5.9 . Panel (a) shows the pull that objects around the Moon feel towards it, always directed towards it. Longer arrows indicate the stron-ger pulls that are felt by objects which are closer to the Moon. Panel (b) shows the gravitational pull of the Moon in the vicinity of the Earth, assuming that the Moon is off the left-hand edge of the frame (not drawn to scale). The Earth responds to this gravitational pull by accelerating towards the Moon, in orbit around it.

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However, because the Earth is a rigid solid body, all parts of it must move together at a common speed, despite the fact that they feel different pulls towards the Moon. The whole Earth moves as if it felt a uniform gravitational pull towards the Moon, and this uniform pull is equal to the average pull that the Moon exerts on the Earth. Roughly speaking, this average pull is equal to the pull that is felt by the material at the center of the Earth. Moving in this way, however, means that some parts of the Earth feel a residual additional pull, over and above what is needed to keep them moving at the same speed as the Earth’s center. Panel (c) shows the strength of this residual pull—a force that is felt only by objects that are rigidly attached to the Earth, and thereby forced by the solid body forces that hold the Earth together to orbit the Moon at the same rate as the Earth’s center.

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Fig. 5.9 The forces that give rise to the Earth’s tides (see the text for details)

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On the surface of the Earth, this residual pull stretches the Earth out in the directions that point towards and away from the Moon, while it pinches the Earth together from the top and bottom as drawn in panel (c). The reason why material that is closer to the Moon feels a residual pull towards it is that it feels a fractionally stronger gravitational pull towards the Moon than the Earth’s center. Likewise, the material on the far side of the Earth feels a fractionally weaker pull towards the Moon than the Earth’s center, and so there is a centrifugal force pulling it outward that the Moon’s gravity is not quite strong enough to counterbalance.

What effect does this ‘pinching’ force from the Moon have on the Earth? If the Earth kept the same face forever turned towards the Moon, the result would be rather simple. The Earth’s surface would become elongated along the line directed towards and away from the Moon. The pinching action of the Moon’s residual grav-ity—its tidal force—would cause sea levels would be higher in these places. However, the reality is more complicated because the Earth rotates on its axis once every 24 h, and so the places on the Earth’s surface where the Moon is pulling the Earth’s oceans up into tides are continually changing. This is what triggers the tides to change every 12 h.

Tide Maps

Naively, then, it might be expected that high tides coincide with the places on Earth where the Moon is directly overhead or underfoot, and low tides to occur when the Moon was close to the horizon. In practice, it is fairly easy to observe that this is not borne out in reality. This pattern is only followed rather weakly, and in some parts of the world, coastal towns separated by a few hundred miles may experience high tides at entirely different times of day, even though they see the Moon at almost exactly the same position in the sky. The story is not quite complete yet.

Figures 5.10 and 5.11 show this reality, as mapped out by geophysicists at the Goddard Space Flight Center (GSFC). The former is a contour map of the ampli-tude of the 12-hourly variation in sea levels induced by the Moon, independent of the influences of other astronomical bodies (see the next section). The contours are labeled with the height, in centimeters, by which high- and low-tides rise above and below the average sea-level at any given location; this is half of the full height dif-ference between high-tide and low-tide water levels.

Figure 5.11 show the phases of the tides at any given location—the offset in when high tides occur, as compared to when they occur at the reference point of Greenwich, London. An offset of 0° means that high tides occur at any given loca-tion simultaneously with when they occur at Greenwich. An offset of 180° means that they occur at the exact opposite times, when Greenwich is experiencing a low tide. Meanwhile, offsets of 90° and 270° mean respectively that the tides occur 3 h after or before they occur at Greenwich.

The tides do not circulate around the globe, completing one half-revolution every 12 h, as might be expected from the simple model just described. The consideration that we’ve missed out is that water can only flow at a certain speed:

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waves take around 6 h to travel from one side of the Atlantic ocean to the other. In shallower water, waves travel much more slowly still, for example taking 6 h to traverse the 300-mile length of the English Channel passing between Britain and France from Plymouth to Dover. This means that the world’s oceans are simply unable to move quickly enough to the rate at which the Moon moves over them.

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Fig. 5.11 The phase of lunar ocean tides around the world, expressed in degrees relative to the tides at Greenwich, as determined by geophysicists at the Goddard Space Flight Center (GSFC). Illustration taken from NASA Technical Publication GTO99.2 (Richard Ray et al. 1999)

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Scratching the side of a coin along the rim of a large bell, the bell does not ring at the frequency at which the coin moves around its circumference, but at the par-ticular note to which the bell has been tuned, the frequency at which its metal natu-rally vibrates when struck. Ripples on the surface of water in a bath tub move at a certain pre-determined speed—determined by the depth of the water—and if the water is disturbed it will tend to swing from side to side with a pre-determined frequency—determined by the size of the bath. The oceans behave in the same way: unable to respond as quickly as the Moon attempts to drag them from side to side, they wobble in a way determined by how quickly they are able to move. The largest tides in the world occur in places like Britain, where the English channel acts like a funnel for waves approaching from the Atlantic, focusing the flow of water into a sizeable current at Dover.

Panel (d) of Fig. 5.9 shows roughly the effect that this has on a global scale. The Moon attempts to pinch the Earth’s oceans into two bulges, on its near and far sides. However, the Earth’s rotation is perpetually carrying these two bulges out of align-ment with the Moon’s position in the sky. The result is that they lag slightly behind the Moon’s current position above the Earth’s surface. Different bodies of water are able to keep up with the Moon’s motion across the sky to differing degrees, depend-ing on how deep they are, but invariably the water simply can’t move quickly enough to keep up.

Spring and Neap Tides

The Moon is not the only astronomical object that exerts tidal forces on the Earth’s surface. Its closeness to the Earth does however mean that it produces stronger tidal forces than any other body. Most astronomical objects are so far away that any variations in their gravitational fields over the surface of the Earth are imperceptibly small, and as a result they produce tides that are immeasurably small. There is, however, one other body whose gravitational field varies from one side of the Earth to the other to a comparable degree, and this is the Sun. As a result, the Sun pro-duces small tides are quite easily measurable in the background behind the Moon’s tides. Even though the Sun is some 390 times more distant than the Moon, its mass is over 25 million times greater, and the difference between the Sun’s gravitational pull on the near and far sides of the Earth is a little under half the corresponding variation in the Moon’s gravitational pull. The tides that this difference produces have around half the height of the lunar tides.

The tides produced by the Sun and Moon sometimes pull in sympathy with each other, and at other times they pull in opposite directions. The solar and lunar tides work together when the Sun and Moon are close to each other in the sky, as they are at new moon, and when they are opposite to each other in the sky, as they are at full moon. At first and last quarter, when the Sun and Moon are separated by around 90°, the solar and lunar tides pull in exact opposite directions. Even though the tidal forces produced by the Sun’s gravity have only about half the strength of

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those produced by the Moon’s gravity, they are large enough to result in tides that are noticeably stronger around the times of new moon and full moon—what are called spring tides—and weaker around the times of first and last quarter—what are called neap tides.

This is shown in more detail in Fig. 5.12 . The left half of the diagram shows the positions of the Sun and Moon relative to the Earth in the two configurations that can give rise to spring tides (not to scale!). The red and blue ovals show the shapes into which the lunar and solar tides are trying to pull the Earth respectively; the lunar tides are pulling more strongly, but both are working to elongate the Earth along the Sun–Earth–Moon line. The resulting lunar and solar high tides occur at the same times, and add together to produce unusually high tides, as is shown at the top.

The right half of the diagram shows the positions of the Sun and Moon relative to the Earth at first quarter and last quarter. This time, the lunar tides are working to elongate the Earth left–right, while the solar tides are working to elongate it up–down. These two sets of tides are in opposition, though as the lunar tides are about twice as large as the solar tides, they prevail, albeit with weakened strength.

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Fig. 5.12 The origin of spring tides and neap tides (see the text for details)

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Tidal Locking

The Moon is unusual among the bodies in the solar system in that it always keeps the same face turned towards the Earth. This is not simply a matter of the Moon not having any rotational motion: if the Moon did not rotate at all, different sides of the Moon would be turned towards the Earth at different times of the month, as it cir-cled around the Earth. For the Moon to keep the same face perpetually turned towards the Earth as it circles around it, it must rotate on its axis with exactly the same period with which it circles around the Earth.

In many ways, this is rather infuriating for observers—only half of the Moon’s surface is ever visible from Earth, and the far side of the Moon was not mapped out until the space age. It does, however, make named features on the lunar surface particularly easy for novices to identify, since they always appear in exactly the same positions.

How did this coincidence come about? It has not, in fact, arisen by chance, but rather by a mechanism called tidal locking. Tidal locking comes about because the Earth’s ocean tides dissipate energy; it takes work to cause the sea levels to rise and fall. Normally, this energy is lost to friction and turbulence within the seawater as it moves around the globe, but there are parts of the world where tidal barrages—rather like hydroelectric power stations—are used to derive useful electricity from it.

As we have already seen from Fig. 5.9 (d), the Earth’s rotation is perpetually carrying the two bulges lifted up by the Moon’s tides out of alignment with the Moon’s position in the sky. This has the long-term effect of slowing the Earth’s rotation, for a reason that is shown in Fig. 5.13 . The Moon’s gravitational field acts more strongly on the tidal bulge nearest to it, pulling the Earth clockwise as shown. This is in the opposite direction to the Earth’s rotation: in other words, the Moon exerts a turning force on the Earth that opposes its rotation. It is this turning force that has caused days to lengthen from 22 h at the time of dinosaurs to 24 h today (see Chap. 4 ).

Curiously, it also has the effect of pulling the Moon forward in its orbit: the tidal bulge nearest to the Moon is always a little ahead of the position on the Earth’s

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Fig. 5.13 The gravitational pull that the Moon exerts on the Earth is slightly stronger on the near side of the Earth than on the far side. As the Moon slightly elongates the Earth into a non- spherical shape, two bulges are created on the near and far sides, one of which feels a stronger gravitational pull than the other, resulting on in twisting force that is gradually slowing the Earth’s rotation

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surface that the Moon lies directly above. Just as the Earth is pulled clockwise, in opposition to its rotation, the Moon is pulled counterclockwise by this gravitational tussle, speeding it up in its orbit. This means that the Moon is acquiring energy from the Earth’s rotation, and gradually migrating into a more distant orbit around the Earth, at a rate of around 38 mm per year.

Given time, the Moon could acquire enough energy by this mechanism to leave the Earth’s orbit altogether, since there is more than three times more energy stored in the Earth’s rotation than would be needed to lift the Moon completely out of orbit around it. However, at the present rate of transfer of energy the process would take over 10 billion years, by which time the Sun will already have become a red giant star and have long since engulfed both the Earth and the Moon.

More imminently, the Moon’s gradual recession away from the Earth puts in danger the coincidence that makes total solar eclipses possible—the coincidence that while the Moon’s diameter is 390 times smaller than that of the Sun, the Moon is also 390 times closer to the Earth. As the Moon grows more distant, it will pres-ent an ever-smaller disk in the night sky. In around 100 million years’ time, anyone still living on Earth will see the last ever total solar eclipse before the Moon shrinks to a size where it is no longer able to entirely cover the Sun.

How does this explain why the Moon always keeps the same face turned towards the Earth? The Earth is not the only body in the solar system to feel tides. The Moon feels tides from the Earth’s gravitational field, and in fact the tides that the Moon feels are considerably stronger than our own, since the Earth is more massive and has a stronger gravitational field. Although tides are normally associated with the oceans on Earth, they also act on the solid surfaces of any rocky body to pro-duce what are called solid tides . These are much less pronounced than the ocean tides on Earth because rocks are not very elastic, but they are still significant. Just as the Moon’s tidal pull on the Earth slows its rotation, so in the past the Earth’s tidal pull on the Moon would have slowed its rotation.

This slowing came to an eventual endpoint when the Moon spun about its rota-tion axis at exactly the same rate as it circles around the Earth. From the Earth, this rate of rotation means that the Moon always presents the same face to the Earth, as we have seen. From the Moon, however, it means that the Earth is always lies directly overhead at exactly the same point on the lunar surface. It means that any observer on the lunar surface always sees the Earth hanging in exactly the same place in the sky, while the stars rotate behind it, circling the sky once a month.

Referring back to Fig. 5.9 (d), the tidal bulges that the Earth lifts in the Moon’s rocky crust do not need to move as it rotates. They remain static, one at the center of the visible near side of the Moon, and the other at the center of its far side. No longer is any energy dissipated by high tides moving across its globe; the Moon remains perpetually elongated along the same axis.

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115D. Ford, The Observer’s Guide to Planetary Motion: Explaining the Cycles of the Night Sky,The Patrick Moore Practical Astronomy Series, DOI 10.1007/978-1-4939-0629-1_6,© Springer Science+Business Media, LLC 2014

The Outer Planets

Among the first facts that most people learn about the solar system is that its planets fall into two distinct categories. The innermost four—Mercury, Venus, Earth and Mars—are the terrestrial planets, with solid rocky surfaces. The outermost four—Jupiter, Saturn, Uranus and Neptune—are the gas giants—objects which are physically much larger and the majority of whose mass is made up of gas rather than solid material (Fig. 6.1 ) .

The distinction between the two groups is sharp. The least massive of the gas giants, Uranus, has more than 14 times the mass and 4 times the diameter of the heaviest and largest terrestrial planet—our own Earth. The distinction between the groups is not only one of size and mass. Despite their large size, the gas giants all rotate much more quickly than any of the terrestrial planets. Moreover, the larger gas giants rotate even more quickly than their smaller counterparts, so that while Uranus—measuring only four Earth diameters across—turns on its axis once every 17 h, Jupiter—measuring 11 Earth diameters across—turns on its axis once every 10 h. In Jupiter’s atmosphere, this rapid rotation drives the most violent weather systems that are found anywhere in the solar system, giving rise to the intricate networks of swirling vortices that characterize its cloud tops. This chapter turns to these outermost members of the solar system.

Observing the Gas Giants

The gas giants are distant bodies, and even though they are objects of gigantic proportions, they still appear rather small from the Earth. It is only when they are viewed through a telescope that they become apparent as disks rather than mere

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points of light. From the Earth, extensive detail is visible on the surfaces of Jupiter and Saturn, but Uranus and Neptune are so far away—at distances of 18 and 29 AU respectively—that it has only become possible within the past few years for the best research-grade telescopes in the world, equipped with adaptive optics, to take images of any features on their cloud tops. In recent years the best amateur imaging equipment has often only lagged behind that used by professional obser-vatories by a decade or two, but it nonetheless seems likely that cloud structures on Uranus and Neptune will remain out of the reach of amateur astronomers for some time to come.

The visible disks of the gas giants do not represent solid surfaces that could be walked upon, but are rather the cloud tops of their extensive gaseous atmospheres. Whereas the clouds that we are familiar with in the Earth’s atmosphere are made up from water droplets, which scatter sunlight to make the clouds appear opaque, the cloud tops of the gas giants are thought to be opaque because of tiny solid crystals, predominantly of ammonia, that are suspended in their atmospheres. However, even if these clouds do not form a solid ‘surface’, it is often convenient to informally refer to them as a ‘surface’, since they do at least form an opaque surface even if not a solid one.

Fig. 6.1 Saturn, as seen from the Hubble Space Telescope. Credit : NASA/HST

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Jupiter

Of all the solar system’s planets, it is Jupiter that presents the most easily observable structure. This is partly because its cloud tops present by far the greatest color con-trasts that are visible on any of the planets. Whereas Mars’s surface varies, for the most part, only between dark reds and lighter reds, and Saturn’s cloud tops vary only between different shades of yellow, Jupiter always shows a full range of colors from deep reds to pale yellows. Jupiter’s visual appeal also, however, stems from the fact that it is so large that, even despite its great distance, it nonetheless presents a disk whose diameter is rivaled in size only by that of Venus, measuring around 43–48 arcseconds in diameter.

High-resolution images of Jupiter reveal around a dozen bands which run parallel to its equator, and which alternate in color between pale yellow and dark red (see Fig. 6.2 ). The light-colored bands are called zones , while the darker bands are called

Fig. 6.2 Jupiter’s clouds show sharp color contrasts. Around a dozen bands run parallel to its equator, alternating between dark red belts and pale yellow zones . This image was taken by the Cassini Space Telescope in 2000. Credit : NASA/Cassini

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belts. Even with a crude telescope, it is generally possible to make out the two most prominent dark belts: the north equatorial belt (NEB) and the south equatorial belt (SEB). The gaseous nature of Jupiter’s cloud tops is apparent from the fact that its belts and zones each rotate with slightly differing speeds, generally a little faster at the equator than at the poles. Between them, filamentary high- velocity winds called jets blow alternately east and west at each belt–zone interface.

Jupiter is a world with extreme weather. Within its dark belts, there is rich struc-ture in the form of swirling hurricane-like circulations, called vortices. Just as the Earth’s rather moderate rotation gives rise to weather systems that include cyclones, anticyclones and hurricanes, the gas giants are home to swirling atmospheric circu-lations that are all the stronger on these very rapidly-rotating planets. The most prominent of these is Jupiter’s Great Red Spot (GRS), a hurricane in its SEB which measures around an Earth-diameter in its north–south axis, and roughly twice that diameter in its east–west axis. The GRS has been blowing in Jupiter’s atmosphere continuously for as long as anyone has had telescopes which have been powerful enough to resolve it—at least since the mid-nineteenth century, and there are tenta-tive suggestions that Giovanni Domenico Cassini (1625–1712) may have seen it in 1665. Some theorists now believe that the GRS is large enough to be self- sustaining, and may be a permanent feature.

Since 2000, the south temperate belt (STB)—a little to the south of the SEB—has had its own large hurricane called Oval BA, which has around a third the diam-eter of the GRS and formed from the merger of three smaller circulations which had been known for over 60 years. It appears that new circulations often appear; another example of a large new circulation which has appeared in recent years was the Little Red Spot (LRS) which formed in the planet’s SEB in 2008 and survived for a few months before merging with the GRS. Most circulations appear as light- colored spots against the background of the red belts, but larger circulations some-times appear to turn red. Oval BA was in fact white until 2005, before spontaneously changing to match the color of the GRS.

The origin of the coloration of Jupiter’s belts and zones is not well understood. The bright zones represent up-wellings of warm material, and the clouds tops of these pale-colored zones are at higher altitude than those of the darker belts that separate them. Their yellow color stems from crystals of ammonia embedded within the clouds. The dark belts appear to comprise of cooler sinking material, and it is believed that their deep red color stems from the interaction of the Sun’s ultra-violet light with molecules which convection currents have dredged up from deeper within Jupiter’s atmosphere. However, while chemists refer to these molecules as chromophores, this is merely a generic term for any brightly colored compound, and the precise chemical composition of the chromophores present in Jupiter’s atmosphere is not well understood.

Of all the planets, it is Jupiter where amateurs have the greatest opportunity to make scientifically valuable observations. The origin and evolution of Jupiter’s atmospheric circulations remain poorly understood, and the best way to under-stand them is to catalog and monitor them over long periods. Teams of amateur

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astronomers spread around the time zones of the world are now in a position to monitor them around the clock, and are usually the first to spot when new circula-tions appear.

In recent years, such teams have also made a number of serendipitous discover-ies of unexpected events, including meteors striking Jupiter’s atmosphere. In 2009 July, Australian amateur astronomer Anthony Wesley discovered a dark patch in the planet’s south polar region, which subsequent analysis suggested to be the result of the impact of an object measuring a few hundred meters across into the planet’s atmosphere. A year later, in 2010 August, Wesley went on to discover a second meteor impact, which he this time observed as a bright flash which lasted for around 2 s, and which was later confirmed by Christopher Go, who had also been observing the planet at the same time from the Philippines. Professional observato-ries simply do not have the capacity to observe Jupiter around the clock, and so these amateur observations currently provide the best information we have about the number of small rocky objects which orbit in Jupiter’s vicinity.

Saturn

Although Saturn’s composition is believed to be rather similar to that of Jupiter, its surface has a strikingly different appearance. Its atmosphere is chemically similar to that of Jupiter—composed primarily of hydrogen and helium, once again with a pale yellow color that arises from ammonia crystals which are suspended within it. Like Jupiter, Saturn has a series of alternately bright and dark zones and belts which run parallel to its equator. Its zones are pale yellow, and between them lie belts that are subtly darker in color but lack the dark red color of Jupiter’s belts, for reasons which are not well established. Similarly, the weather on Saturn’s surface reveals itself only in pale shades of yellow, and while it does have sizeable short-lived circulations, these appear only as white, rather than red, spots.

However, interesting though these weather systems are, Saturn is not so much known for the structures that appear in its own atmosphere as for the magnificent system of rings that circle around it. These rings comprise of a thin disk—no more than a mile thick—of tiny lumps of very pure water ice, which measures tens of thousands of kilometers from its inner to its outer edge. For the most part, the rings are so thin that background stars may easily be seen to shine through them when occulted, even though their constituent ice particles glisten with comparable bright-ness to Saturn itself.

The brightness of the rings changes with distance from the planet (see Fig. 6.3 ), and though high-resolution images reveal countless narrow bright and dark bands—similar to the tracks on a vinyl record—several wide bands can be identi-fied which are either brighter or darker than their neighbors. By long tradition, these are assigned alphabetical letters, in order variously of their height above Saturn’s cloud tops and their time of discovery. To the casual observer, only the

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A- and B-rings are likely to be visible—the outer A-ring having a slightly darker color than the inner B-ring, and separated from it by the wide Cassini division. The C-ring lies just inside the B-ring and may be apparent as a slightly darker area on the inner edge of the B-ring.

Beyond the A-ring, there are many fainter ringlets, most of which are well beyond the reach of ground-based telescopes and have only ever been discovered in the space age. Saturn’s complete ring system, including these faint outer wisps, extends several times further from the planet’s surface than is apparent through the eyepiece of an amateur telescope—out to distances of hundreds of thousands of kilometers, or several Saturn radii, above the planet’s surface.

Uranus and Neptune

Uranus and Neptune are too distant for ground-based amateur astronomers to be able to make out any detail on their surfaces, though they can be distinguished by even a small telescope as being disks rather than points of light. Both have a dis-tinctly blue–green tint, which is markedly different from the color of Jupiter and Saturn, and arises because the cloud tops of Uranus and Neptune contain not only significant quantities of ammonia, but also of methane.

Beyond this striking color, however, the cloud tops of Uranus and Neptune are somewhat bland compared to those of Jupiter and Saturn. Even to the Voyager 2 space-craft, the only spacecraft ever to have flown past the solar system’s two outermost planets, Uranus’s clouds appeared to form an almost completely featureless haze. In Neptune’s atmosphere, Voyager 2 revealed a single large dark circulation, appearing similar to Jupiter’s GRS, and a number of wispy white clouds of methane ice.

Fig. 6.3 An artist’s conception of Saturn’s major rings and moons. Credit : NASA

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The Formation of Gas Giants

Until recently it was rather poorly understood why some of the solar system’s planets should be primarily small and rocky, while others are large and gaseous. Even today, some controversy remains. The most widely accepted explanation accounts for the difference in terms of the amount of material that was available to each of the planets as they were forming at different distances from the Sun.

In the solar system’s early history, when the Sun was still surrounded by a pro-toplanetary disk, protoplanets began to form out of conglomerations of disk mate-rial, pulled together by the force of gravity. First dust grains stuck together to form pebbles, and then these coalesced into rubble piles, which were eventually com-pressed together by the force of gravity to cohere into rocky planets.

Planets orbiting further out from the Sun tended to have more material available to them, for three reasons. Firstly, by virtue of tracing out much longer circular paths around the Sun, they could collect together material from a larger volume of space. Secondly, as the newly-formed Sun began to reach a steady rate of heat production through nuclear fusion, it began to produce violent outbursts of high velocity gas from its surface, which still continue in the form of the solar wind. Over time, this solar wind blew the remnants of the Sun’s protoplanetary disk out into interstellar space, but this process worked outward, affecting the inner solar system first. The outer planets may as a result have had much longer to collect together material than the inner planets.

However, perhaps the most important factor in making the outer planets more massive was that they could accumulate not only rock, but also ice. Water is one of the most abundant materials in the solar system. When it is exposed to the near vacuum of space, its properties are rather different from those we are familiar with on Earth. On Earth it forms solid ice at low temperatures, melts at higher tempera-tures to form liquid water, and then boils at 100 °C to form steam. In a near vacuum, by contrast, it is solid below around −50 °C, and turns straight into steam at higher temperatures without passing through a liquid state. Converting temperature into distance from the Sun, this corresponds to water being found in a gaseous state anywhere closer than 4.2 AU from the Sun—roughly the orbit of Jupiter, a line often called the solar system’s snow line —and in the form of ice further out.

These three factors explain why there is a general trend that the masses of the planets increase with distance from the Sun, but does not explain how so much of the mass of the outer planets came to be in the form of gaseous atmospheres rather than solid material. These atmospheres are believed to have arisen from a subse-quent step in the formation of these planets. As each of the planets accumulated material, their gravitational fields became stronger. Gradually, they became able to pick up additional material, not just by physically crashing into it, but also by gravi-tationally drawing it in.

Once a rocky planet has accumulated a mass of around ten times that of the Earth, it reaches a turning point at which it suddenly becomes possible for its

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gravitational field to draw in not just any nearby rocky fragments, but also all of the surrounding gas from the protoplanetary disk in which it is embedded. This becomes a runaway process, since once it begins, the planet’s mass grows rapidly and extends its gravitational influence out to even greater distances still. This run-away process never began on any of the terrestrial planets, since they never acquired enough mass for it to begin, but for each of the four gas giants it led to a sudden and very dramatic increase in mass which explains their vast proportions. The resulting bodies consist of small dense rocky cores, which are surrounded by vast atmospheres which make up the majority of their masses and volumes.

Observing the Outer Planets

The solar system’s outer planets circle the Sun rather slowly, taking decades to complete each circuit. As we saw in Chap. 2 , one way to visualize how each of the planets appears to move across the sky as seen from the Earth is to draw charts of their paths that are centered not on the Sun, but rather on the Earth. The resulting paths are not simple ellipses, but look more like spirograph patterns, since their separation from the Earth changes over time not only as the planets in question move along their own orbits, but also as the Earth itself moves around the Sun.

Figures 6.4 and 6.5 show the paths of Jupiter and Saturn respectively drawn in this way. In both diagrams, the orbits are projected onto the plane of the ecliptic and are orientated with the first point of Aries at the top of the page. The separate effects of each planet’s own slow orbital motion, and that of the much smaller circles that the Earth turns around the Sun, can be rather easily distinguished as they are on very different scales.

Jupiter, for example, revolves around the Sun once every 12 years, at an average distance of a little over 5 AU. As it does so, its distance from the Earth varies between 4 and 6 AU in an annual cycle, depending on whether it is on the same side of the Sun as the Earth or on the far side. In the time it takes the Earth to complete a full revolution around the Sun, Jupiter has moved only a little over 30° around its orbit, and so these close approaches repeat roughly once a year—once every 399 days, to be precise, which is Jupiter’s synodic period (see Chap. 2 ).

Saturn’s motion is slower still: it circles the Sun once every 30 years at an aver-age distance of 9.6 AU. This means that its month-to-month apparent movement is even more strongly dominated by the Earth’s own motion. During each complete revolution it makes around the Sun, its distance from the Earth wobbles between 8.5 and 10.5 AU around 29 times. Its synodic period, at 378 days, is even closer to a year than Jupiter’s, since it progresses by only 12° along its orbit in the time that it takes the Earth to complete each of its revolutions around the Sun (i.e. a year).

The same trend continues for Uranus and Neptune (not shown). Uranus circles the Sun once every 84 years at an average distance of 20 AU. Its distance from the Earth wobbles between 19 and 21 AU 83 times on each circuit around the Sun, and its synodic period is 370 days—a little under 5 days longer than an Earth year.

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Neptune circles the Sun once every 165 years at an average distance of 30 AU, and its synodic period is a mere 2.3 days longer than an Earth year.

Oppositions and Conjunctions

Each of the outer planets finds itself aligned in an approximately straight line with the Sun and Earth on two occasions within each synodic period. Taking Jupiter as an example, there are two possible linear alignments. Either the Sun, Earth and Jupiter can be aligned with the Earth in the middle, or they can be aligned with the Sun in the middle. The alignment with the Earth in the middle is the most interest-ing. It is when the solar system is configured in this way, known as an opposition of Jupiter, that the Earth makes its closest approach to the Jupiter, as the latter planet is overtaken by the Earth in its inside lane in the solar system. As a result, it

Fig. 6.4 The path of Jupiter 2014–2025, plotted relative to the moving Earth and with the direction of the fi rst point of Aries aligned upwards

Earth

Jupiter

5 Jan 20144.21 AU

6 Feb 20154.35 AU

8 Mar 20164.44 AU

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14 Jul 20204.14 AU

20 Aug 20214.01 AU

26 Sep 20223.95 AU

3 Nov 20233.98 AU

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is when Jupiter is at opposition that it appears at its largest in the night sky. Moreover, this celestial configuration also places Jupiter at its furthest point from the Sun in the Earth’s sky—almost directly opposite it—making it visible for most of the night. In short, the moment when Jupiter is at opposition is altogether the best time of year to observe it, though in practice it is visible for much of the night for several weeks around the exact moment of this celestial alignment, and its distance from the Earth is so great that its disk does not appear dramatically larger at the exact moment of its closest approach as compared to at other times of year.

The second occasion when the Earth, Sun and Jupiter find themselves aligned in a straight line is when the Earth is on the far side of the solar system from Jupiter, and the three planets are aligned with the Sun in the middle. At this moment in time, Jupiter appears very close to the Sun in the sky and is at its greatest distance from the Earth. Jupiter is said to be at solar conjunction, and is impossible to observe for a few weeks.

Fig. 6.5 The path of Saturn 2014–2043, plotted relative to the moving Earth and with the direction of the fi rst point of Aries aligned upwards

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Between each of Jupiter’s oppositions and solar conjunctions, its motion relative to the Earth is more complicated than a simple back-and-forth variation in its dis-tance. Projected relative to the Earth, Jupiter appears to turn in annual circles of diameter 2 AU—the exact mirror image of the Earth’s orbit around the Sun—super-imposed on top of its 12-yearly circular trips around the Sun. At some times of year, these circles carry it eastward along the ecliptic (counterclockwise, as seen in Fig. 6.4 ), traveling in the same direction as its long term motion. That is to say, the direction in which Jupiter appears to lie from the Earth moves along the ecliptic in the same direction that the Sun appears to move along it. Jupiter’s counterclockwise motion along the ecliptic in Fig. 6.4 is fastest around the time of its solar conjunc-tion. However, for a few weeks around the time of each opposition, its motion along the ecliptic briefly turns back on itself, and moves westward instead. Figure 6.6 shows how this appears from Earth, using the example of Saturn’s motion between 2015 and 2019.

Historically, this retrograde motion was one of the most glaring problems to confront the philosophers of ancient Greece who attempted to devise models in which planets moved in simple circular paths around the Earth. Even if it is difficult for observers to gauge the distance of Jupiter from the Earth by sight, the path drawn in Fig. 6.4 is still rather obviously not circular, because the direction in which Jupiter appears to lie turns back on itself roughly once each year.

At the moment of opposition, as the Earth overtakes Jupiter on the inside, both planets are momentarily traveling through space in almost exactly the same direc-tion. The Earth, being closer to the Sun, is traveling faster than Jupiter, and so the relative motion of Jupiter as seen from the Earth is rather like that of a slow train being overtaken by an express service: Jupiter appears to drift backwards past the Earth’s window, even though it is in fact always marching forwards along its orbit.

Seasonal Variations

The outer planets are not equally well placed for observation at every opposition. Two factors affect how they appear. First, they drift along the ecliptic from one opposition to the next, sometimes appearing in the southern sky and at other times in the northern sky. When a planet reaches opposition in Sagittarius or Ophiuchus, it rides high in the sky for observers in the southern hemisphere, but appears low on the southern horizon from the northern hemisphere. As atmospheric distortions and light pollution are invariably substantially worse at low elevations, they are usually oppositions where northern observers struggle to obtain good images.

Conversely, when a planet reaches opposition in the northern constellations of Taurus or Gemini, the roles are reversed. Observers in the northern hemisphere are treated to the best views, while those in the southern hemisphere must struggle with the poor atmospheric seeing on their northern horizons. The slow progress of the outer planets along their orbits makes this a particularly infuriating problem. Successive oppositions occur at closely spaced points along the ecliptic, and once

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Saturn moves south of the celestial equator, it will remain in the southern sky for 15 years before returning to the north. The progress of Uranus and Neptune are even slower still, though their disks are small enough that there is little question of seeing structure in their clouds even when they are well placed in the sky, and so poor seeing is a less disruptive problem.

In fact there is a direct connection between the time of year at which each of the outer planets come to opposition and whether they will be best visible from northern or southern latitudes. By definition, a planet lies almost exactly opposite to the Sun in the sky when it comes to opposition. Since both the Sun and planets closely follow the path of the ecliptic across the sky, this means that when the Sun is in the northern sky, around the time of northern summer, planets at opposition lie along the southern half of the ecliptic’s path across the sky. Conversely, when the Sun is in the southern sky, planets reach opposition in northern constellations such as Taurus and Gemini, where they are best viewed from the northern hemi-sphere (see Fig. 6.7 ).

It is not just the declinations of the outer planets which change depending on the time of year at which they reach opposition. Their distances from the Earth also vary from one opposition to the next. Although all of the gas giants have orbits which are very close to being circular, their paths are sufficiently elliptical that their distances from the Sun vary by a few percent over the course of each circuit around the Sun. On any given day of the year, the Earth lies at some particular point along its orbit, which is the same every year. When an opposition of one of the gas giants occurs on that day of the year, it lies alongside that point along the Earth’s orbit.

Fig. 6.7 The outer planets reach opposition when the Earth passes between them and the Sun. This means that from the Earth, Jupiter appears almost directly opposite the Sun in the sky when the solar system is confi gured in this way. If the Sun is in the northern sky, then the planet must appear in the southern sky, and vice versa. Thus, for both northern and southern observers, Jupiter appears highest in the sky when it reaches opposition in the winter months

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in December.

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This means that when any planet comes to opposition on any given day of the year, the time of year defines the point along its orbit where that planet must presently lie, and therefore its distance from the Sun. Thus oppositions of each of the outer planets that occur on different days of the year occur at different distances from the Earth (see Figs. 6.8 and 6.9 ). It should be noted that this effect is quite distinct from the annual variability of the distances and apparent sizes of the gas giants that occur as they cycle between opposition and solar conjunction.

Fig. 6.8 Oppositions of Jupiter occur at different distances from the Earth ( left vertical axis ), depending on the time of year at which they occur, due to the slight ellipticity of Jupiter’s orbit. This means that at closest approach, the size of Jupiter’s disk varies by up to 20 % ( right vertical axis )

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The dates of all of the oppositions of the gas giants between 2000 and 2100 are listed in Tables 6.1 – 6.4 . The third column lists the declination at which each of the oppositions occurs, and the fourth column the maximum diameter of the planet’s disk at closest approach.

Fig. 6.9 Oppositions of Saturn occur at different distances from the Earth ( left vertical axis ), depending on the time of year at which they occur, due to the slight ellipticity of Saturn’s orbit. This means that at closest approach, the size of Saturn’s disk varies by up to 10 % ( right vertical axis )

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Table 6.1 The apparitions of Jupiter, 2000–2100

Date Declination Diameter/arcseconds

2000 November 28 20N 47.6 2002 January 1 23N 46 2003 February 2 17N 44.6 2004 March 4 7N 43.6 2005 April 3 4S 43.3 2006 May 4 14S 43.7 2007 June 5 21S 44.8 2008 July 9 22S 46.3 2009 August 14 15S 47.9 2010 September 21 2S 48.8 2011 October 29 11N 48.6 2012 December 3 21N 47.4 2014 January 5 22N 45.8 2015 February 6 16N 44.4 2016 March 8 6N 43.5 2017 April 7 5S 43.3 2018 May 9 16S 43.8 2019 June 10 22S 45 2020 July 14 21S 46.6 2021 August 20 13S 48 2022 September 26 0S 48.8 2023 November 3 13N 48.4 2024 December 7 22N 47.1 2026 January 10 22N 45.6 2027 February 11 15N 44.2 2028 March 12 4N 43.4 2029 April 12 7S 43.3 2030 May 13 17S 44 2031 June 15 22S 45.2 2032 July 19 21S 46.8 2033 August 25 11S 48.2 2034 October 2 1N 48.8 2035 November 8 15N 48.3 2036 December 12 22N 46.9 2038 January 14 21N 45.4 2039 February 15 13N 44.1 2040 March 16 2N 43.4 2041 April 16 8S 43.4 2042 May 17 18S 44.1 2043 June 20 23S 45.4 2044 July 24 20S 46.9 2045 August 30 10S 48.3 2046 October 7 3N 48.8 2047 November 13 16N 48.2 2048 December 17 22N 46.8 2050 January 19 20N 45.2

(continued)

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Date Declination Diameter/arcseconds

2051 February 19 12N 44 2052 March 21 1N 43.3 2053 April 20 10S 43.4 2054 May 22 19S 44.2 2055 June 24 23S 45.6 2056 July 29 19S 47.1 2057 September 4 8S 48.4 2058 October 12 5N 48.8 2059 November 18 17N 48 2060 December 21 23N 46.5 2062 January 23 20N 45 2063 February 23 11N 43.8 2064 March 25 0S 43.3 2065 April 25 11S 43.5 2066 May 26 20S 44.4 2067 June 29 23S 45.8 2068 August 3 18S 47.4 2069 September 9 6S 48.6 2070 October 17 7N 48.7 2071 November 23 19N 47.8 2072 December 26 23N 46.3 2074 January 28 19N 44.8 2075 February 28 9N 43.7 2076 March 29 1S 43.3 2077 April 29 13S 43.6 2078 May 31 21S 44.6 2079 July 4 22S 46.1 2080 August 8 17S 47.6 2081 September 15 4S 48.7 2082 October 22 9N 48.6 2083 November 28 20N 47.6 2084 December 31 23 N 46.1 2086 February 1 18N 44.6 2087 March 4 8N 43.6 2088 April 2 3S 43.3 2089 May 3 14S 43.7 2090 June 5 21S 44.8 2091 July 9 22S 46.3 2092 August 13 15S 47.8 2093 September 20 2S 48.7 2094 October 27 11N 48.5 2095 December 2 21N 47.4 2097 January 4 22N 45.8 2098 February 5 16N 44.4 2099 March 8 6N 43.5 2100 April 8 5S 43.3

Source : DE405

Table 6.1 (continued)

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(continued)

Table 6.2 The apparitions of Saturn, 2000–2100

Date Declination Ring inclination

2000 November 19 17N 23N 2001 December 3 20N 25N 2002 December 17 22N 26N 2003 December 31 22N 25N 2005 January 13 21N 22N 2006 January 27 18N 18N 2007 February 10 15N 13N 2008 February 24 11N 8N 2009 March 8 6N 2N 2010 March 22 1N 3S 2011 April 3 2S 8S 2012 April 15 7S 13S 2013 April 28 11S 18S 2014 May 10 15S 21S 2015 May 23 18S 24S 2016 June 3 20S 26S 2017 June 15 21S 26S 2018 June 27 22S 26S 2019 July 9 22S 24S 2020 July 20 20S 21S 2021 August 2 18S 18S 2022 August 14 15S 13S 2023 August 27 11S 9S 2024 September 8 7S 3S 2025 September 21 3S 1N 2026 October 4 1N 7N 2027 October 18 6N 12N 2028 October 30 11N 17N 2029 November 13 15N 22N 2030 November 27 19N 25N 2031 December 11 21N 26N 2032 December 24 22N 26N 2034 January 8 22N 24N 2035 January 22 20N 20N 2036 February 5 17N 16N 2037 February 17 13N 10N 2038 March 3 8N 5N 2039 March 16 4N 0S 2040 March 28 0S 6S 2041 April 10 5S 11S 2042 April 23 9S 16S 2043 May 5 13S 20S 2044 May 17 17S 23S 2045 May 29 19S 25S

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Table 6.2 (continued)

(continued)

Date Declination Ring inclination

2046 June 10 21S 26S 2047 June 22 22S 26S 2048 July 3 22S 25S 2049 July 16 21S 22S 2050 July 28 19S 19S 2051 August 9 16S 15S 2052 August 21 13S 11S 2053 September 3 9S 6S 2054 September 16 5S 0S 2055 September 29 0S 5N 2056 October 11 4N 10N 2057 October 25 9N 15N 2058 November 8 13N 20N 2059 November 22 17N 23N 2060 December 5 20N 26N 2061 December 19 22N 26N 2063 January 2 22N 25N 2064 January 16 21N 22N 2065 January 29 18N 18N 2066 February 12 15N 13N 2067 February 26 10N 7N 2068 March 10 6N 1N 2069 March 23 1N 3S 2070 April 5 3S 9S 2071 April 18 7S 14S 2072 April 29 12S 18S 2073 May 12 15S 22S 2074 May 24 18S 24S 2075 June 5 20S 26S 2076 June 16 22S 26S 2077 June 29 22S 25S 2078 July 11 21S 24S 2079 July 23 20S 21S 2080 August 3 18S 17S 2081 August 16 15S 13S 2082 August 28 11S 8S 2083 September 10 7S 3S 2084 September 22 2S 2N 2085 October 6 2N 8N 2086 October 19 7N 13N 2087 November 2 11N 18N 2088 November 15 16N 22N 2089 November 29 19N 25N 2090 December 13 21N 26N

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Table 6.2 (continued)

Date Declination Ring inclination

2091 December 27 22N 26N 2093 January 9 21N 23N 2094 January 23 19N 20N 2095 February 6 16N 15N 2096 February 20 12N 10N 2097 March 4 8N 4N 2098 March 18 3N 1S 2099 March 31 1S 6S 2100 April 13 5S 12S

Source : DE405

Table 6.3 The apparitions of Uranus, 2000–2100

Date Declination Diameter/arcseconds

2000 August 11 15S 3.7 2001 August 15 14S 3.7 2002 August 20 13S 3.7 2003 August 24 11S 3.7 2004 August 27 10S 3.7 2005 September 1 9S 3.7 2006 September 5 7S 3.7 2007 September 9 6S 3.7 2008 September 13 4S 3.7 2009 September 17 2S 3.7 2010 September 21 1S 3.7 2011 September 26 0N 3.7 2012 September 29 1N 3.7 2013 October 3 3N 3.7 2014 October 7 4N 3.7 2015 October 12 6N 3.7 2016 October 15 8N 3.7 2017 October 19 9N 3.7 2018 October 24 11N 3.7 2019 October 28 12N 3.7 2020 October 31 13N 3.8 2021 November 4 15N 3.8 2022 November 9 16N 3.8 2023 November 13 17N 3.8 2024 November 17 18N 3.8 2025 November 21 19N 3.8 2026 November 25 20N 3.8 2027 November 30 21N 3.8

(continued)

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(continued)

Date Declination Diameter/arcseconds

2028 December 3 22N 3.8 2029 December 8 22N 3.9 2030 December 12 23N 3.9 2031 December 17 23N 3.9 2032 December 20 23N 3.9 2033 December 25 23N 3.9 2034 December 30 23N 3.9 2036 January 3 23N 4 2037 January 7 22N 4 2038 January 12 22N 4 2039 January 17 21N 4 2040 January 21 20N 4 2041 January 25 19N 4 2042 January 30 18N 4 2043 February 4 17N 4 2044 February 9 15N 4 2045 February 13 14N 4.1 2046 February 18 12N 4.1 2047 February 23 10N 4.1 2048 February 28 9N 4.1 2049 March 4 7N 4.1 2050 March 9 5N 4.1 2051 March 14 3N 4.1 2052 March 18 1N 4.1 2053 March 23 0S 4.1 2054 March 28 2S 4.1 2055 April 2 4S 4.1 2056 April 6 5S 4.1 2057 April 11 7S 4.1 2058 April 16 9S 4 2059 April 21 11S 4 2060 April 25 12S 4 2061 April 30 14S 4 2062 May 5 15S 4 2063 May 10 17S 4 2064 May 14 18S 4 2065 May 19 19S 4 2066 May 24 20S 3.9 2067 May 29 21S 3.9 2068 June 2 22S 3.9 2069 June 7 22S 3.9 2070 June 12 23S 3.9 2071 June 16 23S 3.9 2072 June 20 23S 3.9

Table 6.3 (continued)

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Table 6.4 The apparitions of Neptune, 2000–2100

Date Declination Diameter/arcseconds

2000 July 27 18S 2.3 2001 July 30 18S 2.3 2002 August 2 17S 2.3 2003 August 4 17S 2.3 2004 August 6 16S 2.4 2005 August 8 16S 2.4 2006 August 11 15S 2.4 2007 August 13 14S 2.4 2008 August 15 14S 2.4 2009 August 17 13S 2.4

(continued)

Date Declination Diameter/arcseconds

2073 June 25 23S 3.8 2074 June 30 23S 3.8 2075 July 4 23S 3.8 2076 July 8 22S 3.8 2077 July 13 22S 3.8 2078 July 17 21S 3.8 2079 July 22 21S 3.8 2080 July 25 20S 3.8 2081 July 30 19S 3.7 2082 August 3 18S 3.7 2083 August 8 17S 3.7 2084 August 11 15S 3.7 2085 August 16 14S 3.7 2086 August 20 13S 3.7 2087 August 24 11S 3.7 2088 August 28 10S 3.7 2089 September 1 9S 3.7 2090 September 5 7S 3.7 2091 September 10 6S 3.7 2092 September 13 4S 3.7 2093 September 17 2S 3.7 2094 September 22 1S 3.7 2095 September 26 0N 3.7 2096 September 29 1N 3.7 2097 October 4 3N 3.7 2098 October 8 4N 3.7 2099 October 12 6N 3.7 2100 October 16 8N 3.7

Source : DE405

Table 6.3 (continued)

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Date Declination Diameter/arcseconds

2010 August 20 12S 2.4

2011 August 22 12S 2.4 2012 August 24 11S 2.4 2013 August 27 10S 2.4 2014 August 29 10S 2.4 2015 September 1 9S 2.4 2016 September 2 8S 2.4 2017 September 5 7S 2.4 2018 September 7 6S 2.4 2019 September 10 6S 2.4 2020 September 11 5S 2.4 2021 September 14 4S 2.4 2022 September 16 3S 2.4 2023 September 19 2S 2.4 2024 September 21 1S 2.4 2025 September 23 1S 2.4 2026 September 26 0S 2.4 2027 September 28 0N 2.4 2028 September 30 1N 2.4 2029 October 2 2N 2.4 2030 October 5 3N 2.4 2031 October 7 3N 2.4 2032 October 9 4N 2.4 2033 October 11 5N 2.4 2034 October 14 6N 2.4 2035 October 16 7N 2.4 2036 October 18 8N 2.4 2037 October 20 8N 2.4 2038 October 23 9N 2.4 2039 October 25 10N 2.4 2040 October 27 11N 2.4 2041 October 29 11N 2.4 2042 November 1 12N 2.4 2043 November 3 13N 2.4 2044 November 5 13N 2.4 2045 November 7 14N 2.4 2046 November 10 15N 2.4 2047 November 12 15N 2.4 2048 November 14 16N 2.4 2049 November 16 17N 2.4 2050 November 19 17N 2.4 2051 November 21 18N 2.4 2052 November 23 18N 2.4 2053 November 25 19N 2.4

(continued)

Table 6.4 (continued)

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Date Declination Diameter/arcseconds

2054 November 27 19N 2.4 2055 November 30 19N 2.4

2056 December 1 20N 2.4 2057 December 4 20N 2.4 2058 December 6 20N 2.4 2059 December 9 21N 2.4 2060 December 10 21N 2.4 2061 December 13 21N 2.4 2062 December 15 21N 2.4 2063 December 18 22N 2.4 2064 December 19 22N 2.4 2065 December 21 22N 2.4 2066 December 24 22N 2.4 2067 December 26 22N 2.4 2068 December 28 22N 2.4 2069 December 30 22N 2.4 2071 January 2 22N 2.4 2072 January 4 21N 2.4 2073 January 6 21N 2.4 2074 January 8 21N 2.4 2075 January 10 21N 2.4 2076 January 13 21N 2.4 2077 January 14 20N 2.4 2078 January 17 20N 2.4 2079 January 19 20N 2.4 2080 January 21 19N 2.4 2081 January 23 19N 2.4 2082 January 25 18N 2.4 2083 January 28 18N 2.4 2084 January 30 17N 2.3 2085 February 1 17N 2.3 2086 February 3 16N 2.3 2087 February 5 16N 2.3 2088 February 8 15N 2.3 2089 February 9 14N 2.3 2090 February 12 14N 2.3 2091 February 14 13N 2.3 2092 February 17 12N 2.3 2093 February 18 12N 2.3 2094 February 20 11N 2.3 2095 February 23 10N 2.3 2096 February 25 10N 2.3 2097 February 27 9N 2.3 2098 March 1 8N 2.3 2099 March 4 7N 2.3 2100 March 6 6N 2.3

Source : DE405

Table 6.4 (continued)

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Space Missions to the Outer Planets

Exploration of the gas giants by spacecraft began in the early 1970s, after a decade in which NASA’s Mariner program had sent ten missions to the terrestrial planets, of which seven had succeeded to the point of returning useful data. The spacecraft that we know today as Voyagers 1 and 2 were originally envisaged as the natural extension of this program—Mariners 11 and 12—but were subsequently renamed to reflect the fact that their designs had little in common with the earlier Mariners, because of the very different environments that they were being sent to explore.

In addition to the challenges and risks of sending spacecraft over much larger distances than had ever been attempted before, including crossing the asteroid belt for the first time, there was the question of how to provide power to the on-board electronics once these probes reached the outer solar system. Solar cells are usually sufficient to provide power for missions to the terrestrial planets, but they are of less use in the outer solar system, where the Sun appears much smaller and fainter than it does from the Earth. By the time a spacecraft reaches Uranus and Neptune, the Sun has receded to appear more like an intensely bright star than a brightly-glowing disk.

To test the feasibility of visiting the outer planets, two initial spacecraft were sent as part of NASA’s Pioneer program—a family of spacecraft whose origins dated back to early preparations for the Moon landings, and which had been used primarily to test new technology rather than to explore the solar system. Pioneer 10 visited Jupiter in 1973, followed by its near-identical twin, Pioneer 11 in the following year. The latter also went on to fly past Saturn in 1979. Both these space-craft were powered by small nuclear batteries rather than solar cells, which took the form of enclosed radioisotope thermoelectric generators (RTGs). Following this precedent, all of the spacecraft which have been sent to the gas giants since have used very similar nuclear power cells, until very recent times. Only in the twenty- first century has the efficiency of solar cells increased, and the power needs of computers decreased, to the point where it is feasible to send a spacecraft to Jupiter which can rely entirely on the Sun’s energy. Juno, launched in 2011 and due to arrive at Jupiter in 2016, is the first spacecraft to do so.

The Pioneer probes carried only rudimentary instruments, including low- resolution cameras that were only capable of taking crude images in red and blue light. The first detailed close-up images of the gas giants were taken by the Voyager probes—also identical twins—that flew past Jupiter in 1979 and Saturn in 1980–1. Voyager 2 also went on to visit both Uranus (1986) and Neptune (1989), and to date is the only spacecraft to have flown past either of the solar system’s outermost two planets.

The Voyagers revealed a wealth of previously unseen detail in the structure of the clouds on Jupiter and Saturn, the first ever images of the surfaces of the moons of the gas giants, and the only images that have ever been taken of the structure of the cloud tops of Uranus and Neptune. The principal limitation of the images they returned was that since the Voyager spacecraft only flew past each of the planets,

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rather than going into orbit around them, they provided only brief snapshots of the appearance of each with little indication of how typical each of these was.

More recently, the Galileo spacecraft (1995–2003) spent 8 years observing Jupiter and its moons, and Cassini (2004–) has spent nearly a decade studying Saturn and its moons. In the coming decade, two new spacecraft will visit Jupiter: Juno will arrive in 2016, followed by the European Space Agency’s JUpiter ICy moon Explorer (JUICE) mission, which is scheduled for launch in 2022 and will focus on studying Jupiter’s three largest icy moons: Ganymede, Callisto, and Europa.

Gas Giants as Planets

As we have already seen, observations of the gas giants have allowed a fairly detailed understanding of the structures of their cloud tops to be pieced together, and spectra have allowed some of the molecules present in their atmospheres to be identified. We have observations of Jupiter and Saturn collected by orbiting space-craft over periods of several years, as well as very detailed images taken by amateur astronomers. Our understanding of Uranus and Neptune is considerably more hazy, based primarily on a small number of images taken by Voyager 2 in 1986 and 1989. In the absence of any proposed future missions to visit them, our understanding of their atmospheres is likely to remain hazy for some time to come.

Our knowledge of what lies beneath the surfaces of the gas giants is consider-ably more vague. The surfaces of rocky planets provide a wealth of information about what lies beneath them. By looking at how heavily cratered the surfaces of the Moon and Mars are, and comparing against theoretical predictions of how often meteor impacts occur, it is possible to estimate how long ago those solid surfaces formed—how long they have been exposed to bombardment from space. Older surfaces are more heavily cratered than newer surfaces. Volcanic processes occa-sionally bring rock samples from the interiors of such planets to their surfaces. And moreover it is possible to land robotic laboratories and rovers on their surfaces. By comparison, the gas giants are rather harder to study.

The standard tools that are used to infer what lies beneath the surfaces of the gas giants are their gravitational and magnetic fields. The former tells of how much mass there is beneath their surfaces, and roughly how this mass is distributed. To have a magnetic field, a planet needs to have a flowing mass of electrically conduc-tive material beneath it surface, and the very intense magnetic fields that surround Jupiter and Saturn point to very large reservoirs of such material which occupy the vast majority of their interiors.

The Earth’s magnetic field is generated by molten iron in its core, but the low densities of Jupiter and Saturn point instead to a less heavy material called metallic hydrogen as the conductor that is present beneath their cloud tops. When hydrogen gas is exposed to extreme pressures, as it is within the interior of a gas giant, the hydrogen atoms no longer group together into pairs, as molecules of H2, but they

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form an extended sea of atoms in which electrons are not tightly bound to particular atoms, but can flow freely. This structure is very similar to that of most metals, and conducts electricity well.

Jupiter’s magnetic field is 14 times stronger than that of the Earth, and disrupts the flow of the solar wind out to a distance of 75 times of the planet’s radius. This means that Jupiter’s magnetosphere—the region in which its magnetic field domi-nates over that of the Sun—is considerably larger than even the Sun’s opaque glow-ing surface. If it were visible to the human eye, it would appear as a disk surrounding Jupiter with an angular diameter slightly in excess even of that of a full Moon.

To date it has not been possible to observationally determine whether the gas giants have rocky cores at their centers, though as we have seen, the most widely favored theories of how they formed require that an initial rocky seed began the process of their formation by gravitationally drawing their gaseous atmospheres together. The Juno spacecraft will make detailed maps of Jupiter’s gravitational field, with the aim of shedding light on how large any rocky core at Jupiter’s center might be.

The interiors of all of the gas giants are thought to be composed primarily of hydrogen and helium, but Uranus and Neptune appear to also harbor significant quantities of water and methane ice beneath their surfaces. Moreover, their mag-netic fields are significantly disrupted, appearing skewed from their centers and misaligned with their rotation axes. This appears to hint at some large-scale asym-metry in the distribution of the metallic hydrogen beneath their surfaces. Until further spacecraft are sent to study them, however, these observations remain little more than tantalizing clues about their internal structures.

The Moons of the Outer Planets

In contrast to the terrestrial planets, each of the gas giants is surrounded by a large family of moons. Without exception, these moons divide neatly into two categories. The innermost moons typically orbit their host planets in a plane which is aligned closely with the equator of that planet’s rotation axis. Their orbits are typically close to circular, and travel in the same direction in which their host planets rotate beneath them. These are regular moons, which are believed to have formed around the gas giants in almost exactly the same way in which the solar system formed around the Sun, from a swirling disk of material, whose central parts turned into a planet, and whose extremities turned into a system of moons around it.

In the latter stages of this process, when the gravitational fields of the gas giants had become strong enough to sweep up all of the gas around them in the Sun’s protoplanetary disk, they acquired swirling disks of material around them. Much of this would have descended onto their surfaces to become part of their massive gaseous atmospheres. However, just as not all of the material circling around the infant Sun ended up in its atmosphere—some became a system of planets around it—not all of the nascent cloud of material around the infant gas giants made it into

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their atmospheres. Some formed into systems of moons around them. Just as the solar system’s planets all circle the Sun in much the same plane, and in the same direction as the Sun’s own rotation, the same is also true of the regular moons of the gas giants.

The outermost moons of these systems typically show rather different properties, however. Their orbits are aligned randomly rather than being in the same plane as the regular moons. They are also often highly elliptical, in contrast to the near- circular orbits of the regular moons. It is generally assumed that these irregular moons did not form in their current positions, but were originally asteroids which have at some point become captured into orbit around one of the planets.

The richness of the systems of moons around each of the gas giants is generally assumed to be the result of their strong gravitational fields, whose influence can still be felt out to large distance around them. This makes them much more likely to sweep up surrounding objects than the terrestrial planets. Moreover, the final stage of the process by which they form—in which they sweep up all of the gas around them in the Sun’s protoplanetary disk—means that unlike the terrestrial planets, they went through a phase of being surrounded by a disk of material in which regular satellites conglomerate together.

Of the terrestrial planets, only the Earth has a single regular moon, which is believed to have formed from a special set of circumstances in which a large body collided with the Earth early in its history (see Chap. 5 ). Mars has two moons, Phobos and Deimos, but these are both irregular moons which it is most likely to have captured from the neighboring asteroid belt.

Some of the largest of the gas giants’ moons are large enough that they might easily be categorized as terrestrial planets if they were in orbit around the Sun. For example, Jupiter’s moon Ganymede and Saturn’s moon Titan are both larger than Mercury. The latter is a particularly curious body on account of the parallels that it shows with our own planet, even though it is ten times more distant from the Sun, making it a frigid world whose average surface temperature is around −180 °C. Titan is much too cold for liquid water to exist on its surface, but it does have exten-sive lakes of liquid methane and other hydrocarbons. Above these, there lies a nitrogen-rich atmosphere of around 1.5 times the thickness of the Earth’s, and a rich array of weather systems which include clouds of methane vapor which form as a result of evaporation from the moon’s surface, and even rainfall. Apart from the Earth, Titan is the only other body in the solar system to have sizeable quantities of liquid on its surface and ongoing weathering due to rainfall. It was to study these processes in more detail that the Huygens probe landed on Titan in 2005, becoming the first—and to date only—spacecraft ever to land on a moon of another planet.

Tidal Locking

The Earth and Moon are not the only bodies in the solar system which feel tides. In fact, the tides felt by many of the moons of the gas giants are much stronger than the Earth’s, and strong enough that all of the known regular moons of the four gas

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giants—8 around Jupiter, 24 around Saturn, 18 around Uranus and 6 around Neptune—are tidally locked to their parent planets (see Chap. 5 ), with the single exception of Saturn’s moon Hyperion.

Being tidally locked to their parent planets means that the rocky surfaces of these regular moons are no longer stretched back and forth by the tidal gravitational fields of their parent planets each time they rotate. Even so, they still feel strong tides from one another’s gravity since it is only possible for them to be tidally locked to one body at a time. An effect similar to this is at work in the surface of Jupiter’s innermost large moon Io, whose rocky mantle is pulled up and down by more than 100 m between its high- and low-tides. The tremendous heat generated by frictional resistance to this motion makes Io by far the most volcanic body any-where in the solar system.

The tides of such moons can reveal details of what lies beneath their surfaces. The height to which such tides rise depends on the flexibility and elasticity of the material which is having to move beneath the moon’s surface in response to the tidal pull being exerted on it. With sufficiently detailed measurements, it is possible to compare how large the tides observed on each moon are with how those moons might be expected to behave given a variety of different possible rock structures beneath their surfaces. To date, the most impressive result from such work has been a tentative detection of liquid water beneath the solid surface of Saturn’s moon Titan. The Cassini spacecraft was able to determine that Titan’s surface experiences tides which have a height of around 10 m—ten times higher than can be reproduced by theoretical models of any plausible solid surface. A team led by Luciano Iess concluded in 2012 that there must be a very large body of liquid water beneath Titan’s surface, able to flow over vast distances to give the crust the appearance of being so very elastic.

Ring Formation

The origin of Saturn’s rings remains poorly understood. Until the visit of the Voyager spacecraft, astronomers wondered why Saturn was the only gas giant to have rings. We now know that all of the gas giants have faint rings of material around them, and so the question is rather why Saturn is the only planet to have such prominent rings around it. In the past, it was widely thought that Saturn’s rings might be a short-lived feature, and that mankind happened to have invented the astronomical telescope at just the right time in the solar system’s history to see them. More recently, the discovery of ring systems around all of the gas giants sug-gests instead that it is usual for gas giants to have ring structures around them.

The reason why the particles which make up Saturn’s rings have not coalesced together into moons is due to the strong tidal forces that any moon would feel in such close proximity to Saturn. Within a certain distance of any planet—typically around 2.4 times that planet’s radius but depending in detail on the planet’s

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density—the tidal forces experienced by any moon in orbit around it become so strong that they overwhelm the gravitational binding that holds that moon together.

In Chap. 5 , we saw that the effect of tidal forces is to stretch moons out in the directions towards and away from their parent bodies, and to compress them side-ways (see Fig. 5.9c ). The closer it lies to its parent body, the stronger these forces become. At a certain point, called the Roche limit after the French mathematician Édouard Roche (1820–1883) who first derived it, they become so strong that they are able to lift material from the surface of the Moon. If the Moon is held together by gravity alone, rather than by solid cohesion, it will disintegrate if it ventures within this distance of its parent body. It is by this mechanism that the solar sys-tem’s comets often disintegrate if they pass too close to either the Sun or Jupiter, though explosive outbursts can also contribute to breaking them apart.

The brightest of Saturn’s rings lie within its Roche limit, and so it is virtually impossible for the particles within them to coalesce together. This association between tidal forces and Saturn’s ring system is given credence by the fact that the outer edge of the brightest rings is at a distance of around 137,000 km from Saturn’s center—around 2.3 Saturn radii—which is very close to the planet’s Roche limit. There are, however, several much fainter rings a material which extend out to beyond six Saturn radii.

Saturn at Opposition

With careful observation, a marked change can be seen in the brightness of Saturn’s rings at around the time when it passes opposite to the Sun in the sky, at around the time of opposition. A similar phenomenon can be observed in the brightnesses of the Moon and Mars, called an opposition surge, but Saturn’s rings provide by far the most easily observable example of the effect (see Fig. 6.10 ).

Fig. 6.10 Saturn, as seen 8 h after opposition on 2008 February 25 00:31 UTC ( left ), and as seen the following day, 2008 February 26 23:27 UTC ( right ). The rings appear markedly brighter close to the exact moment of opposition—this is particularly apparent where they pass in front of the planet’s disk. Images courtesy of David Arditti, http://staglaneobservatory.co.uk/

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What Saturn’s rings have in common with the surfaces of the Moon and Mars is that they are made up of tiny dust-like fragments of solid material which are illu-minated by the Sun’s light. Two effects work in tandem to make dusty bodies appear dramatically brighter when they are at opposition. The easiest of these to understand is called shadow hiding or the Seeliger effect.

Anybody who has ever observed the rough surface of a sidewalk at around sun-set is likely to be familiar with this effect already, from noticing how individual stones cast long shadows late in the day. At around noon, when the Sun is high in the sky, the same sidewalk would appear bright. Looking down on its stony surface from above, there is an exact correspondence between the areas of the sidewalk illuminated by the Sun, and those visible to the observer’s line of sight. Put another way, the shadows of each of the stones are hidden directly behind them, out of sight.

The geometry of Saturn’s rings is similar at around the time of opposition. At this time, the Sun, Earth and Saturn lie in an almost straight line, and the Sun’s rays illuminate the particles that make up Saturn’s rings from almost directly behind the Earth. This means that almost all of the surfaces that are exposed to the Earth’s line of sight are illuminated, rather than lying in the shadow of other particles. For this reason, the effect which is now commonly known as the opposition surge in the brightness of Saturn’s rings is sometimes called the Seeliger effect, after Hugo von Seeliger (1849–1924) who proposed this mechanism for it in 1887.

In more modern times, it has become clear that the Seeliger effect is only one half of the reason for the opposition surge, however. An additional effect called coherent backscatter means that on the microscopic scale of individual light waves, distributions of tiny solid particles preferentially scatter more light straight back towards the source that is illuminating them than they scatter sideways in other directions.

Perhaps the best known demonstration of coherent backscatter is the gegen-schein—a very faint glow of the area of sky opposite to the Sun, which is only visible from the very darkest sites (see Fig. 6.11 ). The glow is produced by small pieces of gritty debris which litter the solar system—the same material which burns up brightly as shooting stars whenever it collides with the Earth’s atmosphere. Much of this debris is released from the surfaces of comets whenever they venture close to the Sun and grow tails, made of outflows of steam that emerge from their icy surfaces as the Sun warms them, but which also have rocky particles suspended in them. Collisions between asteroids in the asteroid belt may also contribute occa-sional new bursts of rocky dust to interplanetary space.

For the most part, this haze of rocky particles is so diffuse that even though it does scatter sunlight, producing a band of light across the sky called the zodiacal light, it is incredibly difficult to observe. Around the point opposite to the Sun in the sky, however, the zodiacal light brightens to form a puddle of light called the gegenschein as a result of coherent backscatter. Yuri Beletsky’s photograph shown in Fig. 6.11 is exceptional in that not only is the gegenschein readily apparent in the center of the frame, but the line of zodiacal light is also apparent on either side, running diagonally through it.

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While the Moon, Mars and Saturn’s rings all show opposition surges as a result of these same two mechanisms, Saturn’s rings are unique in that they encircle a gaseous body that does not undergo any opposition surge. It is difficult to visually detect the opposition surges of the Moon or Mars, because the effect is rather slight and there is a lack of any nearby point of comparison. However, the brightening of Saturn’s rings relative to the disk of the planet behind them is quite apparent.

The Seasons of the Outer Planets

As discussed in Chap. 2 , the Earth’s seasons arise from the fact that its spin axis is not perfectly aligned perpendicular to the plane in which it orbits around the Sun (the ecliptic). As a result, there is one half of its orbit over which its north pole is tipped towards the Sun, and another half over which its south pole is tipped towards the Sun. These two halves of the year are the northern and southern summers respectively.

Fig. 6.11 The solar system’s zodiacal light appears brighter around the point in the sky opposite to the Sun because of the opposition effect. This bright spot in the zodiacal light is called the gegenschein . Image courtesy of Yuri Beletsky (ESO)

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The Earth is not the only planet to experience seasons, though. Inevitably, the rotation axes of all of the planets are to some degree misaligned with the planes of their orbits around the Sun. The greater the misalignment of their rotation axes from their orbital axes—called the obliquities of their ecliptics—the more pronounced their seasons are (see Table 6.5 ). Of the two gas giants on which surface detail can be easily resolved, Jupiter barely has any seasons, since its tropics are only a mere 3° north and south of its equator, but Saturn has seasons not dissimilar to those of the Earth.

Uranus has the most extreme seasons of any of the solar system’s planets. Rather than rotating about an axis which lies at some small angle to the axis of its orbit around the Sun, it is tipped sideways and its polar axis lies very close to the plane of the solar system. This means that the Sun can pass almost directly over Uranus’s poles at midsummer, and Uranus’s arctic and antarctic circles are a mere 8° north and south of its equator. It is not known for certain how Uranus has come to have this unusual rotation axis, but one possibility is that it formed from an oblique col-lision between two similarly-sized objects.

Just as on Earth, the seasons on each of the gas giants mean that regions at any given latitude receive an amount of heat from the Sun which varies as the planet progresses around its orbit. On Saturn, this can lead to subtle color changes in the cloud-tops around its polar regions as they emerge from several years of darkness in the spring, though high-resolution imaging over a long period of time and through a consistent set of color filters is needed to pick these out.

Of greater significance to us observing from the Earth is the effect this has on the inclination of Saturn’s systems of rings and moons to our line of sight. The orbits of the regular moons of both Jupiter and Saturn are closely aligned above each planet’s equator, and the same is also true of Saturn’s rings. As already seen, this almost certainly arose because they formed in a manner similar to how to solar system as a whole formed, from a rotating disk of material, the central portion of which formed into a large central body, but the outer parts of which formed into a

Table 6.5 The obliquities of the ecliptics of each of the planets

Planet Obliquity of ecliptic

Mercury 0.01 Venus 2.64 Earth 23.4 Mars 25.19 Jupiter 3.12 Saturn 26.73 Uranus 82.23 Neptune 28.33

The larger the obliquity, the more pronounced the seasons that planet experiences

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number of separate bodies. Both the rotation of the large central body, and the orbital motion of the bodies around it, arose from the same rotational motion of the disk from which they formed, and so they came to share the same plane.

This means that the orbits of the moons of Jupiter, whose equator is closely aligned with the plane of the solar system, always appear almost exactly edge-on as seen from the Sun. The Earth is not far from the Sun in comparison to the scale of Jupiter’s orbit, and so the view from Earth is a not dissimilar perspective as would be seen from the center of the solar system. If the orbits of Jupiter’s moons were even a little inclined to our line of sight, their paths would appear as ovals when projected onto the sky, skimming not far from its north and south poles, but never actually passing in front of its disk. In practice, however, their orbits appear sufficiently close to edge-on that they pass in front of and behind Jupiter’s disk on each circuit around it. Jupiter is the only planet which has a system of moons which can frequently be observed to cast shadows onto its surface—small Jovian solar eclipses.

As shown in Chap. 4 , these transits and occultations provide a rare example of a regular stream of celestial events whose timing can be predicted with precision in advance. At one time it was hoped that observing them might provide time signals to sailors. By looking up the times at which almanacs predicted that they were going to occur, and comparing these with the local solar times at which they were observed to occur through telescopes on ship, it was hoped that sailors would be able to work out the longitudes of their ships. In practice, however, it proved virtu-ally impossible to observe Jupiter from the rolling deck of a ship in any but the calmest seas.

These Jovian time signals were, however, used in 1676 by Ole Rømer (1644–1710) to make the first determination of the speed of light. Rømer observed that occultations and transits of Jupiter’s moon Io appeared to be retarded by around 16 min when Jupiter was close to solar conjunction, as compared to when it was close to opposition. He correctly interpreted this as evidence that it took light 16 min to traverse the diameter of the Earth’s orbit—the additional distance that Jupiter’s light had to travel to reach the Earth when at solar conjunction. The accuracy with which Rømer could convert this measurement into a speed in meters per second was limited by the difficulty of determining how many meters away the Sun was—what physical distance these 16 light-minutes corresponded to—but it provided the first direct evidence that light traveled through space at a finite speed.

The Inclination of Saturn’s Rings

Saturn’s axis of rotation is inclined at 25.7° to the plane of its orbit around the Sun, and so it experiences seasons similar to those of the Earth—though the 30-year period of its orbit around the Sun means that its seasons cycle 30 times more slowly than those on Earth.

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Most of the time, the orbits of its moons are inclined to our line of sight at such an angle that only the innermost moons, embedded among its rings, pass in front of or behind its disk. All of these moons are much too faint to be observed from Earth, and were discovered only by visiting spacecraft. Saturn’s rings, sharing the same plane as the orbits of its regular satellites, are also well inclined to our line of sight and clearly visible.

Just as on Earth, however, there are two times in each Saturnian year when the Sun passes over its equator—Saturn’s equinoxes. The Earth, not far from the Sun, also passes directly above Saturn’s equator at around the same time. To us, who observe from the Earth’s surface, Saturn’s systems of moons and rings both appear to pass through an edge-on configuration at those moments.

The geometry of Saturn’s rings is shown in Fig. 6.12 . Saturn’s rotation axis, and the planes in which its moons and rings orbit around it, remain fixed in space as it circles around the Sun. On the top-left of Fig. 6.12 , they are tipped up so that Saturn’s south pole is directed towards the Sun and Earth, and the southern face of its rings is presented to the Earth. Conversely, 15 years later, when Saturn reaches the bottom-right corner of Fig. 6.12 , they are tipped such that the northern face of Saturn’s rings is presented to the Earth.

Fig. 6.12 The varying inclination of Saturn’s rings, as seen from the Earth, over the course of each 30-year orbit Saturn makes around the Sun. The scale of the rings and of the Earth’s orbit are exaggerated to make them visible

Southern face ofrings visible

Rings seenedge on

Northern faceof rings visible

Rings seenedge on

Sun Earth

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Figure 6.13 charts the varying inclination of Saturn’s rings, as seen from the Earth, between 2005 and 2065. In addition to the slow 30-year variation which stems from Saturn’s gradual orbital motion around the Sun, there are annual ripples which result from the Earth nodding from side-to-side around the Sun. While the inclination of Saturn’s rings varies smoothly as seen from the center of the solar system, Earth is somewhat offset from that point.

Around the time of Saturn’s equinoxes, when its rings appear close to edge on, it is arguably missing its most stunning feature. However, this unusual perspective

Fig. 6.13 The inclination of Saturn’s rings, as seen from the Earth, 2005–2065. Positive inclinations indicate that the northern face of the rings are presented to the Earth, while negative inclinations indicate that the southern face is presented

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provides a brief window of a few months in which it is possible to appreciate just how wafer-thin Saturn’s rings are. As they pass through their edge-on configura-tion, they narrow to a thin line and become almost invisible. Even if they are not visible in their full glory, they reveal features which are quite invisible at other times. Among the rings there are embedded a handful of small moonlets which orbit in narrow gaps within the rings. Normally these tiny bodies are difficult to pick out from the rings around them, even for passing spacecraft. When the Sun illuminates the rings from the side, however, they become more conspicuous as they cast long shadows over the ring particles around them.

Figure 6.14 shows Saturn’s moon Daphnis, as it appeared to Cassini in June 2009, shortly before the equinox of August 2009. Daphnis is normally visible only as a speck circulating in the 26-mile-wide Keeler Gap in Saturn’s A-ring, also made apparent by the ripples that its gravitational field induces in the ring material behind it, visible to Daphnis’s left in the image shown here. In June 2009, however, Daphnis also cast a long shadow over the ring material behind it, which is visible as an upward-pointing needle of darkness in Fig. 6.14 . Daphnis had in fact been discovered only 4 years earlier, in 2005, when the lengthening shadows cast by the ripples it induces around it brought them to prominence in Cassini images.

Fig. 6.14 Daphnis casting long shadows over Saturn’s rings. Credit : NASA/Cassini

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From Earth, Saturn’s ring-plane crossing events also offer brief opportunities to see the unlit side of Saturn’s rings, appearing as dark silhouettes in front of the planet’s disk. Figure 6.15 shows the changing inclination of Saturn’s rings around the time of four equinoxes, as seen from the Earth (solid line) and from the Sun (dotted line). The Earth’s motion around the Sun means that Saturn’s rings can pass through an edge-on configuration either once, as in 2009 and 2025, or three times, as in 2038–2039 and 2054–2055. By contrast, the inclination of Saturn’s rings as seen from the Sun varies smoothly, and passes through an edge-on configuration on a date separated by up to a few months from when it is seen from Earth.

For brief periods—for example, between March 23 and May 6 in 2025, and between January 22 and April 1 in 2039, the Earth lies on the opposite side of Saturn’s ring plane from the Sun, and the narrow slither on the rings that it can see is unlit. Table 6.6 lists all of the dates between 1979 and 2100 when either the Earth or the Sun will cross Saturn’s ring plane.

Fig. 6.15 The ring crossing events of 2009, 2025, 2038–2039 and 2054–2055. The vertical scale shows the inclination of the Earth’s ( solid line ) and Sun’s ( dotted line ) sightlines to the plane of Saturn’s rings. The angles are marked in degrees

Nov 2038

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Table 6.6 Dates when the Earth and Sun pass through Saturn’s ring plane, 1979–2100

1979 October 27 Earth passes S → N 1980 March 3 Sun passes S → N 1980 March 12 Earth passes N → S 1980 July 23 Earth passes S → N 1995 May 21 Earth passes N → S 1995 August 11 Earth passes S → N 1995 November 18 Sun passes N → S 1996 February 11 Earth passes N → S 2009 August 10 Sun passes S → N 2009 September 4 Earth passes S → N 2025 March 23 Earth passes N → S 2025 May 6 Sun passes N → S 2038 October 15 Earth passes S → N 2039 January 22 Sun passes S → N 2039 April 1 Earth passes N → S 2039 July 9 Earth passes S → N 2054 May 5 Earth passes N → S 2054 August 31 Earth passes S → N 2054 October 9 Sun passes N → S 2055 February 1 Earth passes N → S 2068 June 29 Sun passes S → N 2068 August 25 Earth passes S → N 2084 March 14 Earth passes N → S 2084 March 27 Sun passes N → S 2097 October 5 Earth passes S → N 2097 December 13 Sun passes S → N 2098 April 26 Earth passes N → S 2098 June 18 Earth passes S → N

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Mars

Mars has long attracted a special interest among the planets. Even to the unaided eye it has a strikingly red color, making it easy to understand how ancient cultures often came to associate it with warfare and bloodshed. To the Romans, Mars was the most prominent god of warfare, in whose honor festivals were held every March, shortly before the time of year when most military campaigns took place. In Greek culture, the red planet came to be associated with the god Ares, who embodied the savage destruction of warfare. Ares had two attendants, Deimos and Phobos who embodied terror and fear, after whom Mars’s two small moons are now named (Fig. 7.1 ).

Mars is around one-and-a-half times more distant from the Sun than the Earth, and its relative closeness to our own planet has prompted speculation among scien-tists and science fiction writers alike that its environment might be rather similar to our own. This closeness, together with the fact that its atmosphere is thin and trans-parent unlike that of Venus, means that it is the only terrestrial planet on whose surface relief can easily be mapped out using telescopes on Earth.

Historical Observations of Mars

Spacecraft which have visited Mars have told us that many of the structures that amateur observers can see are mountains and volcanic formations. Bright features at its poles are made of frozen carbon dioxide, which forms a snow-like layer of frost in the winter. Historically, though, there have been many more fanciful ideas about what Mars’s surface might be like. When the Italian observer Giovanni Schiaparelli (1835–1910) reported seeing linear features or ‘channels’ on Mars’s

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surface in 1877, speculation abounded that these might be large-scale engineered structures built by an intelligent race of beings. Although Schiaparelli made no such claim himself, the Italian word for a channel is canali, and the myth of the Martian canals may have been fuelled at least in part by careless translation. Naturally there were many skeptics, but their existence was hard to entirely disprove. To those who suggested that Mars was too cold to be habitable, it could be retorted that perhaps it was the harsh environment that necessitated water-management on a global scale, beyond anything that mankind had ever achieved. To those who suggested that any reasonably-sized water channels would be much too narrow to be visible from Earth, it could be argued that perhaps observers were seeing fertile agricultural land on the banks of the waterway rather than the water itself. On our own planet, the river Nile is much too narrow to be seen from space, but the strip of fertile land along its valley is clearly visible owing to its strikingly different color from the desert around it.

One believer was Percival Lowell (1855–1916), who was encouraged by Schiaparelli’s observations to establish an observatory at Flagstaff, Arizona, in 1894. He went on to dedicate much of the rest of his life to studying these fictitious

Fig. 7.1 Mars, as seen by the Hubble Space Telescope (HST) in 2001. Credit : NASA/STScI

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structures. To the wider public, science suddenly appeared close to finding evidence of extraterrestrial civilizations, and just at a time when the progress of technology over the preceding century had made space travel suddenly seem a much less far- fetched prospect. The question of whether there is life on other planets has always been a staple for science fiction writers, and it’s hardly a surprise that this talk of canals should have coincided with a surge of popular interest in the red planet.

The myth is often told that an overly realistic dramatization of H.G. Wells’s (1866–1946) novel The War of the Worlds (1898) by the Columbia Broadcasting System radio network in 1938 sparked mass public hysteria, outrage and panic among listeners who believed that it was a news bulletin. The truth is that the story was probably grossly exaggerated for political ends, but four decades after it had been written, the novel remained as powerful as ever. Popular hopes and fears that Mars might be home to intelligent civilizations lasted for nearly a century, despite growing scientific evidence to the contrary.

By the early twentieth century, it was apparent that Mars was not only a very cold place, but also had a very thin atmosphere. Even before the space age, spectra of the planet’s disk were able to demonstrate that the pressure on its surface was low enough that animals were unlikely to have enough air to breathe. We now know that the air on Mars’s surface is even thinner than those early measurements suggested—equivalent to the amount of air at an altitude of 35 km above the Earth’s surface. Nonetheless, even as this evidence grew, many people clung on to the idea that there might be plants on Mars.

Seasonal changes in the brightness of Mars’s surface—which tend to spread from the polar regions towards the equator in the spring—came to be known as the wave of darkening and were widely interpreted as being due to the growth of veg-etation. Unlike the canals, these brightness changes are real and can still be seen today, but we now know that they are the result of seasonal dust storms rather than any biological mechanism. There was also other evidence which seemed to point towards vegetation on Mars. As late as 1964, the Encyclopedia Britannica’s entry for Mars explained that:

Evidence that the maria consist of some kind of organic substance was obtained by Sinton at the opposition of 1956 and 1958. All organic molecules possess strong absorption bands near 3.4 micron, the wavelength of the carbon-hydrogen bond resonance. Measures on the spectra of Mars in this region indicate the probable presence of this band. This evidence, taken together with the observation of seasonal changes of the maria make it extremely probable that vegetation in some form is present on Mars.

Humanity’s sudden and rapid exploration of the solar system during the space race reached Mars in the following year, 1965, when NASA’s Mariner 4 probe became the first spacecraft to fly past it, on the evening of Wednesday July 14. It was a momentous evening—simultaneously one of the space race’s greatest feats and biggest disappointments. The mission’s controllers hoped that it might be the day when mankind would glimpse the first compelling photographic evidence of life on another planet. In reality, of course, that was not to be. Though Mariner 4 returned only 22 images—and they were of unusually poor quality even for the time—that handful of images was sufficient to make clear that Mars’s surface was a desolate cratered lunar-like landscape.

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The Earth’s Twin

One of the reasons why the planets have always fascinated people is the innate human thirst to explore the unknown. But the terrestrial planets are also worlds which we can compare to the Earth in order to understand our own planet better. Geologists and climate scientists have the problem that it’s very difficult for them to carry out experiments, since the processes they study act on such large scales that they cannot be replicated in the laboratory. Instead, they are restricted to observing the phenomena that nature itself presents to them. Before the space age, theorists could only speculate about what set of conditions had allowed the Earth to turn into a habitable environment, because they had never been able to study a planet which wasn’t habitable in any detail. In the 1960s, that suddenly changed.

The question of whether there might be life on Mars may have caught the pub-lic’s imagination in a way that no other astronomical research has been able to emulate since, but Mars has a long history of posing new challenges to each suc-cessive generation of space scientists who study it. As we saw in Chap. 1 , Tycho Brahe and Johannes Kepler were troubled in the first decade of the 1600s by their inability to explain the path that Mars takes across the sky in terms of any circular orbit around the Sun. This eventually led Kepler to conclude that planets orbit the Sun following elliptical rather than strictly circular paths.

Ever since that time, it has been well established that Mars follows an orbit around the Sun which lies close to the Earth’s own orbit, and that as a result that it might be rather similar to our own planet. Once Mariner 4 had revealed that Mars is in fact not very Earth-like, the next question seemed naturally to pose itself: why should Mars and the Earth have such different environments? The picture of Mars as a lifeless world was cemented by the Viking 1 (1976–1982) and Viking 2 (1976–1980) landers, the first spacecraft to successfully land on its surface. Images taken from space had shown that Mars’s surface appeared lifeless when viewed from orbit, but the Vikings went further by showing that there wasn’t even any microscopic life to be found: chemical analysis of Martian soil revealed no evidence of bacteria.

The Changing Climate of Mars

Even though Mars is much less Earth-like than many hoped only a few decades ago, its environment is the closest match to our own to be found among the solar sys-tem’s rocky planets—and in the whole solar system, with the possible exception of Saturn’s icy moon, Titan. Mars’s atmosphere is composed primarily of carbon dioxide—as the Earth’s atmosphere probably was early in its history. As we have seen, however, it is also much thinner than the Earth’s, having around 0.6 % of the pressure. Mars’s surface is generally cooler than the Earth’s, as might be expected given its greater distance from the Sun, but it also shows greater variation

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in temperature. Unlike the Earth, it lacks a thick atmosphere which might act as a blanket to keep it warm through the night and cool in the daytime. Without this thermal insulation, the temperature at Mars’s poles can drop as low as −140 °C, but in the afternoon sun, temperatures at its equator can reach highs of around 35 °C.

The low pressure of Mars’s atmosphere means that water tends to exist only in solid and gaseous forms—as ice or steam—and not as a liquid. Although there is ample evidence that large reserves of ice lie buried in its soil, it is unlikely that any of that water has flowed as a liquid on its surface in the past 4 billion years. Nonetheless, photographs of the Martian landscape returned by orbiting spacecraft reveal extensive networks of channels which appear to have been carved by rivers (see Fig. 7.2 ). Moreover, probes on the planet’s surface have found that Martian rocks are rich in salts, especially sulfates, which are only known to form in the presence of water. Together, these findings seem to present clear evidence that liquid water was commonplace on Mars’s surface in its early history. For this to have been possible, it must have had a much thicker atmosphere and warmer climate in past times.

Fig. 7.2 Mars’s surface is littered with channels which resemble dried-up streams and rivers. The channels shown here are on the fl oor of Lyot Crater, and were photographed by Mars Reconnaissance Orbiter in 2010. Credit : NASA/JPL/University of Arizona

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The causes and effects of global-scale climate change are topical questions among atmospheric scientists who study the Earth’s climate, but they are notori-ously difficult to study because they are governed by a branch of mathematics called chaos theory. The climates of terrestrial planets typically have numerous stable configurations in which they can remain for long periods, before spontane-ously shifting into another configuration. On our own planet, such a shift occurred on a small scale in around 10000 BC , at the end of the last ice age, when global temperatures rose. Shortly after this—and very possibly as a result of it—our human ancestors began to farm the land for the first time.

The Earth underwent a much larger episode of climate change around 66 million years ago which led to the extinction of the dinosaurs. For 80 million years prior to this—the Cretaceous period—the Earth had been much warmer than it is presently, perhaps by as much as 15–20 °C, such that cold-blooded creatures were able to survive at latitudes as far north as 75°N. Although the impact of a large asteroid with the Earth appears to have been one factor in triggering the Earth to become a cooler place, it also appears that it had already been cooling for some time prior to the impact.

The transformation that Mars underwent 4 billion years ago was on a much larger scale still, and remains something of a mystery. If Mars had a thicker atmo-sphere in the past, it seems fair to assume that atmosphere was comprised mostly of carbon dioxide, as it is today. But where did all that carbon dioxide go? The Earth is believed to have had a thick carbon dioxide atmosphere in its early history, which thinned over time as the carbon dioxide dissolved in its oceans and eventu-ally reacted with calcium in the water to form limestone. The same mechanism could very plausibly have acted on Mars, except that no evidence of carbon-bearing rocks has ever been found on its surface. When, and if, they are found, they are likely to tell us much more about how thick Mars’s atmosphere was in past times, but for the moment rovers can do little more than play hide-and-seek on the Martian surface looking for them.

Magnetic Field

One clue as to what may have driven this change in the Martian environment is the planet’s magnetic field. Today, Mars does not have a strong global magnetic field like the Earth’s, but there is evidence that once upon a time it did. Some of the rocks on Mars’s surface have their own weak magnetic fields, which is usually indicative that they were magnetized by a strong planet-wide field when they formed. The Earth’s magnetic field shapes the climate of our planet, because it plays a crucial role in deflecting ionizing radiation from the Sun away from the Earth. The Sun is continu-ally producing streams of charged particles called the solar wind, but these are mostly deflected by the Earth’s magnetic field before they can reach the Earth’s surface.

Many complex molecules are unable to form in Mars’s atmosphere without being broken apart, since it lacks a magnetic field to protect it from charged

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particles produced by the Sun. However, if Mars had a magnetic field similar to the Earth’s in its early history, the chemical make-up of its surface and atmosphere would have been very different from that which we see today.

The disappearance of Mars’s magnetic field was most likely triggered by the planet’s gradual cooling after its initial formation. As we saw in the previous chap-ter, a planet must have an electrically conductive fluid beneath its surface in order to have a strong magnetic field. In the Earth’s core, this fluid is molten iron, which remains hot enough to exist as a liquid because the Earth is still cooling. Mars is a smaller planet, and so its interior has cooled much more quickly. Close to its sur-face, this advanced state of cooling is apparent from the lack of much recent volca-nic activity. Some of Mars’s volcanoes are probably still active, but to a much lesser degree than those on the Earth. Beneath its surface, Mars is almost certain rather cooler than the Earth, and has much less convection, making it difficult for its core to sustain a magnetic field.

The Path of Mars Across the Night Sky

Why did Mars cause Tycho Brahe and Johannes Kepler such trouble? They were able to explain the movement of each of the other planets across the night sky easily in terms of circular orbits around the Sun, but Mars’s motion seemed more compli-cated. Figure 7.3 shows a plan view of the solar system in which the orbits of Mars and the Earth are drawn to scale, and it makes apparent how difficult the problem was. On the one hand, Mars has the second most elliptical orbit in the solar system (see Chap. 2 ). But the oval shape of its orbit is made all the more apparent by the fact that it lies close to the Earth, which itself follows a very nearly circular path around the Sun. Specifically, the elliptical shape of Mars’s orbit results in a much larger relative change in its distance from the Earth’s orbit than it does in its relative distance from the Sun.

To visualize how Mars’s orbital motion appears from the Earth, it is useful to follow the example of the previous chapter. Rather than drawing a diagram of its path relative to the center of the solar system, as is done in Fig. 7.3 , its path can be drawn relative to the moving Earth from which we observe it. When we did this in the previous chapter for Jupiter and Saturn, their apparent motions relative to the Earth were comparatively simple. The outer gas giants turn in their large orbits on decade-long timescales, meanwhile the Earth moves in much smaller circles around the Sun each year. The resulting relative motion was a large number of small annual circular deviations from a much larger circular path.

The motion of Mars relative to the Earth is much more complicated, as is shown in Fig. 7.4 . In comparison to the orbits of the gas giants, Mars’s orbit is not much larger than the Earth’s, and it doesn’t take much longer than a year to traverse it. To be precise, Mars orbits the Sun once every 1.9 years, at an average distance of 1.5 AU. This means that its motion relative to the Earth does not straightforwardly separate into short-term wiggles arising from the Earth’s motion, superimposed on

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a much larger and slower-moving circular motion. Instead, the two contributions are of similar sizes.

The distance of Mars from the Earth varies dramatically. When the two planets are next to one another in their orbits—the moment when Mars appears at opposi-tion, opposite to the Sun in the sky—their separation can be less than 0.4 AU. When the two planets are opposite one another in the solar system—the moment when Mars appears at solar conjunction—their separation can exceed 1.6 AU. Correspondingly, the size of Mars’s disk changes dramatically, between being a small and distant speck measuring no more than 6 arcseconds across at solar con-junction, to measuring up to four times that size at opposition.

As Mars passes opposition, its distance from the Earth changes most rapidly. As the Earth overtakes it, traveling faster in its inside lane in the solar system, the two planets are alongside each other for only a couple of weeks. As is shown in Fig. 7.3 , the Earth only needs to be a few degrees ahead of or behind Mars in its orbit for the separation of the two planets to be significantly larger than at the moment of opposition. Figure 7.4 shows that Mars suddenly swoops close to the

Fig. 7.3 The orbits of Mars and the Earth, projected onto the plane of the ecliptic and drawn to scale. See the text for more information

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Earth—inwards towards the center of the diagram—before receding back to its usual distance just as quickly.

Since the apparent size of Mars’s disk varies with its distance from the Earth, this means that it appears to grow in size very rapidly in the days preceding opposi-tion—as it nears the Earth—and then it shrinks just as quickly in the following days. Likewise, it also brightens dramatically for this period of only a few weeks around each opposition. Whereas it makes little difference whether distant planets like Jupiter and Saturn are observed a few weeks before or after an opposition, rather than on the exact day of their closest approach, the same is not true for Mars. Opportunities to get a close up view of the red planet pass quickly.

Returning to Tycho Brahe’s observations of Mars, we can now understand better why Kepler had such difficulty explaining Mars’s path across the sky in terms of a circular orbit around the Sun. The most evident asymmetry in Fig. 7.4 is that Mars’s close approaches to the Earth do not always bring it to exactly the same distance from us. When an opposition occurs at any given time of year, Mars—by the defini-tion of an opposition—must lie immediately alongside the part of the Earth’s orbit where our planet is to be found at that time of year. Whenever Mars comes to an

Fig. 7.4 The path of Mars relative to the Earth (2014–2030). The dates and distances of its closest approaches to the Earth are indicated. See the text for more information

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opposition in late August, for example, it is always at roughly the same point along its orbit, next to where the Earth is to be found in late August. It so happens that this point is very close to the position where Mars makes its closest approach to the Sun—its perihelion. When Mars comes to opposition in August, it comes closer to the Earth than is possible at any other time, briefly passing within a distance of 0.4 AU of us.

This is the significance of the radial distances between the orbits of the Earth and Mars marked onto Fig. 7.3 . These show the distance that separates the Earth and Mars when the latter is at opposition at any given time of year. If Mars were in a nearly circular orbit—as is the case for all of the outer gas giants—it would pass within roughly the same distance of the Earth at every opposition. That not being the case, its oppositions give much closer views of its surface, and it consequently it appears considerably brighter, when it comes to opposition in August as com-pared to February.

The result is a rather curious asymmetry, which gives southern hemisphere observers the best views of Mars. As we saw in Chap. 6 , any planet passes very close to the point exactly opposite to the Sun in the sky at opposition. In the sum-mer, the Sun is in the northern sky, and so it follows that any planet at opposition must lie in the southern sky. Since the best oppositions of Mars occur in August, Mars is inevitably in the southern sky when they take place. Northern hemisphere observers are left struggling to overcome poor atmospheric conditions low down on their southern horizons. This is so much of a problem, that northern observers usu-ally get better views of Mars when it comes to opposition in September or October rather than August. Even though it presents a slightly smaller disk in the fall, this is more than compensated for by its more northerly declination and higher altitude in the northern sky.

Even from Tycho Brahe’s naked-eye observations, it was quite apparent that Mars didn’t move uniformly from one opposition to the next, and it is one of the curious what - ifs of the history of science to wonder how the historical development of astronomy would have been different if our near neighbor in the solar system did not have such an elliptical orbit. If all of Mars’s oppositions occurred at a common distance from the Earth, Kepler would have had no difficulty at all in fitting a cir-cular orbit to Tycho’s observations, and the Greek idea that the planets moved in circles around the Sun would have remained unchallenged. When Newton came to work on his laws of gravity, it was the fact that they reproduced and explained the elliptical orbits that Kepler had found which most convinced him that he was on the right track.

Table 7.1 lists all of the oppositions of Mars between 2000 and 2200. The closest approach distance of Mars from the Earth on each of these occasions depends only on the time of year at which the opposition occurs, and is plotted in Fig. 7.5 .

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Table 7.1 The apparitions of Mars, 2000–2200

Date Declination Diameter/ arcseconds

2001 June 13 26S 20.6 2003 August 28 15S 25.1 2005 November 7 15N 19.9 2007 December 24 26N 15.8 2010 January 29 22N 14.1 2012 March 3 10N 13.9 2014 April 8 5S 15.1 2016 May 22 21S 18.4 2018 July 27 25S 24.3 2020 October 13 5N 22.3 2022 December 8 24N 17 2025 January 16 25N 14.5 2027 February 19 15N 13.8 2029 March 25 1N 14.4 2031 May 4 15S 16.8 2033 June 28 27S 21.9 2035 September 15 8S 24.5 2037 November 19 20N 18.7 2040 January 2 26N 15.3 2042 February 6 20N 13.9 2044 March 11 7N 14 2046 April 17 8S 15.6 2048 June 3 24S 19.5 2050 August 14 20S 25 2052 October 28 11N 21 2054 December 17 26N 16.3 2057 January 24 23N 14.3 2059 February 27 12N 13.8 2061 April 2 2S 14.8 2063 May 14 18S 17.6 2065 July 13 27S 23.3 2067 October 2 0S 23.4 2069 November 30 23N 17.7 2072 January 11 26N 14.8 2074 February 14 17N 13.8 2076 March 19 3N 14.2 2078 April 27 12S 16.2 2080 June 16 26S 20.8 2082 September 1 14S 25.1 2084 November 10 16N 19.7 2086 December 27 26N 15.7 2089 January 31 21N 14.1 2091 March 6 9N 13.9 2093 April 11 5S 15.2

(continued)

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Date Declination Diameter/ arcseconds

2095 May 26 22S 18.6 2097 July 31 24S 24.5 2099 October 18 6N 22.1 2101 December 11 25N 16.9 2104 January 20 24N 14.5 2106 February 22 14N 13.8 2108 March 28 0N 14.5 2110 May 7 16S 16.9 2112 July 2 27S 22.2 2114 September 20 6S 24.4 2116 Nov 23 20N 18.5 2119 January 5 26N 15.2 2121 February 9 19N 13.9 2123 March 15 6N 14.1 2125 April 21 9S 15.7 2127 June 8 25S 19.7 2129 August 19 19S 25.1 2131 November 2 12N 20.7 2133 December 21 26N 16.2 2136 January 28 23N 14.2 2138 March 2 11N 13.8 2140 April 5 3S 14.8 2142 May 18 19S 17.8 2144 July 18 27S 23.6 2146 October 7 1N 23.2 2148 December 3 23N 17.6 2151 January 14 25N 14.8 2153 February 17 16N 13.8 2155 March 23 3N 14.3 2157 April 30 13S 16.3 2159 June 22 27S 21 2161 September 6 12S 25 2163 November 15 17N 19.5 2165 December 30 26N 15.6 2168 February 4 21N 14 2170 March 9 8N 13.9 2172 April 14 6S 15.3 2174 May 30 23S 18.8 2176 August 5 23S 24.6 2178 October 22 8N 21.8 2180 December 14 25N 16.7 2183 January 22 24N 14.4

(continued)

Table 7.1 (continued)

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Date Declination Diameter/ arcseconds

2185 February 24 14N 13.8 2187 March 31 0S 14.5 2189 May 10 17S 17.1 2191 July 6 27S 22.5 2193 September 24 4S 24.2 2195 November 26 21N 18.4 2198 January 7 26N 15.1

Source : DE405

Table 7.1 (continued)

Fig. 7.5 The distance to Mars at each of its apparitions between 2000 and 2160

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The Rotation of Mars

Mars rotates on its axis once every 24 h and 37 min (sidereal rotation period), giving rise to days which are very similar in length to those we experience on Earth. The average length of a Martian day—called a sol—is around 24 h and 39 min; see Chap. 4 for an explanation of why it is 2 min longer than Mars’s rotation period.

The similarity of the length of Martian days to our own 24-h days is a curious similarity between the two planets, but it is also rather infuriating for amateur astronomers who want to observe as much of its surface as possible. Anyone who sets up their telescope at a similar time each night to try to observe the red planet will find that just as our own planet has completed almost exactly one revolution since the previous day, so too has Mars. For example, if an observer only looks at Mars at 9 p.m. each day, the side of Mars which is directed towards the Earth each night will lag behind its position the previous night by only half an hour. To map out the whole of Mars’s surface, the observer has to wait up to 5.5 weeks for a full cycle of Martian longitudes to have been visible at 9 p.m., and for its globe to have rotated all the way around to where it started.

As we have already seen, though, the closeness of Mars’s orbit to the Earth’s means that it very rapidly grows in size and brightness in the weeks before it passes opposition. The window of time in which detailed observations of its surface can be made lasts for only a few weeks at each opposition. Rather than waiting several weeks for Mars to rotate to show particular features at a sociable time in the eve-ning, there is sometimes little option but to stay up all night to maximize the range of Martian longitudes which can be mapped out in a single night when Mars is at its largest.

In recent years, the Internet has made it easier than ever before for amateur groups to work together in international collaborations, and these are especially useful when trying to map out Mars’s surface. In the United States, for example, 9 p.m. falls up to 8 h later than 9 p.m. in Europe, and in that time Mars completes more than a quarter of a revolution. Rather than having one individual observer who stays up all night in one particular geographic location waiting for Mars to rotate, the same coverage of Mars’s surface can be achieved by having a network of observers in different time zones around the Earth, all of whom take images when it is evening in their part of the world. The ease with which images can be sent around the world, combined with the degree to which observations can now be made automatically using computerized telescopes and cameras, now makes it much easier for amateurs to monitor the sky 24-h a day.

The Surface of Mars

The red color of Mars’s surface stems from the presence of a very familiar chemical compound—iron oxide, better known as rust. Like the Earth, Mars is rich in iron, but whereas much of the Earth’s iron has sunk to its core, Mars’s weaker

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gravitational field has led to less pronounced vertical stratification. The precise chemical processes by which this iron has rusted are still debated: it may have occurred when Mars was warmer and wetter in the past, or it may be the result of more complex chemical processes involving perchlorate salts in the Martian soil.

Seen telescopically, Mars’s surface is differentiated into some regions which are bright red, and others which are a duller brown. These differences in color reflect the presence of different materials. Where the surface is bright red, it is typically composed of very fine grains of dust, but where it is darker there are larger rocks. Although the colors reflect different materials rather than different elevations, it is generally the case that the darker rockier parts of Mars’s surface are higher than the dusty deserts around them.

Even crude observations through a small telescope make clear that the planet’s northern and southern hemispheres have very different appearances. The northern hemisphere is brighter as its landscape is dominated by vast dusty plains, while the southern hemisphere is a much duller color since it is rockier and more heavily cratered. This difference in terrain is also reflected in the altitudes of the two hemi-spheres: the plains of the planet’s northern third lie at an average altitude of several kilometers below the more rugged terrain of its southern two-thirds. How this large- scale dichotomy came about is still debated, and it is unclear whether it might be the result of a very large impact in Mars’s northern hemisphere distant past, or some internal geological process.

Many of the most visually interesting features lie around the boundary between the two types of terrain. The easiest feature to spot is Syrtis Major—a large dark- colored protrusion of rocky terrain into the northern hemisphere. Although the dark color of the basalt rocks around it makes it stand out when seen through a small telescope, it is not one of Mars’s largest volcanoes and is gently sloped rather than mountainous. By contrast, the Tharsis region on the opposite side of Mars’s equator is the largest volcanic structure in the solar system. It too appears as a protrusion of Mars’s dull southern rocky terrain into the northern hemisphere (see Fig. 7.6 ), but as its rocks are paler in color, they are much rather harder to spot visually. The size of these volcanic structures is so great that their weight pushing down on the rocks beneath them has deformed the surface around them. An extensive system of can-yons runs eastward from Tharsis, along a full quarter of the planet’s equator. In places these measure up to 300 km wide and 10 km deep, and it quite likely that these are cracks which have opened due to the weight of the Tharsis Montes.

Just like the Moon, Mars’s surface is also strewn with impact craters, although it is sufficiently far away that all but the largest of these are not visible from Earth. One exception is the Hellas basin, which appears as a bright circle in the planet’s southern hemisphere. Measuring 1,800 km across, this is the largest impact crater on the planet.

Many of the features on Mars’s surface can be rather tricky to observe, not just because Mars usually presents such a small disk, but also because the color con-trasts between its different kinds of rock can be extremely subtle. The result is that Mars can appear a rather bland and uniform red-brown color at a first glance. Color filters can greatly help in making structure more readily apparent, however. Since

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most of the rocks and dust grains on Mars’s surface are different shades of red, it is orange and red filters that are especially useful to maximize the contrast between them. Mars’s polar caps—made of carbon dioxide ice which forms like frost in the extreme cold of winter at its poles—appear much whiter than the bare rocks visible at equatorial latitudes, and this contrast is emphasized when viewed through a magenta or blue filter. Finally, yellow filters can be useful when Martian dust becomes airborne, to distinguish these dust clouds from the surface beneath them.

The Moons of Mars

Mars has two moons, Phobos and Deimos (see Table 7.2 ), though both are so small that they are incredibly difficult to observe and remained undiscovered until 1877. Their small sizes mean that they appear very faint from the Earth—shining at

Fig. 7.6 An altitude map of the Tharsis region of Mars, made using the laser altimeter aboard Mars Global Surveyor (MGS). White regions are at the highest altitude, and blue regions are at the lowest altitudes. In the center of Tharsis lie three of the largest volcanoes in the solar system: Arsia Mons, Pavonis Mons, and Ascraeus Mons, known collectively as the Tharsis Montes. To their northwest lies Olympus Mons, the tallest volcano on the planet. Credit : NASA/Mars Global Surveyor (MGS)

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around mag 11.3 and 12.4 respectively. Moreover, the fact that they orbit Mars at distances of only 2.8 and 6.9 Mars radii respectively mean that they are extremely difficult to separate from the glare of their parent planet. Even today, they remain beyond the reach of any but the most skilled amateur observers.

Both objects are so small that their gravitational fields are too weak to have made them spherical, and so like most asteroids they retain an irregular potato-like shape. The similarity between the two small moons and asteroids doesn’t end there: their compositions are also rather similar to that of many asteroids. Since Mars lies close to the solar system’s asteroid belt—which fills the space between the orbits of Mars and Jupiter—it is very plausible that Phobos and Deimos may not have formed at the same time as Mars, but may instead once have been asteroids that became captured into Mars’s gravitational field.

Seen from Mars’s surface, Deimos moves rather slowly across the sky. It circles its parent planet once every 30 h, but Mars itself rotates once every 24.6 h in the same direction. The orbit of Deimos happens to be very nearly aligned with Mars’s equator, and so Mars’s surface and the moon above turn in almost exact synchrony. Like the stars of the Martian sky, Deimos rises in the east and sets in the west, but takes an average of more than 5 Martian days to get from one horizon to the other, while the stars turn much more quickly behind it.

Phobos is in a much lower orbit and circles Mars once every 7.7 h. As a result, it moves across the Martian sky much more quickly. Just like the International Space Station (ISS) around the Earth, Phobos circles its parent planet much more quickly than the planet itself rotates, and so it appears from the Martian surface to rise in the west and set in the east. In the same way that the ISS completes many orbits around the Earth each day, Phobos completes three circuits around Mars in each Martian day, and can rise and set multiple times each day.

Both Phobos and Deimos have been in orbit around Mars for long enough that they have become tidally locked to it (see Chap. 5 ). In other words, the period of time it takes Phobos and Deimos to spin around their rotation axes exactly matches the period of time it takes them to complete a single orbit around their parent planet. Just as the Moon has a near side and a far side, because it turns about its polar axis as it orbits around the Earth to always keep the same face turned towards us, Phobos and Deimos also have near sides and far sides.

As we saw in Chap. 5 , tidal locking comes about because of the energy that is expended in forming tides like the tides of the Earth’s oceans. This works two

Table 7.2 The moons of Mars

Name Diameter (km)

Mass (kg)

Semi-major axis (km)

Orbital period (h)

Phobos 22.2 10.8 9,377 7.66 Deimos 12.6 2 23,460 30.35

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ways: the Moon generates tides on the Earth, but the Earth also generates tides in the Moon’s rocky crust. The Moon always keeps the same face turned towards the Earth, and this means that little energy is now dissipated through tidal stresses in its crust. But the Earth does not always keep the same face turned towards the Moon: looking back at the Earth from the Moon, it does not always show the same face. To do so, it would need to rotate on its axis once a month rather than once every 24 h. The result is that the Earth still has daily tides.

As energy is dissipated moving the Earth’s oceans up and down every 12 h, the Earth’s rotation is gradually slowing down, while at the same time the Moon is gradually drifting away from us because the Earth is slowly transferring some of its rotational energy to the Moon. Eventually the Earth’s ocean tides might be expected to cease, and the Earth will rotate on its axis once every month rather than once every day, although in practice the Sun will reach the end of its life long before that has a chance to happen.

The same process is at work on Mars’s moons. Deimos takes a little longer than a Martian day to complete each circuit around its parent planet, just as our own Moon takes longer than an Earth day to circle around the Earth. This means that the direction of energy transfer between Mars and Deimos is in the same direction that we are familiar with. As is happening to our own Moon, rotational energy is flow-ing from Mars to its moon and Deimos is gradually receding from it.

The situation is different for Phobos, however. Being in a much lower orbit and circling Mars so quickly, the flow of energy works in the opposite direction. If Mars were to always present the same face to Phobos, it would need to rotate very much more quickly than it presently does, and it would need to increase its rotational energy. Instead of drifting outwards, Phobos is draining its orbital energy into mak-ing Mars rotate more quickly, and over time it is spiraling inward as a result.

Already, Phobos is close to Mars’s Roche limit (see Chap. 6 )—the radius within which the tides generated on Phobos will be stronger than the gravitational binding force which holds the tiny moon together. As Phobos gets closer to Mars, these forces will become stronger and will eventually rip the moon apart, probably in around 30–50 million years’ time. Though this is far from imminent on human timescales, it is very imminent in comparison to the age of the solar system—in fact, rather surprisingly so. Why after the solar system has been around for 4.6 bil-lion years, should we find ourselves observing Phobos just a few tens of millions of years before it faces inevitable destruction at the hands of Mars’s gravitational field? If Phobos has been keeping Mars company for billions of years, it would seem an incredible coincidence that we should have discovered it such a short time before its demise.

A more likely explanation, then, is that Phobos and Deimos are relatively recent arrivals in orbit around Mars. There may have been a long succession of asteroids which in the past have found themselves captured into orbit around Mars, and which have ultimately been destroyed a few tens of millions of years later. The orbit of Phobos presents further evidence on top of its composition and shape that until recently it may have been an asteroid rather than the moon of a planet.

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Mars in the Space Age

It has been known since the time of Kepler that Mars neighbors the Earth in the solar system. This has not only raised the prospect that it might have a rather Earth- like climate, but has also suggested that it might be one of the easiest planets to travel to.

Plans to make that journey shifted from the realm of science fiction into a real-istic engineering prospect in the mid-1950s, shortly before the launch of Sputnik 1 (1957) and the subsequent foundation of NASA (1958). One of the best known engineers to turn his mind to the problem was Wernher von Braun, a leading engi-neer on the German V - 2 rocket program who later worked as one of the pioneers of the US space program. His plans were partly intended as fiction, but they were also worked out in great detail, to the point where he was describing exactly what would be needed to fly a crew of 70 people to Mars aboard a fleet of ten spacecraft.

In stark contrast to the delays that have tended to dog most large recent space missions, the early years of the space race were a time when projects tended to be brought forward. Von Braun can hardly have imagined that spacecraft would visit Mars within a decade, though the first missions were also to be on a much smaller scale than his grand designs.

By 1958, NASA felt that a mission to Mars might be possible by 1967, but with the Soviet space program on its heels, that did not seem soon enough. The first suc-cessful American interplanetary space mission came a mere 4 years later, when Mariner 2 flew past Venus. Venus is the closest planet to the Earth, and Mars the second closest, and so the next target for the Mariner program—which encom-passed all of NASA’s interplanetary missions at this time—was clear. By the time Mariner 3 made it to the launch pad in 1964, the Soviets had already made one failed attempted at a mission to Mars, Mars 1 , and had another ready to go.

The story of the first mission to Mars is a rather incredible one. Mariner 3 itself failed soon after launch, leaving NASA with a tricky problem. As we have seen, Mars’s closeness to the Earth in the solar system means that it orbits the Earth at a very similar speed to the Earth, and its synodic period is the longest of any of the planets at over 2 years. Flying spacecraft to Mars is only feasible within a narrow window of time each time it makes a close approach to the Earth, around the time of each opposition. If this window is missed, the next opportunity to fly to Mars doesn’t come around until 2 years later. Anxious to avoid waiting until 1967, and with only 3 weeks remaining until the end of the 1965 launch window the Mariner program’s engineers set about trying to put Mariner 4 on the launch pad within days. Having diagnosed the problems that had caused Mariner 3 to fail—a problem with the housing which protected the spacecraft during its launch and ascent through the Earth’s atmosphere—a new housing was designed, built and tested in time for Mariner 4 to fly a mere 23 days later, on 1964 November 28.

Once launched, further problems with the spacecraft’s design emerged. To thrust in the right direction to find its way to Mars, it needed to know how it was orien-tated in space. A small telescope on the side of the spacecraft was designed to

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automatically search for the bright star Canopus to provide a fixed reference direction in space, but was crude and tended to repeatedly lock onto the wrong reference star, leading the spacecraft to thrust in entirely the wrong direction to get to Mars. It was only as a result of interventions by ground controllers that the space-craft was repeatedly put back on the right track.

As we have already seen, the 22 grainy images that Mariner 4 returned when it eventually reached Mars, revealing the barren and cratered lunar-like landscape with which we are now very familiar, came as a profound disappointment in com-parison to what many had hoped to see. The view of Mars as a lifeless world was cemented by the Viking 1 (operational 1976–1982) and Viking 2 (operational 1976–1980) landing missions, which further ruled out the presence of any micro-scopic lifeforms in the Martian soil.

Up until 1965, the scientific reasons why Mars seemed an interesting planet to explore had remained largely unchanged for more than a century. But within 15 years, the Mariner and Viking programs had entirely rewritten the science case for sending spacecraft to Mars. It had become apparent that searching for life there was almost certainly futile. Instead, the question on everybody’s minds was how Mars had become such a desolate world. To answer that, they needed to better understand its geology and climate.

Technologically, scientists needed more mobile landing craft which were able to sample much wider ranges of environments. However sophisticated the instruments aboard the Vikings had been, they had only been able to sample the one single environment in which they had happened to land. As early as 1979, NASA had drawn up a list of ways in which landing craft could plausibly move around the surface, ranging from wheeled rovers to aircraft and even inflatable vehicles which could roll around the surface.

However, all of these options involved transporting complex machines with many moving parts to another planet, and as a result were both highly risky and costly. At a time when large projects such as the space shuttle were consuming much of NASA’s budget, such a high cost seemed difficult to justify. But it was not cost considerations alone that meant that the Viking missions were the last success-ful missions to Mars for nearly 20 years, until the Sojourner rover touched down on its surface in 1996. Another challenge was the engineering task of designing a rover with a substantial degree of autonomy using the computers available at the time.

Any mission to Mars faces the problem that communications between the Earth and Mars are subject to lengthy delays. Even travelling at the speed of light, radio waves take 8 min to reach the Earth from the Sun, and a further 4 min to travel from the Earth to Mars. When Mars is at its closest to the Earth, communications between the two planets are delayed by a round-trip time of 8 min, and when Mars it at solar conjunction, this delay is extended to nearly 40 min. When the first manned missions fly to Mars, this will mean that mission controllers will need to work out how to communicate effectively with the astronauts once the radio delay becomes too long for direct voice communication to be effective.

But the problem for robotic missions to Mars is in many ways even greater still. Any rover that needs a driver on Earth to control its every movement can only drive

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prohibitively slowly. This was, in fact, how the Sojourner rover was controlled, but its movement was restricted to driving in short straight lines, after which it sent new images of its surroundings back to mission controller who could then consider its next move. As a result, Sojourner never ventured more than 10 m from the spot where it landed. More recent rovers—the Mars Exploration Rovers (MER) Spirit and Opportunity, and the Mars Science Laboratory Curiosity—have been able to venture further only by having a much more autonomous ability to drive them-selves. They are able to transmit approximate maps of their surroundings to mission controllers, who can plan a series of maneuvers which are then carefully followed by the rovers’ on-board computers. It was only in the 1990s, however, that building a robot with such independence first appeared a realistic prospect.

The biggest challenge for the next generation of landing craft on Mars will be to explore what lies beneath the planet’s surface. Given what we now know about the Mars’s environment, it is no longer very surprising that its surface is sterile. Whereas the Earth has a thick atmosphere with an ozone layer in its stratosphere which absorbs much of the Sun’s ultraviolet light, Mars’s top soil is fully exposed to the Sun’s ultraviolet radiation, which tends to break apart complex molecules. Furthermore, Mars’s lack of a magnetic field means that its top soil is also exposed to the ionizing particles that stream out from the Sun through the solar system—the solar wind—which are also prone to damaging complex molecules. Material beneath Mars’s surface, however, is protected from this harsh environment and may have much greater chemical complexity and diversity.

Molecules such as DNA would need to be buried at depths of between a few centimeters and a few meters to survive for long periods, and so there remains the faint possibility that even if there is no life on the planet’s surface, bacteria might thrive beneath the ground. Even if no life is found, the chemical compounds pre-served in the depths of the Martian soil are likely to give us many clues as to the planet’s history. The challenge which must first be overcome, though, is for space scientists is to design a drilling rig that is light enough to be transported to Mars, and yet which is also large enough to excavate to scientifically-interesting depths.

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The Inner Planets

The solar system’s two innermost planets, Mercury and Venus, are inhospitable worlds. As we have seen, Mars’s frigid surface and thin atmosphere provide the closest analog to an Earth-like climate among the solar system’s other planets. By contrast, however, Mercury and Venus demonstrate how even rocky planets, which on paper may have many similarities to the Earth, can evolve into very harsh and ultimately un-Earth-like environments.

From our vantage point, further out in the solar system and looking in towards the Sun to see them, Mercury and Venus always appear close to the Sun in the sky, and as a result they can be rather challenging to observe. Mercury is never more than 28° from the Sun, and Venus never more than 47° from it. Both can be seen only around dawn and dusk, setting and rising no more than a few hours before or after the Sun. At its best, Mercury may be visible for around 2 h after sunset or before sunrise, and Venus for around 4 h. Yet, despite the difficulty of observing them, these two planets can help us to understand much about the unique set of conditions which have made the Earth a habitable place.

Venus as a Planet

For much of the time when it is readily observable, Venus is the third brightest object in the sky after the Sun and Moon. Reaching a peak brightness of mag −4.6, it is considerably brighter than the night sky’s brightest star, Sirius (mag −1.5), and on a moonless night at a dark site it is just about possible to photograph objects casting shadows by Venus’s light. The sight of Venus—often called the morning or evening star—is so remarkable that in modern times its appearance in the evening sky has often been linked with spates of reported UFO sightings.

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Venus’s brightness is due to a combination of three factors. Firstly, it is very nearby: it is the closest planet to the Earth, passing within 0.28 AU of us at closest approach. Secondly, it is a large body—the second largest of the terrestrial planets after the Earth, measuring 95 % of an Earth-width across and having 82 % of the mass of the Earth. Finally, its surface is permanently enveloped with thick layers of highly reflective cloud, which return the majority of the sunlight which it receives back to space rather than absorbing it.

This reflective cloud not only makes Venus a very bright object, but also means that it appears as an entirely featureless disk when viewed from the Earth. Until the space age, astronomers had no maps of Venus’s surface and little idea of what envi-ronment might lie beneath its clouds. It is only within the past decade that ground- based amateur astronomers have first begun to be able to take images of the surface beneath those clouds, using CCD cameras which are sensitive to infrared light and filters that are tuned to specific near-infrared wavebands in which Venus’s clouds are at least partially translucent. The resulting images are notable in that astrono-mers have been battling for hundreds of years to capture images of Venus’s surface through ground-based telescopes, and these are the first such images that have ever been taken, but they are by no means sharp. Perhaps the strongest endorsement that can be made of them is that they show some resemblance to large-scale features which have been mapped out by spacecraft.

The best maps of Venus’s surface that we have were made using radar aboard spacecraft, most notably Magellan (1990–1994), which achieved a resolution of around 100 m. Radar mapping works by directing pulses of radio waves from an orbiting spacecraft towards the planet’s surface. These pass freely through Venus’s atmosphere and are then reflected by its surface, allowing the spacecraft to piece together a map of the landscape below by timing precisely how long it takes these reflected waves to return to it.

The maps returned by Magellan reveal extensive flat volcanic planes, with rela-tively few craters and little sign of any very recent volcanic eruptions. The lack of small craters is most likely the result of Venus’s very thick atmosphere, which means that most small meteors burn up long before they reach the surface. The lack of larger craters, however, cannot be explained away in the same way, since the large impactors which might have generated them would have been easily able to penetrate even a thick atmosphere such as Venus’s. It instead implies that Venus’s surface is relatively young—perhaps only 300–500 million year old, as compared to an age of 4.5 billion years since the solar system’s planets formed. This, as we shall see, is at odds with the lack of any evidence of recent volcanic eruptions, as it implies that the entire surface of the planet was flooded with fresh lava flows rela-tively recently, to wipe away the evidence of any earlier cratering events.

The Environment of Venus

The flat and somewhat featureless world that Venus’s thick cloud layers conceal is a remarkably harsh and inhospitable world (Fig. 8.1 ). At 480 °C, the planet’s

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surface is hot enough that it glows visibly red–brown hot at night, and that many metals such as lead would melt and form liquid lakes were they present. Its atmo-sphere is over 90 times thicker than that of the Earth, making the pressure on Venus’s surface roughly the same as that found a kilometer beneath the surface of the Earth’s oceans—depths to which only the world’s most robust submersible vehicles can dive. Looking up, a hypothetical observer standing on Venus’s surface would see a haze of pale lemon-yellow clouds, composed not of water vapor but of sulfuric acid released by past eruptions of the planet’s volcanoes. At times, this yellow haze even forms into concentrated sulfuric acid rain droplets in the planet’s upper atmosphere, though the heat of its surface means that they invariably evapo-rate long before they reach the ground.

Making calculations of how much energy Venus’s surface receives from the Sun, however, it is easy to form the impression that Venus might be a rather Earth-like place. Not only is Venus similar to the Earth in size and mass, but its relative closeness to the Sun does not greatly affect the amount of heat its surface receives from the Sun. Even though it orbits a little closer to the Sun than us, at 72 % of the distance, this only means that its surface receives three times as much solar radiation

Fig. 8.1 Venus, as seen by the Galileo spacecraft. Credit : NASA/JPL 1996

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as the Earth. Moreover, as we have already seen, the clouds which permanently envelop its surface reflect much of this sunlight back to space. Precise measure-ments of its brightness reveal that its clouds typically reflect 90 % of the sunlight that falls on them back to space. As a result, even though Venus is nearer to the Sun than the Earth, the permanently cloudy weather it endures means that its surface receives less energy from the Sun than the Earth’s surface does. On the basis of this, it might seem likely that Venus would be a world rather like the Earth, but with grayer skies and a cooler climate. Indeed, before the surprises that the space age brought, this was a widely accepted theory of what Venus’s surface would be like, and the fact that it turned out to be so far from the truth makes it interesting to ask why Venus has instead come to be such an extreme world.

The incredible heat of Venus’s surface has little to do with its relative proximity to the Sun, and is instead the result of its dense atmosphere, which is comprised mostly of carbon dioxide. In recent years, the debate about the hazards of climate change on Earth has brought to common knowledge the fact that increased concen-trations of carbon dioxide in a planet’s atmosphere tend to increase its long-term average temperature, as a result of the greenhouse effect. This comes about because carbon dioxide acts like a blanket, increasing the ability of a planet to retain the heat that it receives from the Sun.

Carbon dioxide molecules—and those of other greenhouse gases including methane and water vapor—are able to achieve this blanketing effect because they are transparent to incoming sunlight in the visible part of the electromagnetic spec-trum, but are simultaneously opaque to any outbound infrared radiation which tries to escape from the planet’s surface. If a planet receives energy from the Sun at a constant rate, but its ability to radiate heat back to space becomes less efficient, its temperature must rise until a new balance is reached between energy input and energy output. While the greenhouse effect has been known to science since the nineteenth century, it was only when the first spacecraft flew past Venus in the early 1960s and detected the incredible heat of the surface beneath them that it was appreciated quite how extreme the effect could become.

Since those first observations were made by the Mariner 2 spacecraft in 1962, a wealth of data has been returned by over 20 spacecraft which have flown past or entered into orbit around Venus, allowing much to be learnt about how Venus has come to be such a different place from the Earth. As the nearest planet to the Earth, Venus has always been a particularly inviting target within easy reach for interplan-etary space missions, and this was especially so in the early years of the space age, when many of the challenges of navigating the solar system were being confronted for the first time.

A remarkable amount was achieved within only two decades when the space race was at its height. Not only did spacecraft fly past and enter into orbit around Venus, but they also landed on its surface and took pictures of the environment around them. After NASA’s Mariner 2 (1962) had beaten the Soviets to the prize of launching the first spacecraft to return data while flying past another planet, there was perhaps the added incentive for the Soviets of wanting to trump an American fly-past with something greater.

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That trump card came for the Soviets in 1967, when Venera 4 became the first probe to return temperature and pressure measurements from within Venus’s atmo-sphere, though it failed before it reached the surface. There followed an exception-ally successful series of successors, which in 1970 returned the first data from Venus’s surface (Venera 7), in 1975 returned the first black-and-white images of Venus’s surface (Venera 9), and in 1981 returned the first color images of its surface (Venera 13).

The technical challenges of operating spacecraft in the harsh environment of Venus’s atmosphere are considerable. To keep the electronics of the Venera probes operating for even a few minutes on Venus’s surface they needed to be shielded from both the temperature and pressure of the environment around them. The cir-cuitry had to be housed in a spherical pressure vessel, which had been pre-cooled using a stream of rapidly-expanding gas shortly before its entry into Venus’s atmo-sphere. Once within the atmosphere, some of the Venera craft extended their lives by circulating cooling fluids through large blocks of lithium nitrate trihydrate—a material chosen for its ability to absorb as much thermal energy as possible with minimal change to its temperature—in order to keep the temperature of their elec-tronics within an operational range for as long as possible.

The Earth and Venus: Twins?

The first missions to Venus were motivated in part by the pragmatic consideration of wanting to explore the unknown without needing to travel any further than was strictly necessary. The short flight time to our nearest planet—typically no more than 3 months—minimized the likelihood of spacecraft systems failing in transit. In more modern times, however, it has become clear that Venus has much to offer space scientists beyond mere accessibility. It appears that in its early history Venus may have been an almost identical twin to the Earth, having had a very similar composition to our own planet around 4 billion years ago. Both would have had thick atmospheres of carbon dioxide at this time, and both would have had large amounts of water on their surfaces and in their atmospheres. As a result, the climate and geology of Venus may be able to tell us much about our own Earth, showing us two very different outcomes from what may have been very similar starting conditions.

The crucial difference between Venus and the Earth seems to have been that Venus does not have a magnetic field akin to the Earth’s. Whereas the Earth’s atmo-sphere is protected from the stream of ionizing radiation which the Sun spews out through the solar system—the solar wind—Venus’s atmosphere has no such protec-tion. The most widely accepted explanation of how the Earth and Venus evolved to become such different planets is that Venus’s exposure to the solar wind meant that it was unable to retain any water on its surface in the long term. Gradually, the Sun’s ultraviolet light broke apart water molecules in Venus’s atmosphere. Just as helium balloons rise, the hydrogen atoms which were liberated by this process

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drifted to the top of Venus’s atmosphere, where exposure to the solar wind was suf-ficient to occasionally give them enough energy to escape Venus’s gravity alto-gether. Though this process would have been very slow, over millions of years it would have meant that Venus gradually vented hydrogen atoms to space to become a dry planet.

At the same time as Venus was drying out, the Earth’s atmosphere was becoming thinner. As any soda drinker knows, it is possible to dissolve large volumes of car-bon dioxide in water. In nature, carbon dioxide from the Earth’s atmosphere gradu-ally dissolves in sea water. In time it can react with calcium, which also naturally dissolves in sea water, to form calcium carbonate which can then become deposited in rocks such as limestone, chalk or marble. Over a period of hundreds of millions of years, the majority of the Earth’s supply of carbon became locked up in solid rocks, reducing the amount of carbon dioxide in its atmosphere and in turn its sur-face pressure. Adding up estimates of how much carbon there is locked up in lime-stone around the world, it seems a not dissimilar quantity to that which remains in gaseous form in Venus’s thick atmosphere.

Once these two distinct processes had taken place on each of the planets, tem-peratures on Venus’s surface soared out of control as a result of the greenhouse effect, while those on the Earth were kept in check by the ability of its seawater to clear the carbon dioxide from its atmosphere. Nonetheless, many questions remain. We still do not understand what is different about Venus’s core, which means that it doesn’t produce a magnetic field akin to the Earth’s. A related question is how volcanically active Venus is, and how rapidly heat from its interior is able to escape to its surface. As we have seen, Venus’s present surface is only rather lightly cra-tered, suggesting that it bears the scars of meteor impacts which have occurred only within the past 300–500 million years. The concentrations of sulfurous compounds in its atmosphere also point to recent volcanic eruptions, which would have erased old craters with new lava flows. Yet it has proven very difficult to identify any active volcanoes on maps of Venus’s surface, and there is similarly little evidence of any very recent lava flows.

The solution to this paradox may lie in an important difference between the surface structures of Venus and the Earth. On the Earth, the continents of the Earth drift apart as a result of plate tectonics. Its solid crust floats on top of a flowing mass of runny magma beneath, and different parts of the Earth’s crust are carried in different directions by different magma flows. Volcanic eruptions tend to occur at the boundaries between the plates, where the Earth’s crust is thinnest and weak-est. Venus, however, has no continents and no plate tectonics, because magma only has the consistency needed to flow in quite the right way when it is mixed with water.

Without continental boundaries, it may be that Venus’s surface is geologically very stable for hundreds of millions of years at a time. Gradually, however, heat builds up in the magma just below Venus’s crust during these long stable periods, as without volcanic eruptions the planet’s crust acts as a very efficient blanket. Eventually the stable period ends when this magma becomes so hot that it bursts through the skin above it, typically with such violence that it floods and ultimately

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resurfaces the entire planet. So much heat is released in this brief episode that Venus is able to return to another long period of geological stability before the process repeats.

Mercury as a Planet

Venus is not the only planet whose surface remained uncharted until very recent times. The geography of Mercury’s surface was not mapped out until the visit of Mariner 10 in 1974, and even then the photographs that were returned showed only 45 % of the planet’s globe in detail. The first near-complete maps of Mercury’s surface were made as recently as 2008–2009, using data returned by the MESSENGER spacecraft. The historical difficulty in mapping out Mercury’s sur-face is not that it is enshrouded by cloud: in fact it is so close to the Sun that the combined effects of the Sun’s heat and the solar wind rapidly strip away any gas-eous atmosphere that might form around it. Instead, Mercury is difficult to observe because, as the solar system’s innermost planet, it never appears any further than 28° away from the Sun to ground-based observers. Without any prospect of being able to observe it when the Sun is well below the horizon, astronomers must image it as soon as possible after sunset or before sunrise. Even then, the combination of poor atmospheric seeing close to the horizon and interference from twilight severely limits the observations that are possible.

It is not just ground-based observers who find Mercury a difficult planet to study. Even at its widest separation from the Sun, Mercury is too close to the Sun for most space-based telescopes such as the Hubble Space Telescope to be safely pointed at it without their sensitive optics being placed in peril. Navigating space-craft through the solar system on trajectories which carry them to Mercury is far from straightforward, as is reflected in the fact that only two spacecraft have visited it to date—Mariner 10, which flew past it twice in March and September 1974, and MESSENGER which has been in orbit around it since 2011.

Sending spacecraft to Mercury is difficult for two reasons. Firstly, Earth circles around the Sun at a speed which is fast enough to prevent its falling inward under the Sun’s gravity—at a speed of around 30 km/s. Any spacecraft which is launched from the Earth initially shares this orbital motion through the solar system. If it wishes to travel inwards towards the Sun, and towards the orbit of Mercury, it must burn thrusters to slow itself down.

Just as spacecraft need to burn large amounts of fuel to reach speeds which are fast enough to carry them to the outer planets without the Sun’s gravitational pull drawing them back, they also need thrust hard in order to reduce their speed. In fact, the amount of backward thrust which is needed to reduce a spacecraft’s speed to a point where it can reach the orbit of Mercury is not dissimilar to the amount of forward thrust which is needed to reach Jupiter. Just as spacecraft often use gravi-tational slingshots—taking advantage of the gravity of nearby planets to get an additional kick—to catapult themselves onto trajectories which reach the outer

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planets, the same technique can also be used in reverse to send spacecraft inwards towards the Sun. Both Mariner 10 and MESSENGER made use of Venus’s gravitational field to help slow them down on their way to Mercury.

Even once a spacecraft has reached Mercury, a further problem is encountered if it is to remain in orbit around the solar system’s innermost planet. As any space-craft travels inwards through the solar system, it picks up speed from the Sun’s gravity, in the same way that a ball picks up speed as it rolls down a hill. To be captured into Mercury’s gravitational field and remain in orbit around it, however, a spacecraft needs to be traveling comparatively slowly. Having already performed one hard thrust to reach Mercury in the first place, a spacecraft needs to perform a second hard thrust at the end of its journey to reduce its speed to a point where it can be captured into orbit around Mercury. Mariner 10 never attempted this latter maneuver; its mission controllers had to make do with merely flying past Mercury twice. MESSENGER has been in orbit around Mercury since 2011, but used a sequence of gravitational slingshots over 6 years to help it reduce its speed—in total, one from the Earth, two from Venus, and three from Mercury—before it finally entered orbit around Mercury at its fourth encounter.

The Environment on Mercury’s Surface

Like Venus, Mercury is a very hot place. In the afternoon Sun, temperatures regu-larly exceed 500 °C, making its surface the hottest of any of the planets. Orbiting the Sun at a distance of only 39 % of an astronomical unit, Mercury’s warmth is at least partly the result of its relative closeness to the Sun. An observer on its surface would see the Sun looming in the sky with a diameter 2.5 times larger than that seen on Earth and would feel more than six times as much heat from it as on Earth.

Unlike Venus, however, Mercury has no greenhouse effect to exacerbate its heat. As we have seen, the Sun’s radiation is strong enough in the inner solar system to have blasted away any atmosphere that Mercury might once have had in the past. However, just as a very thick atmosphere can lead to extreme weather, so can a very thin atmosphere. The Earth and Venus have relatively modest differences between their daytime and night time temperatures, because their atmospheres act as blan-kets that keep them warm during the night and cool through the day. In the absence of such thermal insulation, Mercury’s surface is not only a very hot place during the day, but also a very cold place at night.

Moreover, Mercury’s daily rotation on its axis is very slow: it takes 59 days to complete each revolution. Just as each day on the Earth is 4 min longer than its rotation period (23 h and 56 min; see Chap. 4 ), days on Mercury are somewhat longer than its rotation period. On the Earth this effect is small, because the Earth rotates much more quickly than it orbits around the Sun. Mercury’s orbital period, however, is only a little longer than its rotation period—88 days—and this means that Mercury’s days are very considerably longer than its rotation period, at 176 Earth days (around 6 months). Mercury is the only planet whose years are shorter—exactly half the length, to be precise—than its days. Each afternoon on

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Mercury’s surface drags on for thousands of hours, and so it is perhaps unsurprising that Mercury’s surface should be scorching hot after being in directly sunlight for several weeks continuously. Once the Sun sets, the same location on Mercury’s surface is plunged into darkness for thousands of hours, and by dawn its tempera-ture may have dipped below −150 °C.

Even if Mercury’s surface is not a particularly clement place, beneath that sur-face Mercury shows a surprising degree of similarity to the Earth. One of the unex-pected discoveries made by Mariner 10 was that Mercury has a strong magnetic field which, although a hundred times weaker than that of the Earth, is much stron-ger than those of Venus, the Moon, or Mars. This implies that Mercury has a size-able molten iron core similar to that which is at the Earth’s center, and unlike those which are at the centers of the other terrestrial planets. This idea is backed up by measurements of Mercury’s density, which is unusually high and seems to imply a more metallic rather than rocky interior composition.

Mercury is the smallest of the terrestrial planets: it measures only 38 % of an Earth-diameter across, and has a mass of only 5.5 % of the Earth’s mass. For such a small planet to produce a magnetic field with even a hundredth the strength of the Earth’s, its iron core must occupy a large fraction of its internal volume—roughly 42 % of Mercury’s volume, as compared to the 17 % of the Earth’s volume that our own planet’s core occupies. This matches Mercury’s density, which though a little lower than the Earth’s—5.43 g/cm 3 rather than 5.52 g/cm 3 —implies a relatively much larger core once account is taken for the fact that the Earth’s core is heavily compressed by the weight of rock pushing inwards on it, while Mercury’s core is comparatively uncompressed.

Mercury’s surface is similar to that of the Moon in appearance, with volcanic planes similar to the Moon’s maria, separated by more mountainous terrain akin to the lunar highlands. Both bodies appear to have been geologically dead since not long after their formation: their surfaces still show the scars of meteor impacts which occurred 3–5 billions of years ago, indicating that no volcanic eruptions have occurred to flood those craters in the intervening years. Uniquely, Mercury’s sur-face is littered with shallow escarpments called rupes , which often extend over hundreds of miles and in places are over a mile high. These are thought to be akin to the wrinkles that form on the skin of fruit when their interiors dry out and con-tract. It is thought that Mercury’s surface solidified before the mantle below it, and that in the absence of any subsequent volcanism to reshape its surface, wrinkles formed when the mantle below solidified and contracted.

Observing Mercury and Venus

The paths that Mercury and Venus trace across the sky are markedly different from those traced by the other planets. Their relative closeness to the Sun means that at all times they closely follow its annual motion along the ecliptic, in contrast to the abil-ity of the outer planets to pass right around the far side of the sky from the Sun at around the time of opposition. Crucially, when they make their closest approaches to

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the Earth, rather than passing almost directly opposite to the Sun in the sky and appearing at opposition, they instead pass between the Earth and the Sun. Instead of being very well placed in the sky, they are almost completely unobservable owing to their closeness to the Sun. Whereas the outer planets pass through one opposition and one solar conjunction within each synodic period, Mercury and Venus pass through two solar conjunctions within that time—one on the far side of the Sun, a superior conjunction, and the other on the near side of the Sun, an inferior conjunction.

It is rather straightforward to know when is the best time to observe the outer planets—the moment when they reach opposition is the same moment when they are visible for the greatest number of hours of the night, when they are at their clos-est to the Earth, when they present the largest disks, and moreover also when they appear at their brightest. The situation is considerably more complicated for Mercury and Venus. These planets make their closest approach to the Earth and appear largest at the moments of their inferior conjunctions, when they are almost completely unobservable on account of their closeness to the Sun.

The moment when they are visible for the longest period of time before sunrise or after sunset is the point in time when they appear at their greatest separation from the Sun in the sky, which can be worked out with a little geometry (see Fig. 8.2 ). Within each synodic period, this happens twice—once when the planet is to the east of Sun, visible on the western horizon in the post-sunset evening sky, and once when it is to the west of a Sun, visible on the eastern horizon in the morning sky. At these two moments, the planet is said to be at either greatest elongation east (evening sky), or greatest elongation west (morning sky). Tables 8.1 and 8.2 list all

EarthVenus

The SunInferior solarconjunction

Superior solarconjunction

Greatest elongation east(evening star)

Greatest elongation west(morning star)

Fig. 8.2 Venus moves very quickly from the evening sky to the morning sky, but takes much longer to make the return journey. See the text for details

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Table 8.1 The apparitions of Mercury, 2010–2050

Greatest elongation east

Inferior conjunction

Greatest elongation west

Superior conjunction

04/01/2010 27/01/2010 14/03/2010 08/04/2010 28/04/2010 26/05/2010 28/06/2010 06/08/2010 03/09/2010 19/09/2010 17/10/2010 01/12/2010 20/12/2010 09/01/2011 25/02/2011 22/03/2011 09/04/2011 07/05/2011 12/06/2011 20/07/2011 17/08/2011 03/09/2011 28/09/2011 14/11/2011 04/12/2011 23/12/2011 07/02/2012 05/03/2012 21/03/2012 18/04/2012 27/05/2012 01/07/2012 28/07/2012 16/08/2012 10/09/2012 26/10/2012 17/11/2012 05/12/2012 18/01/2013 16/02/2013 04/03/2013 31/03/2013 11/05/2013 12/06/2013 09/07/2013 30/07/2013 24/08/2013 09/10/2013 01/11/2013 18/11/2013 29/12/2013 31/01/2014 15/02/2014 14/03/2014 26/04/2014 25/05/2014 19/06/2014 13/07/2014 08/08/2014 21/09/2014 16/10/2014 01/11/2014 08/12/2014 14/01/2015 30/01/2015 24/02/2015 10/04/2015 07/05/2015 30/05/2015 25/06/2015 23/07/2015 04/09/2015 30/09/2015 16/10/2015 17/11/2015 29/12/2015 14/01/2016 07/02/2016 23/03/2016 18/04/2016 09/05/2016 05/06/2016 07/07/2016 16/08/2016 12/09/2016 28/09/2016 27/10/2016 11/12/2016 28/12/2016 19/01/2017 07/03/2017 01/04/2017 20/04/2017 17/05/2017 21/06/2017 30/07/2017 26/08/2017 12/09/2017 08/10/2017 24/11/2017 13/12/2017 02/01/2018 17/02/2018 15/03/2018 01/04/2018 29/04/2018 06/06/2018 12/07/2018 09/08/2018 26/08/2018 21/09/2018 06/11/2018 27/11/2018 15/12/2018 30/01/2019 26/02/2019 15/03/2019 11/04/2019 21/05/2019 24/06/2019 21/07/2019 10/08/2019 04/09/2019 20/10/2019 11/11/2019 28/11/2019 10/01/2020 10/02/2020 26/02/2020 23/03/2020 04/05/2020 04/06/2020 01/07/2020 22/07/2020 17/08/2020 01/10/2020 25/10/2020 10/11/2020 20/12/2020 24/01/2021 08/02/2021 06/03/2021 19/04/2021 17/05/2021 11/06/2021 05/07/2021 01/08/2021 13/09/2021 09/10/2021 25/10/2021 29/11/2021 07/01/2022 23/01/2022 16/02/2022 02/04/2022 29/04/2022 21/05/2022 16/06/2022 16/07/2022 27/08/2022 23/09/2022 08/10/2022 08/11/2022 21/12/2022 07/01/2023 30/01/2023 17/03/2023 11/04/2023 01/05/2023 29/05/2023 01/07/2023

(continued)

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Greatest elongation east

Inferior conjunction

Greatest elongation west

Superior conjunction

09/08/2023 06/09/2023 22/09/2023 20/10/2023 04/12/2023 22/12/2023 12/01/2024 28/02/2024 24/03/2024 11/04/2024 09/05/2024 14/06/2024 22/07/2024 19/08/2024 05/09/2024 30/09/2024 16/11/2024 06/12/2024 25/12/2024 09/02/2025 08/03/2025 24/03/2025 21/04/2025 30/05/2025 04/07/2025 31/07/2025 19/08/2025 13/09/2025 29/10/2025 20/11/2025 08/12/2025 21/01/2026 19/02/2026 07/03/2026 03/04/2026 14/05/2026 15/06/2026 13/07/2026 02/08/2026 27/08/2026 12/10/2026 04/11/2026 21/11/2026 01/01/2027 03/02/2027 18/02/2027 17/03/2027 28/04/2027 28/05/2027 23/06/2027 16/07/2027 11/08/2027 24/09/2027 19/10/2027 04/11/2027 11/12/2027 17/01/2028 02/02/2028 27/02/2028 11/04/2028 09/05/2028 02/06/2028 27/06/2028 25/07/2028 06/09/2028 02/10/2028 17/10/2028 20/11/2028 31/12/2028 16/01/2029 09/02/2029 26/03/2029 21/04/2029 12/05/2029 08/06/2029 09/07/2029 19/08/2029 15/09/2029 01/10/2029 30/10/2029 14/12/2029 31/12/2029 22/01/2030 09/03/2030 04/04/2030 23/04/2030 21/05/2030 24/06/2030 02/08/2030 29/08/2030 15/09/2030 11/10/2030 27/11/2030 15/12/2030 05/01/2031 20/02/2031 18/03/2031 04/04/2031 02/05/2031 08/06/2031 15/07/2031 12/08/2031 29/08/2031 24/09/2031 09/11/2031 30/11/2031 18/12/2031 02/02/2032 29/02/2032 17/03/2032 13/04/2032 23/05/2032 26/06/2032 23/07/2032 12/08/2032 05/09/2032 22/10/2032 13/11/2032 30/11/2032 12/01/2033 12/02/2033 27/02/2033 26/03/2033 07/05/2033 07/06/2033 04/07/2033 25/07/2033 20/08/2033 04/10/2033 28/10/2033 13/11/2033 23/12/2033 26/01/2034 11/02/2034 09/03/2034 21/04/2034 20/05/2034 14/06/2034 08/07/2034 04/08/2034 16/09/2034 12/10/2034 27/10/2034 02/12/2034 10/01/2035 26/01/2035 19/02/2035 05/04/2035 02/05/2035 25/05/2035 20/06/2035 19/07/2035 30/08/2035 26/09/2035 11/10/2035 12/11/2035 24/12/2035 10/01/2036 02/02/2036 19/03/2036 13/04/2036 04/05/2036 31/05/2036 02/07/2036 11/08/2036 08/09/2036 24/09/2036 22/10/2036 06/12/2036 24/12/2036 14/01/2037 02/03/2037 27/03/2037 15/04/2037 12/05/2037 17/06/2037

Table 8.1 (continued)

(continued)

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Greatest elongation east

Inferior conjunction

Greatest elongation west

Superior conjunction

25/07/2037 22/08/2037 07/09/2037 03/10/2037 19/11/2037 08/12/2037 28/12/2037 12/02/2038 10/03/2038 27/03/2038 24/04/2038 01/06/2038 07/07/2038 04/08/2038 22/08/2038 16/09/2038 01/11/2038 23/11/2038 10/12/2038 24/01/2039 22/02/2039 10/03/2039 06/04/2039 17/05/2039 19/06/2039 16/07/2039 05/08/2039 30/08/2039 15/10/2039 07/11/2039 23/11/2039 05/01/2040 06/02/2040 21/02/2040 19/03/2040 30/04/2040 30/05/2040 25/06/2040 18/07/2040 13/08/2040 26/09/2040 21/10/2040 06/11/2040 14/12/2040 19/01/2041 04/02/2041 01/03/2041 14/04/2041 12/05/2041 05/06/2041 30/06/2041 28/07/2041 09/09/2041 05/10/2041 20/10/2041 23/11/2041 03/01/2042 19/01/2042 12/02/2042 29/03/2042 24/04/2042 16/05/2042 11/06/2042 12/07/2042 22/08/2042 18/09/2042 04/10/2042 03/11/2042 17/12/2042 03/01/2043 25/01/2043 12/03/2043 07/04/2043 26/04/2043 24/05/2043 26/06/2043 05/08/2043 01/09/2043 18/09/2043 15/10/2043 30/11/2043 18/12/2043 08/01/2044 23/02/2044 20/03/2044 06/04/2044 04/05/2044 10/06/2044 17/07/2044 14/08/2044 31/08/2044 26/09/2044 11/11/2044 01/12/2044 20/12/2044 04/02/2045 03/03/2045 20/03/2045 16/04/2045 25/05/2045 29/06/2045 26/07/2045 14/08/2045 08/09/2045 25/10/2045 16/11/2045 03/12/2045 16/01/2046 15/02/2046 02/03/2046 29/03/2046 10/05/2046 10/06/2046 07/07/2046 28/07/2046 23/08/2046 07/10/2046 31/10/2046 16/11/2046 27/12/2046 29/01/2047 14/02/2047 12/03/2047 24/04/2047 23/05/2047 17/06/2047 11/07/2047 07/08/2047 19/09/2047 15/10/2047 30/10/2047 06/12/2047 13/01/2048 28/01/2048 22/02/2048 07/04/2048 04/05/2048 27/05/2048 22/06/2048 21/07/2048 01/09/2048 27/09/2048 13/10/2048 14/11/2048 26/12/2048 12/01/2049 04/02/2049 22/03/2049 16/04/2049 07/05/2049 03/06/2049 05/07/2049 14/08/2049 11/09/2049 27/09/2049 25/10/2049 09/12/2049 27/12/2049 17/01/2050 05/03/2050 30/03/2050 18/04/2050 16/05/2050 20/06/2050 28/07/2050 25/08/2050 10/09/2050 07/10/2050 22/11/2050 11/12/2050 31/12/2050

The four columns list the dates when Mercury is at greatest elongation east (first), inferior conjunction (second), greatest elongation west (third) and superior conjunction (fourth). All dates are listed in dd/mm/yyyy format. Source : DE405

Table 8.1 (continued)

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Table 8.2 The apparitions of Venus, 2010–2075

Greatest elongation east

Inferior conjunction

Greatest elongation west

Superior conjunction

11/01/2010 19/08/2010 29/10/2010 08/01/2011 16/08/2011 26/03/2012 06/06/2012 15/08/2012 28/03/2013 01/11/2013 11/01/2014 23/03/2014 25/10/2014 06/06/2015 15/08/2015 26/10/2015 06/06/2016 12/01/2017 25/03/2017 03/06/2017 09/01/2018 17/08/2018 26/10/2018 06/01/2019 14/08/2019 24/03/2020 03/06/2020 13/08/2020 26/03/2021 29/10/2021 09/01/2022 20/03/2022 22/10/2022 04/06/2023 13/08/2023 23/10/2023 04/06/2024 10/01/2025 23/03/2025 31/05/2025 06/01/2026 14/08/2026 24/10/2026 03/01/2027 11/08/2027 21/03/2028 01/06/2028 11/08/2028 23/03/2029 27/10/2029 06/01/2030 18/03/2030 20/10/2030 02/06/2031 11/08/2031 21/10/2031 02/06/2032 08/01/2033 20/03/2033 29/05/2033 04/01/2034 12/08/2034 21/10/2034 01/01/2035 09/08/2035 19/03/2036 30/05/2036 08/08/2036 21/03/2037 24/10/2037 04/01/2038 16/03/2038 18/10/2038 30/05/2039 08/08/2039 19/10/2039 31/05/2040 05/01/2041 18/03/2041 27/05/2041 01/01/2042 10/08/2042 19/10/2042 29/12/2042 07/08/2043 17/03/2044 27/05/2044 06/08/2044 18/03/2045 22/10/2045 01/01/2046 13/03/2046 15/10/2046 28/05/2047 06/08/2047 16/10/2047 28/05/2048 03/01/2049 15/03/2049 24/05/2049 29/12/2049 07/08/2050 16/10/2050 27/12/2050 05/08/2051 14/03/2052 25/05/2052 04/08/2052 16/03/2053 19/10/2053 30/12/2053 11/03/2054 13/10/2054 26/05/2055 04/08/2055 14/10/2055 26/05/2056 31/12/2056 13/03/2057 22/05/2057 27/12/2057 05/08/2058 14/10/2058 25/12/2058 03/08/2059 12/03/2060 23/05/2060 01/08/2060 13/03/2061 17/10/2061 27/12/2061 08/03/2062 10/10/2062 23/05/2063 01/08/2063 12/10/2063 24/05/2064 29/12/2064 11/03/2065 19/05/2065 24/12/2065 02/08/2066 11/10/2066 22/12/2066 31/07/2067 10/03/2068 20/05/2068 30/07/2068 11/03/2069 14/10/2069 25/12/2069 06/03/2070 08/10/2070 21/05/2071 30/07/2071 09/10/2071 21/05/2072 27/12/2072 08/03/2073 17/05/2073 22/12/2073 31/07/2074 09/10/2074 20/12/2074 29/07/2075

The four columns list the dates when Venus is at greatest elongation east (first), inferior conjunction (second), greatest elongation west (third) and superior conjunction (fourth). All dates are listed in dd/mm/yyyy format. Source : DE405

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the occasions on which Mercury and Venus will reach maximum elongation east or west in coming years.

Venus does not take the same amount of time to pass from the evening sky into the morning sky as it takes to return the other way. In fact, it typically takes less than 5 months to go from greatest elongation east to greatest elongation west, but it takes more than 14 months to make the return journey. Mercury moves in a simi-lar way, but the difference is much less pronounced. There are two equivalent ways of picturing why this is the case. First, as Fig. 8.2 shows, Venus’s position in space when it reaches greatest elongation east or west is not far separated from the point where it comes to inferior conjunction. As Venus travels around its orbit at a roughly constant rate, it naturally takes much longer for it to travel the much greater distance needed to get around the right-hand side of Fig. 8.2 .

An equivalent explanation is that Venus moves across the sky much more quickly when it is at its closest to the Earth, around the time of inferior conjunction, than it does when it is further away from us (see Fig. 8.3 ). Since Venus is closer to the Earth when it is moving along the ecliptic from east to west than it is when it is making the return journey, this motion is comparatively quick. The difference is less pro-nounced for Mercury, whose distance from the Earth varies to a much lesser extant.

The Phases of Mercury and Venus

As we have seen, Venus appears largest when it is at inferior conjunction, but is visible for the longest period before or after sunset when it is at greatest elongation. The question of when it is at its brightest is more complicated, because not only

Earth

Venus

Fig. 8.3 Venus moves very quickly across the sky when it is close to the Earth. See the text for details

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does its apparent size change with its distance from the Earth, but its state of illumination also changes. Like the Moon, Mercury and Venus show phases. When they are close to superior conjunction, the Earth sees almost exactly the same side of them as is being illuminated by the Sun, and so their disks appear fully illumi-nated, like a full moon. At inferior conjunction, however, the Earth sees almost exactly the opposite side to them as the Sun sees, and so they appear almost completely unilluminated (see Fig. 8.4 ).

Whenever Mercury or Venus are actually observable, they show intermediate phases, reaching half phase when they are at greatest elongation east or west. It was this observation, made by Galileo within a few months of his first pointing a tele-scope at the night sky in 1609, which gave him conclusive evidence that Mercury and Venus circled around the Sun, rather than following some more complicated motion around the Earth which just happened to always place them close to the Sun in the sky. Working out when they appear at their brightest, however, depends on two effects which work in opposition to each other. When Mercury and Venus appear largest, their disks are completely unilluminated. As they move away from inferior conjunction, they appear as widening crescents, but as those crescents widen they also get smaller as they recede from the Earth.

The calculation works differently for the two planets. The variation in Mercury’s distance from the Earth is comparatively slight, and so it continues to brighten in the night sky long after inferior conjunction, as it waxes from being a crescent, through half phase, to become gibbous. It is already lost to the Sun’s glare close to the time of superior conjunction before it reaches its peak brightness. Venus’s distance from the Earth, on the other hand, varies by a factor of more than six

TheSun

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GreatestElongation

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Fig. 8.4 Mercury and Venus show phases as they circle around the Sun

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between inferior and superior conjunction. This means that its disk is very much larger in the short space of time around inferior conjunction, as it flies past the Earth, than it is at any other time. For this reason, it is at its brightest when it is still a crescent, roughly half way between inferior conjunction and when it reaches greatest elongation east or west.

Transits of the Sun

As the only two planets that lie closer to the Sun than the Earth, Mercury and Venus are also the only two planets which can ever pass inferior solar conjunction. That is to say, they are the only two planets which are ever able to pass between the Earth and the Sun. If their alignment is exactly correct, it is possible for them to appear to briefly pass directly in front of—or transit—the Sun’s disk as they do so (Fig. 8.5 ). The geometry of a transit of Mercury or Venus is similar to the geometry of a solar eclipse—in both cases an astronomical body is passing in front of the Sun and blocking some of its light. The only difference is that Mercury and Venus are much more distant than the Moon, and so their ‘eclipses’ are always annular rather than total. Put another way, Mercury and Venus appear as much smaller objects in the sky, and are never even remotely large enough to entirely cover the Sun’s disk. Just as solar eclipses do not occur every time there is a new moon, because the Moon’s orbit is slightly inclined to the ecliptic (see Chap. 5 ), not all inferior solar conjunctions coincide with transits. On average, Mercury transits the Sun roughly once every 20 years, while Venus does so rather more rarely—roughly once every 180 years (see Tables 8.3 and 8.4 ) and did so most recently in 2004 and 2012.

Fig. 8.5 The 2004 transit of Venus, photographed on June 6 by Jan Herald. Credit : Jan Herald

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Nowadays, transits are primarily curiosities which attract the interest of amateur astronomers because they are so rare. There is little that can scientifically be learnt from them. In past centuries—specifically the seventeenth through to the nineteenth centuries—however, great effort was put into sending observing parties to far flung parts of the globe to observe them, because of the possibility that they might be used to refine our knowledge of the distances to astronomical bodies. At inferior conjunction, Venus comes close enough to the Earth that it has a sizeable parallax, meaning that it appears in slightly different parts of the night sky as seen from dif-

Table 8.3 Dates of the transits of Mercury, 2000–2100

Date Midpoint (UTC)

2003 May 7 07:53 2006 November 8 21:42 2016 May 9 14:59 2019 November 11 15:21 2032 November 13 08:55 2039 November 7 08:48 2049 May 7 14:26 2052 November 9 02:32 2062 May 10 21:39 2065 November 11 20:08 2078 November 14 13:44 2085 November 7 13:37 2095 May 8 21:09

Source : Seven Century Catalog of Mercury Transits : 1601 CE to 2300 CE , Fred Espenak, NASA. Available for download from http://eclipse.gsfc.nasa.gov/transit/catalog/MercuryCatalog.html

Table 8.4 Dates of the transits of Venus, 1630–2200

Date Midpoint (UTC)

1631 December 7 05:21 1639 December 4 18:27 1761 June 6 05:19 1769 June 3 22:26 1874 December 9 04:07 1882 December 6 17:06 2004 June 8 08:21 2012 June 6 01:31 2117 December 11 02:52 2125 December 8 16:06

Source : Six Millennium Catalog of Venus Transits : 2000 BCE to 4000 CE , Fred Espenak, NASA. Available for download from http://eclipse.gsfc.nasa.gov/transit/ catalog/VenusCatalog.html

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ferent places on the Earth’s surface. This effect is rather slight, however: the displacement is roughly one arcminute from one side of the Earth to the other, and so an incredibly detailed star chart would be needed to detect it. Until very recently, there were no star charts which were up to the job, but transits of Venus provided a rare opportunity to make observations of events whose start and end times would differ slightly as seen from different places on Earth, as a direct result of Venus’s parallax. If a team of keen-sighted observers at widely spaced locations around the world, each equipped with a very good clock, could time exactly when they saw a transit begin and end to within an accuracy of a few seconds, it was hoped that the time differences in their observations would be easily apparent once they got home. With subsequent analysis, these time differences would reveal how large Venus’s parallax was, and ultimately how far away Venus is.

In practice, the results of such experiments were mixed. In part this was due to a catalog of observing mishaps, but the observations were also hampered by an optical illusion known as the black drop effect which made it very difficult for observers to pick out the precise start and end times of transits. In essence, observ-ers found that Venus’s disk appeared elongated into an elliptical drop, and without a clear idea of exactly where its edge lay, they found it difficult to say exactly when that edge touched the Sun’s disk. Measurements of Venus’s parallax were made, but their accuracy was poor, and it was not until the advent of radar (see Chap. 1 ) that the distance to Venus was determined with any precision.

The Geometry of Transits

As we have already seen, the geometry of transits of Mercury and Venus is directly comparable to that of solar eclipses, and so it is worth revisiting how eclipses come about before describing how transits come about. As we saw in Chap. 5 , the reason why the Moon doesn’t produce a solar eclipse every time it passes new moon is that its orbit is slightly inclined, or tipped up, relative to the plane of the Earth’s orbit around the Sun—the ecliptic. At most new moons, the Moon skirts to one side of the Sun, rather than actually passing in front of it. Two points can be identified around the Moon’s orbit called its nodes, which are the two points where it passes through the plane of the ecliptic. It is only when a new moon happens to coincide with the Moon passing one of these two nodes that a solar eclipse takes place.

Similarly, the orbits of Mercury and Venus are slightly tipped up relative to the plane of the Earth’s orbit around the Sun. If this were not the case, they would pass in front of the Sun at every inferior conjunction, rather than usually passing to one side of the Sun. Figure 8.6 shows this geometry in more detail. The two points where the orbits of Mercury or Venus pass through the plane of the ecliptic are called their nodes, and it is only when an inferior conjunction happens to coincide with the planet passing through one of these nodes that the alignment of the Sun, Earth, and Mercury or Venus is close enough to a straight line for a transit to be seen.

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To be more specific: Venus passes inferior conjunction once within each synodic period, once every 584 days. The geometry of the Earth, Sun and Venus as Venus passes inferior conjunction is shown in Fig. 8.7 . For a brief period of around 7.5 h, Venus’s ecliptic longitude—its position along the path of the ecliptic across the night sky, the direction which is orientated into or out of the page as shown in Fig. 8.7 —is sufficiently well aligned that Venus may appear in front of the Sun. This is how long it takes for the Earth and Venus to move far enough along their orbits for Venus to drift by half a degree relative to the Sun, crossing its face from

Sun

Venus

Earth

Node

Fig. 8.6 The orbits of the Earth and Venus, both of which are very close to being circular but appear as ovals here because of three-dimensional perspective. The grid marks the plane of the Earth’s orbit—the ecliptic. While the Earth’s orbit lies within this plane, Venus’s orbit is inclined to it by 3.4°. The dotted line shows the true orbit of Venus, while a solid line shows the projection of Venus’s orbit onto the ecliptic plane. If Venus passes inferior conjunction when it is much above or below this plane, it appears from the Earth to pass to the side of the Sun rather than directly in front of it. Venus can only pass in front of the Sun when an inferior conjunction happens to coincide with it being close to one of its two nodes

SunEarth

Venus

Plane of the Ecliptic

Plane of Venus’s Orbit

Fig. 8.7 Although Venus’s orbit around the Sun is inclined by only 3.4° relative to the Earth’s orbit, it can appear from the Earth to wander much further from the ecliptic plane than this—by more than 8.5°. The reason for this is that Venus comes very close to the Earth at around the time of inferior conjunction, and even if the angular separation of the Earth and Venus as seen from the Sun is no more than 3.4° at this moment in time, the angular separation of the Sun and Venus as seen from the Earth is much larger at the same instant

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the east to the west. A transit will only occur, however, if Venus is also very close to one of its two nodes at the same time. As Venus crosses a node, there is a period of around 48 h during which it lies close enough to the ecliptic plane—its ecliptic latitude is close enough to zero—for transits to occur. In other words, a transit of Venus is only seen if one of the 48-h windows which occur twice each time Venus circles the Sun—i.e. once every 112 days—happens to coincide with a 7.5-h win-dow around the time of each inferior conjunction. This means that there is roughly a 1.8 % chance of a transit of Venus occurring at any given inferior conjunction, and such transits occur on average roughly once every 89 years.

Transits of Mercury happen rather more often. Mercury passes inferior conjunc-tion once every 116 days, and as it does so, there is a window of around 6.2 h during which its ecliptic longitude is sufficiently well aligned with the Sun’s position that a transit may be seen. Mercury circles the Sun once every 88 days, and passes through one of its two nodes on average once every 44 days. At each node-crossing, there is a window of around 38 h within which a transit may occur. In summary, a transit of Mercury is seen whenever one of a series of 38-h windows which occur twice every time it circles the Sun—i.e. once every 44 days—happens to coincide with a 6.2-h window around the time of each inferior conjunction. This means that there is roughly a 3.6 % chance of a transit of Mercury occurring at any given infe-rior conjunction, and such transits occur on average roughly once every 8.8 years.

Unlike the Moon’s nodes, the nodes of Mercury and Venus do not precess around the ecliptic on human timescales, and their orbits remain essentially fixed in space. This means that the lines connecting the nodes of Mercury and Venus lie in fixed directions in space. The line connecting the nodes of Mercury intersects the Earth’s orbit at points that it passes through in May and November, and so these are the only 2 months of the year in which transits of Mercury can occur. Similarly, the line connecting the nodes of Venus intersects the Earth’s orbit at points that it passes through in June and December.

Transits of both Mercury and Venus are rather rare events because of the exact-ness of the straight-line alignment that they need to form between the Earth and Sun. It is much rarer for Venus to pass in front of the Sun than for Mercury to do so, for a combination of reasons. First, Venus’s greater distance from the Sun means that its orbital speed is slower, and it takes longer for it to complete each revolution around the Sun. This means that it comes to inferior conjunction less often, and so there are fewer opportunities for it to pass in front of the Sun.

However, as we have seen, Venus is also much less likely than Mercury to transit the Sun at any given inferior conjunction. This is because even though the inclina-tion of Venus’s orbit relative to the ecliptic is small—only 3.4°—it can appear from the Earth to wander much further from the ecliptic plane than this. The reason for this is that Venus is much closer to the Earth than it is to the Sun at around the time of inferior conjunction (see Fig. 8.7 ). The inclination of Venus’s orbit—the angle of 3.4°—describes how far separated Venus can appear from the ecliptic plane as seen from the Sun. From the Earth, any slight vertical displacement of Venus from the ecliptic plane results in its having a much larger angular separation from that plane.

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Cycles of Transits

Although transits of Venus happen on average roughly once every 89 years, they do not come at regular intervals. For example, they often come in pairs separated by 8 years (see Table 8.4 ). As we have seen previously, when calculating the dates of phenomena that depend upon the coincidence of two events which occur in cycles that have different periods, it is useful to look for time periods that are very close to being multiples of both periods. For example, while there are a non-integer num-ber of lunar months in a year, there are very nearly 235 lunar months in 19 years—the Metonic Cycle (see Chap. 5 ). This means that the date of Easter Day, which depends both on the timing of the March equinox and the phases of the Moon, comes close to repeating itself every 19 years, though the requirement that it fall on a Sunday means the repetition is far from exact.

Similarly, transits of Venus are seen whenever a node crossing coincides with an inferior conjunction—there must be a coincidence between a set of periodic events that occur every 112 days (half an orbital period) and another set of events that occur once every 584 days (synodic period). Pairings of transits come about because of the very close alignment between the period of time that it takes Venus to complete 13 revolutions around the Sun (2,921.1 days) and the period of time that it takes the Earth to complete 8 revolutions around the Sun (2,922.0 days). This means that after a period of 8 years, both the Earth and Venus return to almost exactly the same positions around their orbits. However, because Venus completes its 13 revolutions a few hours before the Earth completes its 8 revolutions, Venus is a little ahead of its exact position 8 years previously, and at most two transits can take place at 8-year intervals before the alignment becomes so inexact after the next iteration of the cycle that no transit occurs.

There are other time intervals that commonly separate transits of Venus. For example, in 121.5 Earth years, Venus completes fractionally more than 197.5 revo-lutions around the Sun, placing both planets on the opposite sides of their orbits. In 105.5 Earth years, Venus completes fractionally fewer than 171.5 revolutions around the Sun.

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The Deep Sky

Deep sky observers often associate each of the seasons of the year with particular kinds of deep sky object. March and April are the season of galaxies, when the Virgo and Coma galaxy clusters are visible from both northern and southern hemi-spheres, and when our near neighbors like Andromeda (M31), Triangulum (M33) and the Whirlpool (M51) are high in the sky. June and July are the season of globu-lar clusters, when these tight balls of stars can be found in rich numbers scattered in and around the constellation of Sagittarius. In the northern hemisphere, the Great Hercules cluster, M13, rides high in the sky.

Open clusters of stars are more widely spread across the sky and can be found at any time of year, but are most numerous in the evening sky in autumn and winter in the northern hemisphere, and spring and summer in the southern hemisphere.

So far, the focus has exclusively been on how cycles in the movement and visi-bility of the planets are produced by the geometry of the solar system. We have seen that different constellations become visible at different times of year, as a result of the Earth’s orbital motion around the Sun. In this brief chapter, we turn our atten-tion beyond the solar system, to relate the seasonal changes in the types of deep sky object that are visible to the larger scale structures that exist in the Milky Way galaxy and beyond.

As the Sun moves along the ecliptic over the course of the year, objects at dif-ferent right ascensions become visible in the midnight sky. If deep sky objects were distributed uniformly across the sky, this would mean that different individual objects would come into view at different times of year, but similar types of object would be on display all the year around. In practice, deep sky objects are far from uniformly distributed (see Fig. 9.1 ).

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Open clusters closely follow the line of the Milky Way across the sky, with sec-ondary clumps around the Large and Small Magellanic Clouds in the southern hemisphere, at declinations of around 70° S and right ascensions of 1 and 5 h. Globular clusters also follow the line of the Milky Way, but congregate especially around Sagittarius and Ophiuchus, at a right ascension of 18 h. Galaxies, by contrast, are mostly seen only well away from the line of the Milky Way, and there are sizeable clumps of them around a right ascension of 13 h, in Virgo and Coma Berenices. Just as the motions of the planets reveal the structure of the solar system, the distribution of deep sky objects across the night sky reveals the larger structures that surround the Earth.

The Structure of the Milky Way

The solar system lies around two-thirds of the way out from the center of the Milky Way, a flat disk-like grouping of around a hundred billion stars (see Fig. 9.2 ). The Milky Way’s center lies at a distance of around 24,000 light-years, in the direction of the constellation Sagittarius. The Galaxy’s disk of stars appears to form a line across the night sky, because the Earth’s vantage point within that disk makes it difficult to see more than that it is surrounded by a thin sheet of stars.

Looking at each of the constellations through which the line of the Milky Way passes is equivalent to looking in different directions within the plane of the Milky Way. It might be expected that the Milky Way would look radically more impressive in the direction of Sagittarius and Scorpius, looking straight towards the center of the Galaxy, than in the direction of Orion which points almost directly outward towards the Galaxy’s outskirts. In practice the Milky Way’s band of light is a little wider and brighter than average around Sagittarius, but not dramatically so. There is so much material in the Galaxy, including dust which attenuates light, that it is gen-erally not possible to see more than 15–20 % of the way to the Galaxy’s center in visible light. Because of this fog, we appear to be at the center of the small portion of the Galaxy that is close enough to the Earth to escape disappearing into the haze.

It is this fog that also means that very few galaxies are seen in the deep sky close to the line of the Milky Way. It is not that there aren’t likely to be vast numbers of galaxies in these directions, but it is quite impossible to see them with so much else in the way. As a result, there is a part of the sky called the zone of avoidance (see Fig. 9.3 ) which appears almost entirely devoid of galaxies.

Open Clusters

Conversely, the distribution of open clusters across the sky closely follows the line of the Milky Way, since these are groupings of young stars which form from gas within the Milky Way’s disk. As with the Milky Way’s stars, there is no particularly marked over-density of open clusters in the direction of Sagittarius, even though the Milky

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Way extends vastly further in that direction than others, through the center of the Milky Way and beyond. Once again, the Galaxy’s dust acts rather like fog, and we appear to sit at the center of the small portion of it that we can see.

TheSun

Zone of Avoidance

Fig. 9.3 Very few galaxies are visible in the band of sky where the Milky Way appears, because foreground material obscures them. This part of the sky is called the zone of avoidance

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Fig. 9.2 The structure of the Milky Way’s spiral arms, projected onto the plane of the galaxy’s disk. The Sun lies on a spur branching from the galaxy’s Perseus arm, sometimes called the Orion spur since it is visible in the direction of that constellation. The circle around the Sun lists the constellations through which the plane of the galaxy’s disk passes

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In fact, there are considerably more open clusters around the constellations of Puppis and Monoceros, looking almost directly away from the galactic center, than there are around Sagittarius. The distribution of open clusters across the sky is more strongly affected by the whereabouts of our local star-forming regions than the larger scale structure of the Galaxy. The Earth lies close to the center of a ring of star-forming regions called Gould’s Belt, whose origin is not well understood. This doughnut-shaped ring of young stars measures around 3,000 light-years across—10 % of the Earth’s distance from the center of the Galaxy—and includes many of the brightest stars in the sky, including the stars that make up the familiar forms of Orion, Canis Major, Crux, Scorpius, Cepheus and Perseus.

The Sun is positioned a little way outside the inner edge of one of the Galaxy’s spiral arms, called the Perseus Arm, though it spans many constellations. Looking towards Orion and Taurus, Gould’s Belt may touch the Perseus Arm, forming a structure that resembles a spur of the Perseus Arm. Two of the best-known deep sky objects, the Pleiades and the Orion Nebula, form part of this spur structure. Thus, open clusters are most numerous in the northern fall and winter skies, because it is at these times of year that the midnight sky, looking almost directly outward in the Milky Way, is directed towards the spiral arm that runs closest to the Sun.

Globular Clusters

Globular clusters are spread in almost the exact opposite distribution along the line of the Galaxy, appearing most numerous in a circular clump around Sagittarius. They also typically appear spread some distance away from the central line of the Milky Way’s plane, rather than following it as tightly as do open clusters. In con-trast to open clusters, which are loose collections of typically a few dozen recently- formed stars, globular clusters are spherical distributions of very large numbers of stars—typically millions—which appear to be as old as the Milky Way. Their origin remains a matter of debate, but some of them may be the remains of small dwarf galaxies that collided with the Milky Way long ago, and whose stars remain grouped together in compact balls that orbit around the Milky Way’s center. In any case, they form a spherical distribution around the Milky Way’s center (see Fig. 9.4 ), spending most of their time outside the plane of its disk, except when they fly through the disk, twice on each orbit, every few tens of millions of years.

Because most globular clusters lie some way above or below the plane of the Milky Way, our line of sight to them is not so badly affected by the fog of dust in the plane itself. Thus, most of the globular clusters in the night sky lie at consider-ably greater distances then open clusters, and their distribution across the sky better represents the larger-scale structure of the Galaxy. The spherical distribution of such clusters around the center of the galaxy is actually visible from the Earth, as a circular distribution centered around the constellation of Sagittarius. These are the constellations that form the midnight sky in the northern summer, and so it is with these months that globular clusters are associated.

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Galaxies

Galaxies external to the Milky Way can only be seen when the Earth’s sightline to them lies considerably away from the plane of the Milky Way’s disk, where they are not hidden behind foreground material. Even aside from this, it is clear that they are clumped together, especially around the constellations of Virgo and Coma Berenices. Galaxies are not spread uniformly through space, but are gregarious. Small numbers of galaxies form structures called groups. The Milky Way is part of the Local Group, of which Andromeda (M31) and Triangulum (M33) are the two other large members. In addition, the Local Group contains at least 50 much smaller dwarf galaxies, and probably many more which have yet to be discovered.

Looking a little deeper, to galaxies that appear rather smaller because of their greater distances, there are numerous small groups of galaxies around the Local Group. In Ursa Major, Bode’s Galaxy (M81) forms a group with its smaller com-panion M82 and other associated objects, as do the clumps of galaxies in Fornax and Dorado.

Galaxies sometimes congregate together into much larger structures still, which are called clusters, though the dividing line between large groups and small clusters is fuzzy. By far the most prominent example of a galaxy cluster in the night sky is also the nearest such object—the Virgo Cluster. In Fig. 9.1 this congregation of galaxies is readily apparent at around right ascension 13 h; declination 15°N.

By looking at how deep sky objects are distributed around the night sky, it is possible to learn about some of the largest three-dimensional structures in the Universe, in much the same way that the movement of the planets describes the local structure of our solar system.

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Fig. 9.4 The Milky Way’s globular clusters form a spherical distribution around its center. This figure is an artist’s impression of how they would appear from a distance

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Extrasolar Planets

People have long wondered whether other stars have planetary systems like our own solar system. It is a question that has direct relevance to our place in the Universe. Do most stars have planetary systems, or is ours a rare quirk of nature? Among planetary systems, is ours typical, or extraordinary? How common are potentially habitable planets?

Until the 1990s, the planets of the solar system were the only such bodies that had ever been observed, and it was only possible to speculate whether similar bod-ies might be common or rare elsewhere in the Universe. This changed in 1992, when the first detection was made of a planet orbiting a star other than our own—an extrasolar planet or exoplanet—and since then, many hundreds of further discover-ies have been made. Based on the number that have been found, the first indications are that planetary systems are very common, and that our own galaxy alone is likely to contain many billions of them. It would appear that the planets found around other stars are an assortment of both gas giant and terrestrial planets. For the first time, it has become possible to objectively think about our own solar system as one of a large family of planetary systems—and perhaps as a fairly typical member of that family.

Direct Detection

Taking images of planets in orbit around other stars is very difficult, and in most cases impossible, for two reasons. First, the distances at which planets orbit their parent stars are tiny compared to the distances that separate stars, which means that planets appear very close to their parent stars in the sky. For example, an Earth-like planet orbiting our nearest star, Proxima Centauri, would appear slightly less than

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an arcsecond away from it. Most of the sky’s brightest stars are at least ten times more distant than this, making any planets around them appear at even smaller separations from them still.

Moreover, planets do not produce their own light, but only reflect that of their parent stars. Seen from a large distance, the Earth would appear to shine with around a billionth the light of the Sun. The solar system’s largest planet, Jupiter, would appear around four times brighter. Even though Jupiter is over ten times larger than the Earth, it also orbits the Sun over five times further out, meaning that its surface, although large, is less brightly illuminated.

To date, a handful of direct observations have been made of the light of planets around other stars, the first of which was made by the European Southern Observatory’s Very Large Telescope (VLT) in 2004. However, the planets observed in this way have inevitably shown little similarity to those of our own solar system, by virtue of the fact that any systems as compact as our own would be quite impos-sible to detect. Instead, the systems discovered have had very large planets—typi-cally several times more massive than even Jupiter—in very distant orbits about their parent stars, where their light is easier to distinguish from their parent’s glare. So massive are many of these planets, that several claimed discoveries have subse-quently had to be withdrawn, after the objects found have turned out to be so mas-sive that they are able to fuse hydrogen in their cores: by definition, these are not large planets, but small faint stars in binary orbits around brighter companions.

Planets Around Pulsars

Of much greater interest have been planetary systems uncovered by a range of more subtle techniques, that indirectly detect the presence of planets by measuring the influence that they have on surrounding objects. Not only have these tech-niques allowed a vastly greater number of planets to be discovered, but they have also allowed the detection of planetary systems which are much more like our own.

Planets exert a gravitational pull on any objects that happen to be around them. When a planet orbits its parent star, it is not strictly the case that the planet travels in circles while the star remains stationary. Just as the planet feels a gravitational pull towards the star, the star also feels a gravitational pull back towards the planet. However, because the star is much more massive—it has much more inertia—it moves over much smaller distances in response to this force. Strictly speaking, the two bodies both circle around their combined center of mass, but this is very much closer to the star than it is to the planet (see Fig. 10.1 ).

It was the detection of such a gravitational pull that was used to make the first ever discovery of an extrasolar planet, found in 1992 around the pulsar PSR B1257 + 12. Pulsars are a type of neutron star that emit pulses of radio radiation at very regular intervals, keeping time with similar precision to the best atomic clocks on Earth. If such stars have planets, their back-and-forth wobbling motion

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is relatively easy to detect, since the pulsar’s radio pulses take longer to reach Earth when they have further to travel. Even though the distance over which the pulsar moves may be very small by astronomical scales, the regularity of such a star’s pulses is precise enough that even a tiny retardation can be detected. In the case of PSR B1257 + 12, this movement was found to be over a distance of around 900 km—enough to produce a difference in pulse arrival times of around 3 ms. However, the pulsar itself pulses with vastly greater time precision than this, once every 6.2 ms.

One limitation of this method is that it cannot detect any side-to-side motion of the pulsar within the plane of the sky, but only changes in its distance from the Earth. Specifically, if our line of sight were to align exactly with the axis of a planet’s orbit, there would be no detectable signal, since the pulsar would merely trace tiny circles in the sky without any significant change in its distance. Conversely, if a planet’s orbit were to be seen edge on, the variation in its host star’s distance from us would be equal in magnitude to the full diameter of its wobbling circular path. For all realistic orientations which lie somewhere in between these two cases, the signal would be of intermediate strength.

A more serious limitation of this method is that it only works to find planets around pulsars. Not only are pulsars rare and rather faint stars, but they are also the remnant cores of stars that remain after supernova explosions. Any planetary sys-tems which remain around them are unlikely to show much similarity to our own solar system, having once been in orbit around a star which swelled up to several times its original size to become a red giant, and which then produced such an extreme terminal burst of radiation.

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Fig. 10.1 As a planet circles around its host star, both objects feel gravitational pulls towards one another. This means that it is not strictly true that the star remains stationary while the planet circles around it; instead, both objects circle around their common center of mass. However, because the star is very much more massive than the planet, their combined center of mass is much closer to the star than to the planet, and it appears as if the star were very nearly stationary

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Indirect Detection: Radial Velocity

With a little modification, a similar technique can be applied to more normal stars. As these stars wobble back and forth, a minute alternating redshift and blueshift is produced in their spectra as a result of the Doppler effect. Typically, the wobbling motion is at speeds of no more than a few meters per second, and perhaps much less still, but this motion shifts spectral features in the star’s spectrum to alternately shorter and longer wavelengths, albeit by only one part in a hundred-million. To detect such a tiny shift in the wavelengths of spectral features, it is necessary to identify an incredibly sharply-defined feature to keep track of, and to have a very high resolution spectrometer. The first discovery to be made by this technique was of a planet orbiting 51 Pegasi, found in 1995 by Swiss astronomers Michel Mayor and Didier Queloz. To date, several hundred further discoveries have followed.

Indirect Detection: Transit Method

The principal drawback of searching for planets by looking for wobbles in the spectra of stars is that it is not easy to continuously monitor a large number of stars. A high-grade spectrometer is needed, and each spectrum requires painstaking analysis. Only one, or at most a handful, of stars can be observed at once, and so a systematic survey of all of the stars of the night sky would be a very time- consuming business. In the absence of any knowledge as to which stars might have easily-detectable planets, it is difficult to know where to start.

For this reason, an alternative method has proven more popular in recent years, which can be readily applied to much larger numbers of stars in each single obser-vation. It makes use of the fact that a planet orbiting around a star may occasionally appear to pass in front of it, causing the star’s light to become slightly dimmer for a few minutes or hours. Such an event is termed a transit —a generic term for any event in which one astronomical body passes in front of another—and so this method is called the transit method .

The transit method can only detect planets whose orbits happen to be inclined almost exactly edge-on to our line of sight, since planets orbiting in any other orientation never appear to pass directly in front of their host stars. The exactness of the alignment which is needed depends on both the physical size of the planet and on the size of its orbit, but can be precisely quantified for any given configura-tion. For example, an Earth-like planet, in an Earth-like orbit, has a chance of around 0.5 % of producing transits when seen from a very large distance. A crucial assumption made when analyzing such observations is that the orientation of plan-etary systems are entirely random and uncorrelated between stars, so that even if only 0.5 % of Earth-like planets are detectable, these 0.5 % are a randomly selected and representative sample. Once a few such planets have been identified, a reasonable estimate of their total number can be found by multiplying the num-ber observed by 200.

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This rather low efficiency with which the transit method is able to detect planets is more than compensated for by the ease with which very large numbers of stars can be simultaneously monitored. It is true that, as compared to a hypo-thetical perfect technique for detecting all Earth-like planets, the transit method needs to observe 200 times as many stars for each discovery it makes. But, there is no shortage of stars in the night sky, and the principal factors that limit any search for exoplanets are observing time and the power of the computers that analyze the data afterwards. The transit method has the advantage that a single image of the night sky can contain a thousand or more stars, each of which can be individually monitored.

A greater technical challenge for anyone trying to implement it is that planets are relatively small in comparison to stars, and even when they do transit their host stars, they only block a tiny fraction of that star’s light. Seen from afar, the dimming of the Sun’s light when it is transited by Jupiter would be less than 1 %, and its dimming when transited by a small terrestrial planet like the Earth would be less than 0.01 %. Moreover, there are many other phenomena that cause stars to appear to vary in brightness of their own accord, ranging from intrinsic variability in the stars themselves, to weather conditions in the Earth’s atmosphere.

To separate out transits from other sources of variability, detailed analysis is needed. The crucial hallmarks of a genuine transit are that the star’s light dims very rapidly when the planet first moves in front of it, remains steady for the duration of the transit, and then brightens again very rapidly at its conclusion. Furthermore, transits happen at regular intervals—on each orbit of the planet. Typically the dis-covery of a planet cannot be announced until it has been observed to make several transits, each separated by a well-defined orbital period. If the planet fails to re- appear on cue, any claim of its discovery is clearly bogus.

Among instruments that have used the transit method from the ground, SuperWASP uses two robotically controlled observatories, scanning the northern and southern skies from La Palma and South Africa in an entirely automated fash-ion. Using wide-field camera lenses, coupled with high-grade CCD cameras, each image taken by SuperWASP measures more than twenty degrees across. However, despite the excellent weather conditions at both sites, atmospheric conditions severely limit the project’s ability to pick out the very modest transits that are pro-duced by small planets. Space-based instruments have the advantage of being free from such atmospheric interference, and at the time of writing, two space-based telescopes are working exclusively on searching for transits—COROT (2006–2012) and Kepler (2009–2013)—the latter continuously monitoring 145,000 stars.

Selection Biases and Hot Jupiters

All of the methods described above have a much greater chance of discovering large planets as compared to any smaller siblings that orbit the same stars. For the radial velocity method, what matters is the planet’s mass: the more massive the star, the greater its gravitational pull on its host star, and the larger the wobbles in that

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star’s position. For the transit method, what matters is the planet’s physical size: larger stars block out more of their host star’s light when they pass in front of it.

In addition, both methods preferentially detect planets that are very close to their parent stars. For the radial velocity method, what is detected is the velocity of the star’s movement along our line of sight to it, and this is greatest when the star is pulled back and forth by the strong short-range gravitational pull of a planet that is close to it. For the transit method, the edge-on orientation that is needed for transits to occur must be much more exact for planets in the outskirts of a planetary system than for those close in to its center. Moreover, discoveries made by both methods are not generally considered secure until the planets found have been observed to complete multiple orbits, repeating with a well-defined period. The Earth’s orbital period is a year—and Jupiter’s is nearly 12 years—which means that discovering planets like these takes several years, even if their signatures are spotted straight away. By contrast, planets in much closer orbits around their parents yield the required body of evidence much more quickly.

In one sense, it is not surprising, then, that a large fraction of the extrasolar planets that have been discovered to date have been rather on the large side, and that their orbits have tended to be on the close side. But what is surprising is that many of these planets have been found to be larger than Jupiter, whilst simultaneously circling stars in orbits that are closer even than that of Mercury. According to theo-ries of planetary formation, gas giants should not be able to form that close to a star, but only in the planetary system’s outskirts, beyond its snow line. Moreover, such objects don’t appear to be mere occasional flukes of nature, but have been discov-ered in substantial numbers, suggesting that they are actually quite commonplace. As a class of planet, they have been given the name hot Jupiters to reflect the fact that, of all the solar system’s planets, they are likely to resemble Jupiter most closely in composition and structure, while also being much hotter on account of their being so much closer to their parent stars.

Planetary Migration

The only way to reconcile theories of planetary formation with these observations is to suppose that hot Jupiters must have formed much further out in their planetary systems, beyond their snow lines, but then to have subsequently undergone a drastic inward migration. In this picture, it is supposed that most planetary systems broadly resemble our own at the point when they are newly formed—with any terrestrial planets in relatively close orbits around their parent stars, and any gas giants further out. But something happens to some of these systems that later causes them to undergo a radical change in structure, and for their gas giants to migrate inwards.

Such a migration would involve the transfer of a very large amount of energy: the gravitational potential energy of a gas giant when it is in a circular orbit at a distance of tens of astronomical units from its parent star—as are the solar system’s gas giants—is vastly greater than that of the same gas giant when it is in an orbit which measures a fraction of an AU across—as are most hot Jupiters. Where does

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that energy go? It is like rolling a cannon ball down a steep incline, and expecting it to come to a halt at the bottom without dissipating its energy by smashing into something.

One possibility is the gas giant’s energy gets transferred to another planet: that there is some mechanism by which gravity can exchange energy between two plan-ets, such that one becomes much more tightly bound to its parent star while the other becomes much less tightly bound. Perhaps the latter may even achieve escape velocity—which is to say it may escape the star’s gravitational field altogether.

Another possibility is that such migrations occur when the planetary system’s host star has a close encounter with one of its near neighbors—when a nearby star flies close past the planetary system and perhaps perturbs the gravitational field that its planets feel enough to briefly disrupt their orbits. Such events are called tidal interactions, since they are analogous to the perturbations that the Moon contributes to the Earth’s gravitational field, and computational simulations of such encounters suggest that they can indeed often lead to some planets being ejected from plane-tary systems, while others end up in very tightly bound orbits.

One of the striking features of our own solar system is that the planets all orbit the Sun in the same plane, and that this is closely aligned with the Sun’s own rota-tion axis. As we saw in Chap. 3 , this fits neatly with the idea that the Sun and all its planets formed from a common rotating and collapsing disk of material. At the end of this process, the Sun’s own rotation and the orbits of its planets all ended up aligned with the rotation axis of this original disk. However, it is also striking that not all of the exoplanet systems that have been discovered have followed this pat-tern, which theories of planetary formation might suggest to be universal. Specifically, it is those systems with hot Jupiters that tend to deviate from it. In these systems, there tends to be very little correlation between the star’s own spin axis and the planes of the orbits of its planets. Where there are multiple planets, they often orbit their parent star in entirely different planes. By contrast, those exo-planets systems which are more like our own in having their gas giants confined to their outskirts, tend also to share its flat planar structure.

This gives credence to the idea that hot Jupiters form when planetary systems are disrupted by close encounters with other stars, since one of the predicted effects of such encounters is that they may radically alter the orbital planes of planets.

Free Floaters

If any of these present models are correct, however, they suggest that galaxies typi-cally have large populations of free-floating planets, that have been cast out of planetary systems and left to drift through their galaxy’s interstellar expanses. We can suppose that such planets must be very cold, dark and lonely worlds, experienc-ing perpetual nighttime. The average temperature of solid particles in the Milky Way is between 15 and 20 K—equivalent to around −255 °C—and it is towards this eventual temperature that such planets will eventually cool as they lose any of their residual warmth.

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Such planets, however, are very challenging to detect. Planets normally only shine by reflecting the light of their parent stars. They do produce thermal infrared radiation, but this relies upon their being warmer than their surroundings: once such planets have cooled down, even this infrared emission is indistinguishable from that of surrounding dust. Two methods are, however, available to detect them. First, if there are a large number of them in the galaxy, then they ought to pass in front of stars from time to time. Although this might be expected to dim the light of the obscured star, in fact the opposite happens. The planet’s gravitational field bends space in its vicinity as a result of Einstein’s general theory of relativity, and this means that the planet acts like a small lens, magnifying the observed image of the star. This effect, termed microlensing , more than counterbalances the fact that the planet absorbs some of the star’s light, because the planet’s gravitational field extends far beyond the planet’s surface.

Searching for free-floating planets by detecting their microlensing events is very similar to searching planetary systems by the transit method: both require the brightnesses of large numbers of stars are monitored over a long period. However, instead of looking for brief dips in the brightnesses of any of the stars, brief enhancements in their brightnesses are searched for. In practice, the same observa-tions can often be used for both purposes. However, microlensing events are very much harder to verify, since they are one-off coincidental alignments that never repeat. Genuine transit events recur at regular intervals, and if they do not, they can be discarded as spurious. But when a free-floating planet passes in front of a star, it only briefly makes itself known to the world before drifting onwards through the darkness of the galaxy, almost certainly never to be seen again by human eyes.

Early results have suggested that microlensing events are very common indeed, and that there may be significantly more free-floating planets in the Milky Way than there are stars. However, given the difficulty in verifying individual microlens-ing events and the impossibility of making any follow-up observations, consider-able uncertainty remains.

The first direct detection of light from a free-floating exoplanet was made in 2012, using the Canada–France–Hawaii Telescope (CFHT) and the Very Large Telescope (VLT). A patch of sky around a group of recently-formed stars—the AB Doradus moving group—was systematically scanned for faint objects. This particu-lar patch of sky was chosen working on the assumption that planetary systems are most likely to undergo catastrophic rearrangements in their early history, and that the vicinity of a group of young stars might therefore be the most likely place to a spot a recently-ejected planet, which might still have enough residual warmth to produce a faint infrared glow. A single such planet was detected, CFBDSIR2149-0403, indeed glowing faintly in infrared light, which was believed to have a mass of between four and seven times that of Jupiter. Though one such detection provides little information about how common such objects might be, it nonetheless demon-strates that the brightest free-floating planets are now within reach of the world’s largest telescopes, and that there may be a realistic prospect of detecting a sizeable number of them in coming years.

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Exotic Systems

To date, one limitation of exoplanet searches has been that the data analysis has had to be done entirely automatically. For example, the Kepler Space Telescope has been continuously monitoring the brightnesses of 145,000 stars to search for transit events, and it would not be practical for any human research team to manually inspect such a vast dataset by hand. Instead, computers must be programmed to identify transits and to distinguish them from other sources of stellar variability. Such computerized searches tend to pick up only those events that match research-ers’ prior expectations. Computers are good at spotting things for which they have been programmed to look, but they lack the intelligence to spot unexpected patterns which may represent quite unexpected discoveries.

When searching for transits, these computer programs typically reject any plan-ets which appear to be in unlikely orbits, on the grounds that they are almost cer-tainly spurious. It has rapidly become evident, however, that planets are not restricted to being found in the places where we might expect to find them. For example, it is difficult to imagine how a planet might form around a close binary pair of stars, rather than a single star, where they would be subjected to a gravita-tional field that was forever fluctuating as their two suns circled around each other. Remarkably, several planetary systems have been found in which one or more planets orbit in exactly such an environment. More extreme still, one exoplanet has been discovered in an environment where anyone on its surface would see four separate suns in its sky. This planet itself orbits around a binary pair of stars, while another pair of stars orbits around the first pair at a much larger distance.

This latter system was discovered by the Planet Hunters project, a citizen sci-ence project which is part of the wider Zooniverse collection of projects, of which Galaxy Zoo was the first and remains the most famous. Planet Hunters operates by inviting visitors to their website to visually inspect data from the Kepler Space Telescope, and to look for and flag any transit events that appear. To date, hundreds of thousands of people have contributed to the project, and with such a large army of volunteers it has been able to compete with the computerized pipelines that are more usually used to identify transits. Because humans can spot patterns even when they occur in unexpected ways, Planet Hunters has been able to find planets that the automated search systems have rejected as being too improbable to be real.

Where Next?

A picture has emerged from exoplanet search programs in recent decades, in which planetary systems appear to be very common adornments around stars, and in which they even seem to form quite readily in environments where it was previ-ously thought quite impossible that they might do so. It seems that there may be at least as many planets in our galaxy as there are stars. The first indications are that

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our own solar system is probably quite a typical specimen of an undisturbed planetary system, but it also seems that many other planetary systems have had rather more violent histories than our own, in which their gas giants have undergone large migrations. Though a lot of questions have been answered in a very small number of years, it is likely that progress in coming years will go far beyond simply enlarging the catalogue of known exoplanets.

To better understand how protoplanetary disks can manage to condense diffuse clouds of minute dust particles into large rocky bodies, what is needed is an infrared telescope that can detect the thermal emission of such disks, whilst simultaneously being able to image them with a sufficiently high resolution to separate their light out from that of the stars at their centers. The Atacama Large Millimeter Array (ALMA), an array of 64 sub-millimeter-wave antennas at an altitude of 5,000 m in the Chilean Andes that resembles an array of radio telescope dishes in appearance, is likely to make substantial progress here.

To understand more about the environments of extrasolar planets, it is necessary to know more about them than simply their radii and masses. Presently, transit and radial velocity detections offer little, if any, information beyond this. Two space- based telescopes have been proposed that would have been able to take images of exoplanet systems with sufficiently high resolution to single out the light from Earth-like terrestrial planets in orbit around some of our closest neighbor stars. By taking spectra of them, they would have been able to determine the compositions of their atmospheres. However, both of the projects considered to date were deemed too ambitious to warrant government funding, and were shelved indefi-nitely in 2007. This decision is understandable: the European project, Darwin, would have involved flying three telescopes of similar size to the Hubble Space Telescope in a formation, with the positions of each of the individual telescopes monitored to within a few tens of nanometers—about a hundred times the width of an atom. The American Terrestrial Planet Finder (TPF) would have been similar in design. Though these projects would have carried huge pricetags, which they are likely to share with any similarly capable telescopes that may be proposed in the future, the recent pace of exoplanet discoveries makes it likely that their time will eventually come.

The rate of progress that exoplanet search programs have made in advancing our understanding of the Earth’s place in the Universe has been unparalleled in the his-tory of science. Even if much has been achieved in only two decades, it seems that the next few decades may hold more exciting discoveries still.

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Appendix A

Astronomical Imaging

Camera technology has developed remarkably quickly over the past two decades. Just as daylight photography has been transformed by the arrival of digital cameras—which are now so small and cheap that they can be embedded into laptops, smartphones and tablet computers—many of the same devices are also ideally suited for astronomical photography. Before their sudden arrival, photo-sensitive films had been the only technology available for astronomical photogra-phy, and had been in use for almost 150 years.

In the 1990s, digital cameras were crude devices, ideal for beginners who wanted the instant feedback that their displays could provide, or who liked the ease of not having to develop endless rolls of film. But they could not compete with the high-end film cameras used by more serious photographers, since their sensors lacked the very high resolution that could be reached by the best film cameras. Each pixel in a digital camera is a tiny light-sensitive electronic component, which needs to be wired up. Making these pixels small enough to rival the resolution that could be achieved by the traditional method of spreading light-sensitive chemicals across a film proved very challenging.

Since then, however, digital cameras have sold in such vast numbers that it has become economic to put a vast development effort into building sensors with ever- larger numbers of ever-smaller pixels. At the time of writing, cameras are routinely built with more than ten million pixels (megapixels), fabricated and sold at a cost of much less than a thousandth of a cent per pixel. The turning point came in around 2005, when the resolution of moderately-priced digital cameras had become high enough that even most professional photographers found their images no longer inferior to those produced by film cameras, but their instant feedback much more convenient to use.

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Simultaneous with the revolution that has occurred in daylight photography, astrophotographers have also almost universally hung up their film cameras in favor of digital devices. Digital sensors have turned out to perform substantially better than film in low-light conditions, meaning that the gap between the image quality achieved by terrestrial and astronomical photographers has closed considerably. Even though developing cameras specifically for astronomical use is highly expen-sive, it has been possible to merely repackage chips built for webcams into cases that can be mounted onto the back of a telescope. This is a fast-moving area, and so this appendix does not recommend particular camera models, but it provides an overview of some of the techniques used by astrophotographers which are likely to remain constant in years to come.

Historical Astrophotography

The art of astrophotography is almost as old as that of photography itself. The nineteenth century polymath John Herschel was not only an astronomer, but also a chemist who experimented with early photographic films, inventing the cyanotype process in 1842. The intrinsic faintness of astronomical objects has always been a challenge for those trying to capture them on film. Indeed, the principal problem that almost all astrophotographers struggled to solve until very recently was to find ever-more sensitive films or sensors, which would reduce exposure times to within reasonable bounds. The first known successful astrophotograph was taken by John Draper (1811–1882) in March 1840, who caught the Moon on film with a 20-min exposure. The improvement in technology that has occurred in the 170 years since then is demonstrated by the fact that a modern astrophotographer would typically use an exposure of around a tenth of a second or less to take the same image today of this, the night sky’s brightest object.

By the mid nineteenth century, progress was being made in developing more sensitive films and the range of objects accessible to astrophotographers was grow-ing. In 1850, Vega became the first star to be captured on film, photographed by William Bond (1789–1859) and John Whipple (1822–1891). The following year’s solar eclipse was the first that is known to have been photographed. The first image of the spectrum of a star followed in 1863. Faint fuzzy objects—nebulae—proved considerably more difficult, and the first image of the Orion nebula (M42) was not captured until 1880, by Henry Draper (1837–1882) using a 51-min exposure through an 11-in. refractor.

Many of the problems with which the pioneers had to grapple remain current today. Any telescope that is used for astrophotography must remain firmly centered on the same particular patch of sky for the whole duration of each exposure, to avoid forming a blurred image. The telescope must follow the sky’s diurnal rota-tion, and although a motorized drive can help, inevitably any device that simply rotates the telescope in right ascension once every 23 h and 56 min will have defects that cause it to drift over time. Among these, the telescope’s mount may not be

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properly aligned to the celestial pole, causing the drive to rotate the telescope about the wrong point; alternatively, the drive motor itself may not move at a perfectly steady rate; or the drive motor may not run at quite the right speed. Moreover, even the sturdiest mount may have some susceptibility to being shaken by the wind. To correct for any or all of the above, a device called a guider—which may be either human or automated—is usually needed to monitor the alignment of long expo-sures and occasionally give the telescope a nudge.

Three years after Henry Draper’s initial image of the Orion nebula, Andrew Common (1841–1903) and George Calver (1834–1927) pioneered a new mecha-nism for manually guiding telescopes over long periods, which allowed them to expose a single piece of film for 90 min in 1883 (see Fig. A.1 ) without appreciable drift in the telescope’s pointing. Later in the same decade, the Paris Observatory was confident enough about the new technology to establish a world-wide collab-orative project to photographically survey the whole sky—the Cartes du Ciel—though this over-ambitious project ended up taking decades to complete, and the last observations not taken until 1950. The full survey was eventually published, nearly 80 years later, in 1964.

The Advantages of Digital Sensors

Despite over a century of refinements to the chemistry of photographic films, digi-tal sensors have brought three immediate advantages over film photography. Firstly, the sensors themselves are intrinsically much more sensitive to light. Even the most sensitive films—often chemically modified by astronomers using a range of tech-niques collectively called hypersensitization—only respond to a few percent of the photons of light that fall on them. By contrast, modern charge-coupled devices (CCDs) typically have quantum efficiencies in excess of 70 %, meaning that more than 70 % of photons falling on them are detected, and correspondingly that expo-sures of a fraction of the length are needed to reveal comparable detail.

Secondly, digital sensors have vastly superior dynamic range to film. Many astronomical objects have large contrasts between bright features and fainter struc-tures that are visible around them. This is especially true in the deep sky: the central regions of galaxies and globular clusters often vastly outshine their extremities. But it is also an issue that affects any planetary imager who wants to photograph the Moon occulting Jupiter, Mars passing through the Pleiades, or the moons of Saturn alongside their parent planet. Mars’s two moons Phobos and Deimos are so faint that they are almost impossible to separate from its glare, and even with modern sensors, anyone who manages to capture an image of either can count themselves an astrophotographer of the highest caliber.

Photographic film invariably has poor dynamic range, because individual pho-tons are more likely to trigger chemical reactions in the film in the presence of other photons. In other words, well illuminated areas of photographic film are more sensitive to light than less illuminated areas. This effect, known as reciprocity

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Fig. A.1 The development of astronomical photography: the Orion nebula (M42), as photo-graphed by Henry Draper (1880; top-left ), Andrew Common and George Calver (1883; top- right ) and by the Hubble Space Telescope ( bottom )

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failure, makes it very easy to take images where bright areas of the frame are over- exposed, while darker areas are simultaneously under-exposed. By contrast, modern CCDs work by counting the number of individual photons that land on each individual detector element (pixel), and so their response is very nearly linear: a pixel which reports twice the illumination of another pixel received twice as many photons during the course of the exposure.

Perhaps the greatest revolution brought by digital sensors, however, has been the immediate feedback that they provide. In the past, focusing was a highly approxi-mate art, with no direct means of assessing the sharpness of the image that was falling onto a piece of film until it came to be developed. Effects such as the thermal contraction of a telescope tube over the course of the night due to the falling ambient temperature were virtually impossible to mitigate. The result was that pho-tographic setups gradually drifted in and out of focus. By contrast, it is now possible to routinely take test images throughout the night, and the focal position of a camera can be periodically adjusted. The task remains one of the most tedious aspects of astrophotography, but the results are far superior to what was possible in the past.

The immediacy with which images taken by digital cameras can be accessed has allowed them to feed data directly into telescope control software. In the past, the only way to ensure a telescope remained properly aligned on a target was to mount a separate guidescope on the back of the telescope. The alignment of this guides-cope would be adjusted, usually with thumbscrews, until a bright guide star lay on its cross-hair. Then, the telescope would be manually nudged by the photographer whenever the guide star drifted. Often this process would be continued for hours on end in freezing cold conditions.

Lately, autoguiders have eased the boredom and thermal discomfort of this pro-cess. They work by mounting a second CCD onto the back of a telescope, which feeds its images directly into the telescope’s drive software. The software identifies stars in these images, and continuously monitors their positions, subtly adjusting the telescope’s drive rate to keep them in fixed places.

Imaging Setups

The quickest and simplest way to photograph the night sky is to mount a consumer digital camera onto a tripod and to open its shutter for around 30 s. This can pro-duce compelling images of the constellations and, from a dark enough site, of the Milky Way. However, to see fainter objects, and to obtain less grainy images, it is necessary to collect light over a longer period. Using a static tripod, this is difficult, since any single exposure of longer than 30 s will begin to blur due to the sky’s rotation. Two solutions are possible: either the camera can be mounted onto the back of a telescope which does track the sky, or multiple photos can be taken and subsequently co-added in a software package which can shift them into alignment—a process called stacking. The freely-available package RegiStax is commonly used to do this.

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Higher magnification can be achieved with an SLR camera by removing its front lens and mounting the camera body onto the back of a telescope with an adaptor called a T-ring. The image formed by the telescope’s primary mirror or lens can then be focused directly onto the camera’s sensor. This configuration is called prime focus imaging, since the image formed by the telescope’s primary mirror or lens is not subsequently magnified by an eyepiece. It is generally used for deep-sky observing, since it achieves a moderate magnification over a wide field-of-view.

Still higher magnification can be achieved by placing an additional lens between the camera’s sensor and the image formed by the primary lens, which acts as a magnifying glass. This lens may either be integral to the camera, or a standard eyepiece, in which case the configuration is called eyepiece projection. This is more often the technique of choice for planetary imagers, since the planets present very small disks which need to be highly magnified to reveal much surface detail.

Reducing Noise

Any camera records not only an image of the pattern of light it receives, but also unwanted noise which makes images appear grainy. Each pixel of a charge coupled device (CCD) counts the number of photons that have landed on it by storing elec-trical charge in proportion to the amount of light it has received. Noise can arise in this counting process from a variety of sources. For example, read-out noise stems from inaccuracies in the process of measuring how much charge has accumulated on each pixel at the end of the exposure, and transmitting these data back to the computer driving the camera. Pixel noise is associated with malfunctioning or over- sensitive pixels in an array. Thermal noise stems from a gradual accumulation of charge on each pixel from processes other than the detection of light. The last of these is an especial concern for astrophotographers, as it accumulates over time and affects long exposures especially badly.

Much of the nuisance of thermal noise can be alleviated by the fact that it accumulates in a way that is roughly independent of the amount of light received by the detector. An image taken through a telescope with its lens cap on—called a dark frame—should be completely dark in the absence of thermal noise. In practice such an image will not be perfectly dark, and the amount of light that each pixel claims to have detected can be used to measure how much thermal noise it generates. It is subsequently possible to simply subtract such dark frames from images taken of the sky. For best results, dark frames should be taken in the field, and perhaps repeatedly at intervals through the night, since thermal noise can depend on ambient conditions—especially temperature, as its name suggests. Dark frames should also ideally be taken with the same exposure length as will be used to image the sky, since although it is usually a fair approximation to assume that thermal noise accumulates at a steady rate, and that a frame with twice the length of exposure will have exactly twice as much thermal noise, this may not be perfectly borne out in reality.

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Pixel noise is a more difficult problem to alleviate. Individual pixels in digital cameras have different sensitivities to light. This may be intrinsic to the electronics of the pixels themselves, or may reflect the presence of dirt in the camera or else-where in the telescope tube. Even if the camera’s optics are perfectly clean, the edges of images are often less well exposed than the center of the frame—an effect known as vignetting. Vignetting can stem from a variety of causes in particular telescopes, including obstructions in the optical path that reduces the telescope’s effective aperture for off-axis light. In wide-field imaging, a camera’s effective aperture is invariably reduced towards the edge of the frame, since its front aperture presents a smaller collecting area for incoming light when viewed obliquely (at an angle) as compared to when viewed straight-on—an effect known as natural vignetting.

Such non-uniformity can be corrected by first taking an image of a uniformly illuminated white screen, called a flat frame. A perfectly calibrated detector should record a perfectly smooth image when pointed at such a screen. If there is any deviation from constant brightness in the image that a camera produces, this is a measure of its intrinsic non-uniform sensitivity, which can later be corrected in software. Because non-uniform sensitivity can stem from imperfections in both the camera itself, and the telescope it is attached to, such flat frames should ideally be taken through the entire optical chain that will later be used to image the sky. The camera should be mounted in approximately the same focal position on the tele-scope that will later be used to return a focused image of the sky. This ensures that any dirt in the telescope tube presents exactly the same obstruction to the flat frame as it will to any subsequent images of the sky.

In practice, it is not always straightforward to find a suitably blank surface for taking flat frames. Any brightness gradient across the surface will lead to miscali-bration, and can easily lead to an end result that is far worse than would have been achieved if no flat frame had been used at all, and the camera had been assumed uniformly sensitive. Commonly, either the twilight sky or an out-of-focus image of a flat observatory wall may be used. A more portable and easily reproducible solu-tion is to place an electroluminescent (EL) panel over the telescope’s aperture. Such panels are usually much brighter than is wanted for viewing through a telescope, but some opaque material can be used to cover it, providing it doesn’t introduce any pattern into the light.

Noise concerns planetary and deep sky imagers in different ways, and this often means that the cameras of choice for the two groups differ. Specifically, deep sky objects are often desperately faint, and imaging them requires thermal noise to be kept to an absolute minimum over long time periods. High-end sensors are often fitted with heatsinks to help keep them cool. For planetary imaging, a much higher magnification is wanted, and, as later sections will show, a large number of short, fast exposures are usually taken. This means that thermal noise is less of a con-cern, but read-out noise must be kept to a minimum. In practice, it has often been found that cheap consumer webcams have been designed to meet almost exactly the same noise requirements. Many successful planetary imagers have used the Philips ToUcam range of webcams in recent years, with a little modification to its

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mounting. More recently still, however, this trend has reversed somewhat. At the time of writing, the majority of consumer webcams are now built using cheaper CMOS sensors rather than CCDs. CMOS sensors have significantly worse noise characteristics, and so planetary imagers have once again had to return to using high-end sensor chips.

The Atmosphere

The atmosphere poses two problems for astrophotographers. Firstly, water vapor and other tiny particles in the atmosphere mean that it is never quite transparent. This is at its most obvious when the sky is cloudy, but even on supposedly clear nights, some haze typically remains, and depending how much there is, the sky is said to have good or bad transparency. This has two effects: it attenuates the light from astronomical objects and, more seriously, it reflects light pollution coming from below, usually giving the sky a faint uniform orange glow when observed from a built-up area. Haze also scatters moonlight when the Moon is above the horizon, making it very difficult to observe faint objects.

Transparency is a serious issue for deep sky observers because of the faintness of most nebulae: only a very little haze is enough to entirely swamp their diffuse glow. The light of the Moon is a particular menace, being such a bright source of scattered light that even when the atmosphere is comparatively clear, it is virtually impossible to image deep sky objects when it is far above the horizon. For plane-tary imagers, transparency is much less of an issue. The planets are all quite bright, which means their light has little trouble in exceeding the sky background. Moreover, a diffuse haze that appears to cover large portions of the sky tends to decrease in brightness when it is magnified. Even if the haze appears bright to the naked eye, the eye is seeing the total amount of scattered light that comes from areas of sky measuring arcminutes across—the smallest angular scales that the eye can resolve. The total amount of scattered light coming from any given patch of sky which measures only a few arcseconds across will be much less. Yet this is the typical field-of-view of a telescope that is being used to view the planets, and so this is the amount of scattered light that will appear in the frame and that the light of the planet must compete against. On occasion, I have found it quite possible to observe the brighter planets through a telescope even when they have appeared to be entirely shrouded in cloud to the naked eye, though never with any particular clarity.

The second problem that the atmosphere poses is of much greater nuisance to planetary imagers: seeing . When any of the planets are observed at high magnifica-tion, their surfaces appear to be shrouded in a rippling heat haze. To the eye, the effect is most apparent when looking at the Moon, on account of its brightness and the large contrasts that can be seen where crater rims cast sharply-defined shadows along the terminator. When long-exposure photographs are taken, the camera records an average of this rippling motion over the duration of the exposure, and

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the result is a blurred image. Typically all detail is lost on length scales smaller than an arcsecond or two. Since most of the planets only present disks a few arcseconds across, this seriously restricts the amount of detail which can be seen.

The origin of atmospheric seeing is turbulence between masses of air in the Earth’s atmosphere which have different temperatures. Heat haze appears above the spout of a kettle, because boiling hot air is rising out of the spout, and just as light refracts (bends) when it passes through a glass lens, it also refracts when passing through pockets of air with different temperatures. The refractive index of air dif-fers depending on the air’s temperature. The turbulent mass of air above a boiling kettle is rather like a chaotically arranged lens, whose components are swirling around. The Earth’s atmosphere forms a very similar optical arrangement, since the air closer to the ground is much warmer than the air above it, but convection leads the warm air to rise and the cooler air to sink.

Atmospheric seeing and transparency are typically much less of a problem at high-altitude sites, since much of the Earth’s weather arises at low altitudes in its troposphere, which mountain tops commonly lie above. This is why most profes-sional observatories are situated at the tops of some of the world’s highest moun-tains. However, relocation to such exotic locations is rarely an option for amateur observers, except perhaps for short trips, and so alternative solutions must be found.

Lucky Imaging

Until recently, visual observers could generally glimpse much higher resolution views of the planets than it was easily possible to capture with a camera. Staring at the rippling heat-haze-affected image of the disk of a planet, a visual observer will see occasional moments of clarity, when it is possible to see minute details which are normally blurred from view. In other words, the distorting effect of atmospheric seeing is not constant, but fluctuates on timescales of around a tenth of a second. Staring for long enough, the human eye is remarkably adept at putting together the fragments of detail seen in these moments of clarity, forming a mental picture of details which are lost to view most of the time. By contrast, a simple still photo-graph merely averages the swirling motion of the atmosphere over the full length of the exposure, to produce a blurred end result.

In planetary imaging, the greatest revolution of digital astrophotography has undoubtedly been in enabling a technique that allows astrophotographers to com-pete on much more even terms with visual observers, using a technique called lucky imaging . Instead of taking a single still exposure of the sky, a video camera is mounted onto the back of a telescope—typically a webcam is used—and a series of very short exposures is recorded. The term lucky imaging itself originates from a 1978 paper by the atmospheric scientist David Fried (1933 –), though the tech-nique was first attempted around two decades earlier using early cine cameras. For the technique to work, each frame of the video must be exposed for no more than around a tenth of a second—a timescale short enough that individual frames can

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catch moments of good seeing as conditions fluctuate. The simplest way to analyze the resulting video is to simply assess its individual frames for sharpness, and to keep only the best. These can then be added together to form a synthetic long expo-sure, based only on those moments of the best seeing. Historically this was a size-able computational task, done after the event, but now software packages commonly offer the facility to work in real time as the observation is being made.

The limitation of lucky imaging is that it only works if individual frames, each exposed for only a fraction of a second, detect enough light for their sharpness to be meaningfully assessed. This means that it is much better suited to planetary imaging than to deep sky photography. While the planets are generally bright enough that such exposures show some limited detail, the same is not true for nebu-lae, unless they happen to share a field with an exceptionally bright star which can be used as a indicator of seeing. Nonetheless, lucky imaging has been applied to the deep sky: in the 2000s, a team at the Institute of Astronomy in Cambridge began exploring its use for bright nebulae, using research-grade telescopes with apertures of 2 m and larger. With this much light-collecting area, it is possible to detect some structure in frames as short as a tenth of a second, and in many cases the team’s final processed images were able to achieve a resolution of better than 0.15 arcsec-onds—surpassing that of the Hubble Space Telescope (HST).

Numerous software packages are available which allow amateur planetary imag-ers to use lucky imaging, and many of them are freely available. The best known and most widely used is RegiStax. Alternatives include AviStack, which at the time of writing has facilities to not only select the best frames from a video, but also to correct the distortion of poorer frames and extract useful information from them.

Image Brightness and Magnification

Any telescope or other optical aid for imaging the night sky serves two purposes. Firstly, it magnifies small structures to allow fine detail to be seen. Secondly, it collects as much light as possible, using a large aperture, to make faint structures appear brighter. The relative importance of these two functions depends on the object being observed.

Deep sky objects are typically very faint and diffuse, but not necessarily very small. For example, our closest large companion galaxy, the Andromeda Galaxy (M31), measures five or six times the diameter of a full moon from side to side. However, it is almost invisible to the unaided eye because its dim light is diffused over such a large patch of the sky. More distant deep sky objects are typically much smaller, but also much fainter still, and their faintness remains the principal prob-lem in any attempt to observe them.

By contrast, all of the planets are fairly bright. With the exceptions Uranus and Neptune, they are bright enough to be visible to the naked eye, and even those two exceptions are within reach of binoculars. However, they present another challenge in that their disks are very small and they require substantial magnification to show any detail at all; when they are viewed visually, at least 100× magnification is needed.

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The total amount of light collected by any telescope depends only on the size of its front aperture. The pupil of a human eyeball typically measures up to 9 mm across in dark conditions, while a telescope might have an aperture that measures 8-in. (200-mm) across. By collecting light over an area that is 500 times larger, the telescope can collect 500 times more light from the sky than the human eye. However, this does not necessarily correspond to making the sky appear 500 times brighter, since the telescope also magnifies objects. Magnifying objects means that their light appears to be spread over a larger area. Taking the example of a telescope with a camera attached, as the telescope’s magnification is increased, the light from any resolved object falls over a larger number of pixels in the camera. Since the total amount of light gathered by the telescope is fixed by how large the telescope’s aperture is, and the object’s light is being spread between a larger number of pixels, each must register a lower degree of illumination when higher magnifications are used.

A convenient measure of the effective light-gathering power of a telescope, which takes into account its magnification, is the telescope’s focal ratio. This is defined as the ratio of the telescope’s focal length to the diameter of its aperture. A telescope with a large focal ratio is said to be slow —objects appear highly- magnified and faint, and photographic exposures need to be long—while telescopes with smaller focal ratios are said to be fast, since their magnifications are lower and shorter photographic exposures are needed with comparable cameras.

The exception to this rule is objects which are not resolved by the telescope. A point-like star or a small moon of Jupiter looks equally point-like when viewed through a telescope. That is to say, if a camera were attached to the back of the telescope, all of the star’s light would be directed towards a single pixel of the detector. For such objects, the spreading-out effect of the telescope’s magnification is imperceptible and can be ignored. To continue the example given above, the star would appear 500 times brighter when through an 8-in. telescope as compared to the naked eye, assuming it was sharply focused.

This means that images that contain a mixture of stars and resolved objects—either planets surrounded by nearby stars, or nebulae with embedded stars—appear differently depending on the magnification used. Resolved objects get fainter as magnification is increased; stars do not. The moons of Jupiter will appear brighter in comparison to the planet’s disk when higher magnifications are used.

Color Imaging

CCDs are intrinsically sensitive to all colors of visible light. They also have sensi-tivity to some wavelengths beyond those that are humanly visible, including most near-infrared light and some near-ultraviolet light. To make color images, filters which only transmit particular colors of light must be placed in front of the sensor. In consumer cameras, individual pixels have tiny red, green and blue filters mounted in front of them, usually arranged in a pattern called a Bayer filter in which there are two green-sensitive pixels for every one red and one blue pixel.

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This roughly mimics the performance of the human eye, which is considerably more sensitive to green light than to red or blue. The camera itself is wired to combine the information from the variously colored pixels to produce an RGB color image.

High-end CCDs used by amateur astronomers are more usually monochrome. These chips are often designed for use in security cameras, and are well-suited for the needs of astronomers because they are optimized to work well in low-light conditions. Usually they are either sensitive to the full range of colors to which CCDs are naturally responsive, or they have an in-built filter which blocks infrared light and restricts their sensitivity only to visible light. With such sensors, color images can be built up by taking multiple exposures with a sequence of different color filters placed in front of the sensor, a process that can be automated with a motorized filter wheel. The resulting images can then be combining in software. These sensors offer much greater flexibility, because they do not restrict the observer to using only three colors of filter that are pre-built into the camera. For the planets, it means that any choice of color filters can be used, to maximize the color contrasts of the planet’s features. For deep-sky observers, it opens up the pos-sibility of using narrow-band filters such a hydrogen-alpha and oxygen-III, that only collect light from specific spectral lines that appear bright in particular envi-ronments within nebulae.

Some may claim that taking such false-color images is slightly dishonest, since color contrasts are enhanced for artistic effect beyond what would be visible to the human eye—assuming, that is, that it had the sensitivity to see these objects in the first place. However, it must be remembered that the features revealed by false- color images are no less real than those that are apparent to the eye. By using color channels other than those that have evolved in the human eye, it is possible to see structures to which the eye is not intrinsically very sensitive. Color vision is not the same among all animals—many birds have a much better ability to distinguish colors than humans, which allows them to distinguish different types of berries which may be good or bad to eat. No doubt, if the survival of our ancestors had depended upon being able to see structures within astronomical objects, we would have evolved with very different eyes. Visual observers today would be able to see astronomical objects with much more vivid color contrasts than the subtle shades of yellow that often disappoint those newcomers who have grown used to viewing the Universe through the eyes of the Hubble Space Telescope.

Invariably, taking color images means reducing the amount of light collected by a CCD. Whenever a color filter is placed in front of a camera’s sensor, it throws away any light that is of the wrong color. In turn, this means that longer exposure times are needed. Given that exposure times for astronomical photos are usually already painfully long, this can be a problem. The very deepest images of the sky are invariably attained by using no color filter at all, making use of as much light as can possibly be recorded. Where cameras are supplied with infrared-blocking filters, these are often removed, to roughly double the range of wavelengths over which their sensors can collect light.

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For deep sky imaging, a common compromise is to take an LRGB image. To do this, four exposures are taken—often themselves composites of many shorter expo-sures that have been stacked together. The first is a luminance frame, taken in unfiltered light. This is often exposed for a full half of the observing time available, to attain the deepest and sharpest possible image of the brightness features in an object. This is then followed by shorter exposures through red, green and blue fil-ters, typically each lasting for one sixth of the total observing time. The luminance frame is used to set the brightness of the final image, while the filtered images are used only to set the colors of the pixels, which can tolerate being much noisier.

For imaging the planets, however, RGB imaging is still generally preferred. Features on the surfaces of the planets tend to manifest themselves as color con-trasts rather than as particularly sharp brightness contrasts, and so it is more impor-tant to have good color discrimination than a good response to low light levels.

Which Telescope?

In summary, the most pressing requirement on any telescope which is to be used for astrophotography is that it must be able to track the sky’s diurnal rotation as accurately as possible, using a reliable drive mechanism. This generally also means that the telescope’s mount must be accurately polar aligned, and that it must be as sturdy as possible to minimize wind shake. The need for accurate tracking might intuitively seem to be less of a priority for planetary imagers than for deep sky observers, since the exposures they take are relatively short. However, accurate tracking is important to planetary imagers too, since the magnifications they use are much higher, and so their images are much more sensitive to any slight drift of the field.

The need for a large aperture is less immediately pressing for astrophotogra-phers than for visual observers, since it is always possible to compensate for a smaller aperture by exposing for longer. Nonetheless, small-aperture telescopes suffer from diffraction which compromises image quality; 4-in. telescopes are lim-ited to a resolution of around an arcsecond, while an 8-in. telescope can achieve twice that resolution. While both these examples would be perfectly adequate in the absence of any correction for atmospheric seeing, planetary imagers who hope to use lucky imaging to achieve sub-arcsecond resolution would benefit from using at least an 8- or 12-in. telescope.

For deep-sky objects, for which lucky imaging is presently not feasible on an amateur budget, the only reason to use telescopes with apertures larger than 5 in. is to reduce exposure times. While there are strong incentives for doing so when col-lecting light from the faintest objects, a recent trend has been the use of small high- quality refractors for deep-sky imaging. Though it is prohibitively expensive to build refractors much larger then 4 in. in diameter, the best refractors produce sharper images than reflectors, since they do not have a secondary mirror obstruct-ing their aperture.

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Appendix B

Sources

Most of the tables of data in this book were computed by the author from models of the motion of the planets published by the Jet Propulsion Laboratory (JPL) in California. Since the 1960s, JPL has published a series of Development Ephemerides (DEs) which are used to support NASA’s space program by providing the best pos-sible information on the positions of the planets at any given moment in time. This book is based on DE405, which was published in 1998 and traces the positions of the planets to better than arcsecond resolution over the period 1600–2200.

DE405 was computed on the basis of a wide range of information about the current and historical positions of the planets, ranging from direct telescopic observation, radar distance estimates, and data from visiting spacecraft. The motion of each planet according to Newton’s laws of gravity was then simulated forwards and backwards in time to produce a table of planetary positions over the 600 years period. The resulting ephemeris is freely available from the JPL website at ftp://ssd.jpl.nasa.gov/pub/eph/planets/ascii/ although these files do not contain readable ephemerides, but rather daily lists of coefficients which may be used to compute ephemerides from Chebyslev poly-nomials. The data in this book was derived from DE405 using custom software written by the author which searches the ephemeris for alignments between astronomical bod-ies which correspond to events of interest. This same software is also used by the author’s website, In-The-Sky.org, to present live information about what it in the sky.

The dates of transits and eclipses were not computed from DE405, but taken from the following NASA publications:

Five Millennium Canon of Solar Eclipses , NASA/TP-2006-214141 Five Millennium Canon of Lunar Eclipses , NASA/TP-2009-214172 Seven Century Catalog of Mercury Transits: 1601 CE to 2300 CE , Fred Espenak, NASA Six Millennium Catalog of Venus Transits: 2000 BCE to 4000 CE , Fred Espenak,

NASA

231D. Ford, The Observer’s Guide to Planetary Motion: Explaining the Cycles of the Night Sky,The Patrick Moore Practical Astronomy Series, DOI 10.1007/978-1-4939-0629-1,© Springer Science+Business Media, LLC 2014

Glossary

Aphelion The point along a planet’s orbit where it recedes to its greatest distance from the Sun.

Arcminute One sixtieth part of a degree. Arcsecond One sixtieth part of an arcminute, equal to one 3,600th of a degree. Asterism A grouping of stars which are not one of the internationally- agreed

constellations. Astrolabe A complex instrument, most commonly used to tell the time or to forecast

when particular objects will rise and set. One side of the instrument has a sight which can be used to approximately measure the altitudes of objects in the sky. The other side has a crude brass star chart. The astrolabe’s origin is obscure—some people attribute its invention to the Greek astronomer Hipparchus—but it remained in widespread use until the invention of the telescope.

Astronomical unit A unit of distance, approximately equal to the Earth’s average distance from the Sun, 150 million km.

Babylon A city 50 miles south of modern Baghdad, where astronomical observa-tions were made by astrologers throughout much of the fi rst and second millen-niums BC .

Bode’s law A pattern observed by Johann Bode in 1772—and by Johann Titius several years earlier—that each of the gas giant planets orbit the Sun at roughly twice the distance of their inner neighbours, while the terrestrial planets are a little more closely spaced. The pattern is now thought to have little theoretical basis other than pure coincidence.

Circumpolar In the northern hemisphere, an object is circumpolar if it is close enough to the north celestial pole that it never sinks beneath the horizon. In the southern hemisphere, the same term is used for objects that are close to the south celestial pole.

232

Conjunction Any occasion when two astronomical objects appear very close to each other in the sky. Specifi cally, planets are said to be “at conjunction” when they make closest approach to the Sun. Planets at conjunction are invariably unobservable, unless they transit the Sun.

Constellation One of 88 areas into which the sky was divided by the IAU in 1930. Prior to 1930, and stretching back into prehistory, constellations were group-ings of stars that came to be associated with mythical characters, technological inventions or animals, but which did not have well- defi ned boundaries.

Decan One of 36 groupings of stars whose time of rising was used by astronomers in ancient Egypt to tell the time at night.

Declination The celestial coordinate which is the counterpart to latitude on the Earth’s surface; it measures the angle by which an object lies north or south of the celestial equator.

Doppler effect A phenomenon which means that light from objects which are receding from the observer appears redder than usual, while light from objects which are travelling towards the observer appears bluer than usual.

Draconic month The time interval between successive occasions when the Moon passes through one of its two nodes; equal to 27.21 days.

Dwarf planet A term introduced by the IAU in 2006 for bodies which are slightly smaller than planets. A dwarf planet is a celestial body that (a) is in orbit around the Sun, (b) has a nearly round shape, but in contrast to a planet (c) has not cleared all of the rocky debris from the neighbourhood of its orbit.

Eccentricity A numerical measure of how much an elliptical orbit deviates from being circular. An ellipse with an eccentricity of zero is exactly circular.

Ecliptic The path that the Sun traverses across the sky over the course of each year. Equinox One of the two occasions each year when the Sun crosses the celestial

equator, in March and September. Fusion The nuclear process by which stars are powered. In the cores of most stars,

hydrogen atoms are joined together to form heavier helium atoms, a process which releases a vast amount of energy.

Gas giant A planet whose mass is mostly in the form of gas, with no more than a small rocky core at its centre.

Gaia A spacecraft operated by the European Space Agency, launched in 2013 to measure the parallaxes of a billion stars to determine their distances.

Giant impact hypothesis A theory proposed by Hartmann and Davis in 1975 that the Moon was formed when a large planet, similar in size to Mars, collided with the Earth 4.5 billion years ago.

Giant molecular cloud A vast assemblage of interstellar gas, out of which stars may form.

Globular cluster A tight condensation of hundreds of thousands of stars, which are usually extremely old. Their origin and eventual fate remain poorly understood.

Great circle A circle in the sky which divides the sky into two equal halves. Hipparcos A spacecraft operated by the European Space Agency between 1989

and 1993, which measured the parallaxes of more than a hundred thousand stars in order to determine their distances.

Glossary

233

Inferior planet A planet which orbits the Sun more closely than the Earth. There are two inferior planets: Mercury and Venus.

Kuiper belt A collection a rocky bodies which lie around the outskirts of the solar system, at a distance of 30–50 AU from the Sun. The minor planet Pluto is the best known Kuiper belt object.

Late heavy bombardment A violent episode of meteor impacts which the Moon and Earth are believed to have experienced 4 billion years ago, evidenced by the number of Moon craters dating from this period.

Lightyear A unit of distance equal to the distance that light travels in a year, around 9,500 billion km.

Lunar calendar A system of timekeeping in which the time of year is determined by the Moon’s cycle of phases, rather than the Sun’s cycle of solstices and equinoxes. The Muslim calendar is an example.

Meridian The line across the sky which connects the cardinal points north and south on the horizon and passes through the zenith.

Metonic cycle A calendric cycle which is based on the almost exact match between the length of 19 years and 235 lunar months.

Micrometer A unit of distance equal to one millionth of a meter. Moving group A grouping of stars which are close to each other in space, but not

bound together by gravity. Several of the stars of the Big Dipper are a moving group, which may once have been an open cluster.

Mural quadrant A quadrant mounted on a north–south wall, used to measure the altitudes of objects when they transit.

Neap tide Unusually weak tides which occur when the Moon’s phase is around fi rst quarter or last quarter.

Nodes The points where an object’s orbit crosses the plane of the Earth’s orbit around the Sun.

Occultation An event in which one astronomical object passes behind another. Oort cloud A collection of icy bodies in the very far reaches of the solar system,

at a distance of around 50,000 AU from the Sun. The Oort cloud has never been directly observed, but most comets are thought to have begun life as Oort cloud objects.

Open cluster A loose condensation of stars, close together in space and which cannot escape one another’s gravitational fi eld. The stars within such a cluster formed from a common molecular cloud, and have not yet dispersed through space.

Opposition A planet is said to be at opposition when it lies in the opposite direction to the Sun in the sky. When it lies in that direction, the planet is at its closest to the Earth, and appears highest in the sky at around midnight, making it ideally placed for observation.

Parallax The amount by which a star’s position appears to wobble from side to side over the course of the year due to the Earth’s changing perspective on the Universe as it orbits the Sun. In practice, the parallaxes of stars are so minute that incredibly sensitive telescopes are needed to detect them.

Glossary

234

Penumbra The shadowed region behind an astronomical body, especially the Earth or Moon, within which the Sun’s disk is partially obscured.

Perihelion The point along a planet’s orbit where it makes its closest approach to the Sun.

Planet Defi ned by the IAU in 2006 as a celestial body that (a) is in orbit around the Sun, (b) has a nearly round shape, and (c) has cleared all of the rocky debris from the neighbourhood of its orbit.

Planetary nebula A compact type of nebula which is formed when the outer layers of a star are expelled as their cores turn into white dwarfs. Planetary nebulae often have complex geometric shapes.

Proper motion The rate of a star’s movement across the sky due to its drifting motion through space relative to the Sun.

Protoplanetary disk A disk of gas and dust surrounding a young star, out of which planets may form.

Proplyd See protoplanetary disk. Quadrant An instrument used to sight the altitude of objects above the horizon,

often with the naked eye. Red giant star A star which is near the end of its life, and whose outer layers have

puffed up to many times their original size. Retrograde motion The westward movement of the superior planets across the

sky for a few weeks around the time that they are at opposition, in contrast to their usual eastward movement across the sky.

Right ascension The celestial coordinate which is the counterpart to longitude on the Earth’s surface.

Sextant An instrument used to sight the angular distances between objects in the sky.

Sidereal day The time taken for the stars of the night sky to complete one revolu-tion around the celestial poles. Equal to 23 h and 56 min.

Sidereal year The time taken for the Earth to complete one revolution around the Sun, such that the Sun returns to exactly the same point in the sky where it lay a year earlier. Equal to 365.2564 days.

Solar calendar A system of timekeeping in which the time of year is determined by the Earth’s changing seasons, and in which months are no longer tied to the Moon’s 29-day cycle of phases.

Solstice One of the two occasions in each year when the Sun reaches its furthest points north or south of the celestial equator.

Spring tide Unusually strong tides which occur around the time of new moon and full moon, when the tidal pulls of the Moon and Sun are closely aligned.

Superior planet A planet which orbits the Sun at a greater distance than the Earth. The only two planets which are not superior planets are Mercury and Venus.

Supernova A catastrophic explosion which occurs at the ends of the lives of high-mass stars. The fi reball produced by a supernova can outshine an entire galaxy of stars for a few days.

Glossary

235

Synodic period The time taken for an astronomical object to return to the same position in the sky relative to the Sun. In the case of the Moon, this is the time interval between successive new moons. In the case of the planets, this is the time interval between successive oppositions.

Terrestrial planet A planet with a rocky surface, like the Earth and unlike Jupiter or Saturn.

Transit (1) An event in which one astronomical object passes in front of another. Transits of Mercury or Venus are occasions when these planets pass in front of the Sun, appearing as small dark disks blocking part of the Sun’s light.

(2) The moment when the sky’s daily rotation carries a star or planet across the observer’s meridian.

Tropical year The period of time between successive summer solstices, equal to 365.2422 days.

Umbra The shadowed region behind an astronomical body, especially the Earth or Moon, within which the Sun’s disk is entirely obscured.

Vernal equinox Another name for the March equinox. White dwarf The compact remnant of a Sun-like star which has run out of fuel.

White dwarf stars are typically of similar size to the Earth, yet have similar masses to the Sun.

Zenith The point in the sky directly above the observer’s head. Zodiacal constellation One of the constellations through which the Sun passes on

its annual path across the sky. There are 12 traditional zodiacal constellations, each spanning an equal 30° length of the ecliptic. Today, the Sun passes through 13 modern constellations; the additional constellation is Ophiuchus.

Zodiacal light A faint glowing band across the sky which follows the line of the ecliptic. The glow is produced by tiny interplanetary dust grains in the plane of the solar system.

Glossary

237D. Ford, The Observer’s Guide to Planetary Motion: Explaining the Cycles of the Night Sky,The Patrick Moore Practical Astronomy Series, DOI 10.1007/978-1-4939-0629-1,© Springer Science+Business Media, LLC 2014

A Alcock, George , 37 Analemma , 68, 69 Andromeda galaxy (M31) , 9, 14, 58, 199,

204, 224 Apollo landings , 82 Arthur, President Chester , 37 Asteroids , 14, 17, 25, 49, 59, 60, 70, 82, 139,

142, 145, 160, 171, 172 Astronomical unit (AU) , 25, 184, 210, 231 Atacama Large Millimetre Array (ALMA) ,

60, 214 Atomic clock , 71, 73, 206 Autoguider , 219

B Babylon , 1, 73, 231 Barnard's star , 3, 4 Bayer fi lter , 225 Bessel, Friedrich , 31 Blue moon , 88–90 Bond, William , 216 Brahe, Tycho , 10, 158, 161, 163, 164 Brocchi's cluster , 6

C Calver, George , 217, 218 Canals, Martian , 156 Carbonates, on Mars , 182

Carbon dioxide , 155, 158, 160, 170, 180, 181, 182

Cassini, Giovanni , 118 Celestial sphere , 30–32, 34, 37, 39, 58, 64, 70,

83, 85, 97, 126 Challis, James , 19 Chaos theory , 17, 160 Charge-coupled device (CCDs) , 178, 209, 217,

219, 220, 222, 225, 226 Christmas, date of , 62, 63 Clavius, Christopher , 62 Climate change , 160, 180 Color fi lter , 147, 169, 226 Columbus, Christopher , 91, 99 Comet , 10, 12, 15–16, 25, 37, 70, 144, 145, 233 Common, Andrew , 217, 218 Constellations , 3, 5, 6, 8, 9, 14, 34–42, 45, 48,

63, 64, 89, 99, 125, 127, 199, 201, 203, 204, 219, 231, 232, 235

Coordinated universal time (UTC) , 72, 94, 144, 194

Corot spacecraft , 209 Couch Adams, John , 19

D Dark frame , 220 Deimos , 79, 142, 155, 170–172, 217 Delta T , 72, 73 Doppler effect , 31, 208, 232 Draconic month , 104, 232

Index

238

Draper, Henry , 216, 217, 218 Draper, John , 216

E Eagle nebula , 53, 54 Easter, date of , 89, 90, 198 Eccentricity, orbital , 25, 67, 232 Eclipse , 72–74, 85, 87, 90–102, 104, 105, 113,

148, 193, 195, 216, 229 Ecliptic , 23, 39, 40, 41, 43, 45–48, 58, 59,

63–67, 71, 84, 85, 99, 101–104, 122, 125, 126, 127, 146, 147, 162, 185, 191, 193, 195, 196, 197, 199, 232, 235

Egyptian pyramids , 1, 6 Einstein, Albert , 19 El Nino , 9 Encyclopedia Brittanica , 157 Ephemeris time (ET) , 71 Equation of time , 66, 67–69 Equinox , 26, 38, 41, 42–48, 62–65, 85,

89, 102, 149, 150–152, 198, 232, 233, 235

Evaporating gaseous globule (EGG) , 54 Exoplanet. See Extrasolar planet Extrasolar planet , 2, 3, 205–214 Eyepiece projection , 220

F First point of Aries , 42, 48, 122, 123, 124 Fixed stars , 3–5 Flat frame , 221 Focal ratio , 225 Fusion, nuclear , 9, 50, 51, 54, 121

G Gaia observatory , 31 Galaxy , 3, 4, 5, 6, 9, 14, 31, 57, 58, 199,

201–204, 205, 211, 212, 213, 224, 234

Galaxy cluster , 199, 204 Galaxy Zoo , 213 Galileo, Galilei , 13, 14 Gas giants , 25, 28, 49, 59, 60, 79, 115–122,

127–129, 139–143, 147, 161, 164, 205, 210, 211, 214, 231, 232

Gegenschein , 145, 146 Giant impact hypothesis , 80–81, 232 Giant molecular cloud (GMC) , 50, 52, 53,

54, 232 Gilbert, William , 79

Globular cluster , 199, 201, 203, 204, 217, 232

Gould’s belt , 203 Great circle , 232 Greatest elongation , 186, 189–193 Great Red Spot , 118 Greenhouse effect , 180, 182, 184 Gregory XIII, Pope , 62 Gyroscope , 43–45, 102

H Halley, Edmund , 16 Halley's comet , 15–16 Harriot, Thomas , 13, 79 Harrison, John , 18 Heliacal rising , 6, 9 Hellas basin , 169 Herschel, John , 7, 62, 216 Herschel, William , 14, 19 Hipparcos space observatory , 31, 232 Hooke, Robert , 14–16 Hot Jupiter , 209–211 Hubble's law , 31 Hubble Space Telescope , 31, 53, 116, 156,

183, 214, 218, 224, 226 Hven, island of , 11 Hypersensitization , 217

I Intercalary month , 90 International Astronomical Union (IAU) , 35,

232, 234 Iron, on Mars , 168 Irregular moon , 142 Islam , 6, 90 Isotope , 79, 80

J J2000.0 coordinates , 48 Jeans, James , 52 Jet Propulsion Laboratory (JPL) , 17, 20, 229 Jewish calendar , 89 Julian calendar , 62 Julius Caesar , 62, 63

K Kepler, Johannes , 10, 12–15, 28, 66, 158, 161,

163, 164, 173, 209 Kepler spacecraft , 213

Index

239

L Lacaille, Louis de , 35 Lascaux caves , 1 Late heavy bombardment , 82, 233 Leap second , 71–75 Leap year , 61–62 Le Verrier, Urbain , 19 Lilius, Aloysius , 62 Limestone , 160, 182 Local Group , 204 Local solar time , 66, 67, 148 Longitude , 18, 32, 34, 37, 38, 45, 46, 47, 67,

73, 148, 168, 196, 197, 234 Lowell, Percival , 7 LRGB imaging , 227 Lucky imaging , 223–224, 227 Lunar Reconnaisance Orbiter , 82 Lunar standstill , 103 Lunation , 84, 88, 89, 99 Lunisolar calendar , 89, 90, 104

M Magellan , 178 Magnetic fi eld , 14, 80, 81, 140, 141, 160, 161,

175, 181, 182, 185 Man in the Moon , 79 Mariner 2 , 173, 180 Mariner 4 , 157, 158, 173, 174 Mariner 10 , 183–185 Mayor, Michel , 208 Mean time , 65–67, 69, 70, 71 Meridian , 18, 33, 37, 68, 233, 235 MESSENGER , 183, 184 Metonic cycle , 90, 104, 198, 233 Microlensing , 212 Migration, planetary , 210–211 Milky Way , 3, 4, 6, 7, 9, 13, 23, 31, 51, 54, 56,

57–59, 199–204, 211, 212, 219 Milky Way, center of , 4, 23, 57, 201, 202 Moon

formation of , 79–81 orbit of , 84–85 phases , 83

Moving group , 54, 212, 233

N NASA , 20, 53, 57, 78, 94, 96, 101, 109, 116,

117, 120, 151, 156, 159, 170, 173, 174, 179, 194, 229

Newton, Isaac , 14–17, 164 Node , 99–105, 195, 196–198, 232, 233

Noise, imaging , 221, 222 Noon , 64–70, 75, 145

O Obliquity of the ecliptic , 65, 67 Open cluster , 7, 54, 199, 200–203, 233 Opposition , 111, 113, 123–129, 144–146, 148,

157, 162, 163, 164, 168, 173, 185, 186, 192, 233–235

Opposition surge , 144, 145, 146 Oresund straight , 11 Orion nebula , 3, 54, 203, 216–218 Oval BA , 118

P Parallax , 10, 12, 13, 31, 32, 91, 98, 194, 195,

232, 233 annual , 26, 31

Penumbra , 92, 93, 94, 97, 98, 234 Phases

of Mercury and Venus , 191–193 of the Moon , 83, 84, 89, 90, 91,

105, 233 Phobos , 79, 142, 155, 170, 171, 172, 217 Planetesimal , 59, 60 Planet Hunters , 213 Plasma , 50, 52 Plato , 8 Polynesia , 5 Precession of the equinoxes , 42–48 Prime meridian , 37 Protoplanetary disk , 55, 59, 60, 80, 121, 122,

141, 142, 214, 234 Proxima Centauri , 5, 205 Pulsar , 206–207

Q Quantum effi ciency , 217 Queloz, Didier , 208

R Radar , 20, 30, 31, 178, 195, 229 Radial velocity method , 208, 209, 210 Rayleigh scattering , 99 Reciprocity failure , 217 Red giant star , 51, 113, 234 RegiStax , 219, 224 Regular moon , 141, 142, 143, 147 Retrograde motion , 125, 234

Index

240

Riccioli, Giovanni , 79 Ring-plane crossing event , 152 Rings, planetary , 57 Roche limit , 144, 172 Romer, Ole , 148 Rovers, on Mars , 140, 160, 174, 175 Royal Greenwich Observatory (RGO) , 18, 34, 37

S Saros cycle , 90 Schiaparelli, Giovanni , 155, 156 Schwabe, Heinrich , 19 Seeing , 99, 125, 127, 155, 156, 183, 222, 223,

224, 227 Seeliger effect , 145 Sexagesimal system , 38 Sidereal month , 84 Sidereal year , 63, 234 Snow line , 121, 210 Solar conjunction , 85, 124, 125, 128, 148,

162, 174, 186, 193 inferior , 193 superior , 186

Solar wind , 51, 54, 121, 141, 160, 175, 181, 182, 183

Solid tides , 113 Sol, Martian day , 168 Spiral arms , 31, 202, 203 Sputnik I , 20, 173 Stacking , 219 Star trails , 34, 35 Stephenson, Richard , 72, 73, 74 Sunspot , 19 Supernova , 10, 12, 207, 234 SuperWASP , 209 Synodic month , 84, 104 Synodic period , 26–28, 30, 122, 123, 173,

186, 196, 198, 235 Syrtis Major , 169

T Telescope , 2, 4, 7, 11, 13–14, 18, 30, 31,

33–35, 53, 60, 72, 78, 79, 82, 88, 115,

116, 117, 118, 120, 143, 148, 155, 156, 168, 169, 173, 178, 183, 192, 206, 209, 212, 213, 214, 216, 217, 218, 219, 220, 221–227, 231, 233

Tharsis volcanoes , 169, 170 Theia , 80, 81 Tidal locking , 112–113, 142–143 Tides, origin of , 106, 111 Time delay, communications , 174 Titan (moon of Saturn) , 79, 142, 143, 158 Transit , 19, 33, 38, 64, 66, 68, 69, 90, 148,

181, 193–198, 208–210, 212, 213, 214, 229, 232, 233, 235

of an extrasolar planet , 208–209 of Mercury or Venus , 193

Transparency , 222, 223

U Umbra , 92–94, 97–99, 101, 102, 235 Uraniborg , 11, 12

V Venera program , 181 Vignetting , 221 Viking 1 and 2 , 158, 174 Virgo cluster , 204 Volcano , 161, 169, 170, 179, 182 von Braun, Wernher , 173 Voyager 1 and 2 , 120, 139, 140 Vulcan , 19

W Wells, H.G. , 157 Wesley, Anthony , 119 Whipple, John , 216 World War II , 20, 72

Z Zodiacal constellations , 41, 42, 235 Zodiacal light , 59, 145, 146, 235

Index