a CentauriProxima "the

nearest of all"

Siriusand itscompanion

Luyten 726-8A and B

Ross 154

e Eridani

Lacaille 9352

EZ AquariiA, B, C

Indie

t Ceti

GJ 1061

Sun

Barnard's Star

Wolf 359

Lalande 21185

Ross 248

Ross 128

Procyonand its companion

61 CygniA and B

Struve 2398Struve 2398A and B

Groombridge 34A and B

DX Cancri

A and B

A and Ba and Bb

-- 3 LIGHT- YE AR S--

THE ASTRONOMICAL COMPANION

The nearest stars

SECOND EDITION

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The illustration on the front cover represents a sphere of space, our stellar neighbor-hood. At the center is our home, the solar system, though all that is visible on this scaleis the light of the Sun. Scattered around are the very nearest stars.

My way of showing their three-dimensional positions is to fix them on stalks, whichstand or hang from a plane. The plane is that of Earth’s equator. So the stars above itare what we call “north” of us; those below are in the southern half of our sky.

The plane is emphasized by a grid of lines, like wires. This serves a second pur-pose, indicating scale: the lines are 3 light-years apart. The radius for this sphere is 12light-years (or 3.7 parsecs, the unit called the parsec being about 3.26 light-years).

It is impossible to show the stars themselves, let alone planets around them, or eventhe orbits of the planets: all are far too small. Instead, the stars are represented by glowsof light, proportional in size to the stars’ “magnitude,” that is, brightness. The Sun’s realwidth is about 1/7,000,000 of a light-year; the Earth’s, 1/740,000,000; even the diame-ter of Earth’s orbit is only 1/31,600 of a light-year, and of Neptune’s orbit (the outer-most major planet) 1/1,000. So the Sun and what we think of as its vast surroundingsare buried microscopically in the center of its glow.

Several of the stars are double or even triple (some can be “split” by a skilledobserver with a telescope, others have been discovered in more indirect scientific ways).In most cases we cannot show the separation between the stars in any literal way: it maybe less than the Sun-Earth distance or hundreds of times more yet still too small for ourscale. Sometimes the partner stars are similar in size and color (like 61 Cygni). Siriusand Procyon—the brightest star in our sky and the one that famously rises into viewbefore it—are brilliant stars which have been found to have tiny white-dwarf com-panions. I’ve artificially shown them, but there’s one case where a companion is so farfrom its primary that it is a whole 1.4 millimeters away in our picture. The nearest sys-tem to us, Alpha Centauri (so far south that it can be seen only from our tropics or south-ern hemisphere), is a beautiful mixture: a Sun-like star, a smaller orange one, and aspecimen of those red dwarfs which seem to be the commonest kind of star. And thatred dwarf, in a huge slow orbit 15,000 Sun-Earth distances (0.24 of a light-year) fromthe other two, is called Proxima Centauri because, at only 4.2 light-years, it is and willbe for several centuries our nearest star of all.

For more about these stars, see the NEAREST STARS section of the book.

The main illustrations running in a series through the book are on the same principle.They originated from my wish to make a drawing of the nearest stars, which neces-

sitated a model. In this model the stars are beads, of six sizes and five colors, on lengthsof bicycle-spoke planted in a square black wooden base. I used the model to make apainting (though it was not easy for the eye to keep the stars and stalks lined up); butthen, wanting to make a balancing picture for the BRIGHTEST STARS—a larger vol-ume in which longer stalks would have to stand from a more remote base—I realizedthat we are dealing not with a cube of space but with a sphere, so the reference planeshould be not a square at the bottom but a disk through the center. To calculate the stars’positions relative to this disk, student friends told me about sines and cosines andshowed me how to write my first computer program—the seed of what became anenormous tree.

The majority of the illustrations are of the same type as that on the front cover. Theyshow a sphere of space centered on our own position, though we rocket away from it tolook on the sphere from outside. The pictured sphere is like one of those transparentplastic celestial globes—except that we can fill it with solid contents and vary themarkings on the spherical surface.

North is always up, and we keep looking from the same direction, a celestial mapposition called 17h 15m, +22°, in the constellation Hercules, near the star Delta Herculisor Sarin. (Sarin is actually two stars in line. They are explained in the BRIGHTESTSTARS picture.) We are looking past Earth toward the opposite point in the sky, 5h 15m—22°, in the constellation Lepus on the south side of Orion. Orionward orientationseems natural, at any rate for those who learned first the stars of northern winter.

It would be possible to show the sphere from any direction, such as straight downfrom the north. But keeping to one viewpoint keeps things clear. I think it will giveyou a rock-steady conception of the whereabouts of everything around us in space, fromthe small scales out to the large.

In these standard pictures we are always looking from the same relative distance: notinfinity (which would make the sphere seem less real) but 3 sphere-radii from the cen-ter. The distance from your eye to the nearest bulge of the sphere is the same as the dis-tance from there to the far surface. This determines the foreshortening. Things on orinside the near part of the sphere look larger. This varying scale is made clear by thegrid-lines, spreading apart as they come toward you.

Some of the pictures, illustrating geometrical systems, are abstract, with no particu-lar distances. Others form a long series with multiplying distances. You are making thestraight voyage out past Sarin, accelerating toward infinity, and looking back at theplace you came from.

The four systems you have to keep thinking about in astronomy are those of theequator, horizon, ecliptic, and Milky Way. So after introducing them I keep all four atleast minimally present throughout the series. Each has its turn as the most relevant, itsplane being the foundation of the model (if we were building a model): the grid stretch-es across it and the stalks are attached perpendicularly to it.

It may seem that in the pictures of vast outer regions the planes relating to our punyEarth have no business. But any plane extends to infinity. More important, the pres-ence of the planes ties together the levels of astronomy, from the observer with treesaround him, to the quasars. It is good to keep them mentally related, because even iflooking out to the quasars we are looking through our galaxy, and through our solar sys-tem, and from our own sloping and spinning foothold.

The horizon is different from the others in that it is only a horizon, an example. It

is the horizon for latitude 40° north (where a lot of people live) and at a certain time: 0hsidereal time, which occurs for instance about midnight in September, 10 p.m. inOctober, 8 p.m. in November, 6 p.m. in December, midday in March, 6 a.m. in June . . .The objects above the horizon plane are those you could see then. Mentally rotate thehorizon a quarter turn to the left for the same night six hours later, or the same time ofnight a quarter of a year earlier. Mentally tip the horizon more steeply, for a moresoutherly latitude.

Look at a picture so that the horizon is horizontal; or look at it from, say, the galac-tic point of view. The picture is round: it has (like the universe) no one top of bottom.

Extensions (some of which I have exploited elsewhere than in this book):—The “stars” shown with stalks to indicate their positions in space can be suc-

cessive positions of a planet or other moving body. (See the solar-system pictures.)—Stalks, besides those perpendicular to a plane, can be drawn to the center or sur-

face of the sphere, so as to show how we see stars projected on the sky. Two or morekinds of stalk can be used at the same time. (See the final “universe” picture.)

—Distances can be made proportional to the logarithms of themselves, so thatobjects near and far appear in the same solid picture. (See the “Logarithmic universe.”)

—Instead of a grid, the plane and distances on it can be indicated by concentriccircles (as in the logarithmic picture, where indeed a grid would be impossible).

—Instead of the whole sphere, a cone or wedge of it can be selected (such as a con-stellation) and shown at a larger scale (as on the back cover of the first edition).

—The center of the sphere can be the Earth (as in the “Moon’s orbit” and“Logarithmic universe” pictures) or a point on its surface (as in the “Horizon” picture)or the Sun (as in the “Earth’s orbit” and most succeeding pictures) or can be shifted tosome other point, such as another star.

—The viewpoint can move in closer toward the surface of the sphere (as in the“universe” picture), increasing the contrast between things near and far.

—The viewpoint can lie in the skin of the sphere or move inside it. The bubble,thus pricked, does not burst, as I at first feared! The whole sphere could still be shown,but would not look like one: it would be bounded by a large circle representing onepoint (the point where your eye is probing through, or the point directly behind you).

—What happens when the viewpoint moves all the way down to the center of thesphere? Instantly the picture becomes a flat map. This is what has happened in the“Star names” maps: they result from the same logic as the solid pictures, with the“standoff,” as I call it, reduced to zero. They could have been drawn as one map: theother half of the sky would become a ring added around the outside, ending at a largecircle which represents the point directly behind the viewer.

In such maps we still have a direction of view: the center of the map. This does nothave to lie on the equator: it can be at the north or south pole (resulting in polar mapsof the usual kind) or at any other point in the sky (see the two small maps in the PRE-CESSION section, with their centers at the ecliptic poles). Of this kind are the mapsdesigned for plotting meteors, each with its center at a meteor-shower’s radiant.

—The method of projection in all the solid pictures is to find, for every object andevery point along a geometric form, what its angular distance and direction from thecenter would be as seen from the viewpoint, and to convert these into distances anddirections on the paper. (It is a process performed by the visual instinct in one leap andby trigonometry in a terrifying number of steps.) When applied to a flat map, thisresults in the type of projection called “equidistant azimuthal.” (Properties of it are thatall great circles through the center appear as straight lines, all others as curves; all direc-tions and distances from the center are true; but, far from the center, shapes becomestretched sideways.) This seems to me the most generally useful projection for astro-nomical maps, since it can give maps of any part of the sky—polar, equatorial, or the“meteor-radiant” kind; and, though looking different, they harmonize because resultingfrom the same logic. However, by changing the equations at a late stage one can getother projections: equal-area azimuthal (which removes stretching-distortion, at the costof falsifying angular distances); stereographic (which removes distortions, but can reachto only a hemisphere of the sky); orthographic (as viewed from infinity, can also reachonly to 90°); gnomonic as on a photographic plate (which cannot be extended to a radiusof 90° or more because the points would fall infinitely far away); rectangular, as in theusual equatorial maps (in which degrees or right-ascension and declination all have thesame scale, so that the poles become lines, and which is not really a “projection” at all).And there are other projections not based on centers.

For the earlier Astronomical Companion, I drew all the illustrations by hand. (Theywere accurate enough, in that I had made a computer calculate many of them, but theplots produced by devices of the time were not of reproduction quality, so I traced overthem.) Freehand, with pens and a few other tools, was flexible, allowing emphases andafterthoughts; and people told me they liked it, because it gave a feeling of personalcommunication, as with sketches made on a blackboard or during a conversation.

But some were less clear than neat plotting could make them. And the book hadbeen created back in the time of paste-up and photographic plates; everything needed tobe digitized. And there have been decades of new information, discoveries, star dis-tances; every large diagram needed to be revised. Having in the meanwhile developedthousands of ways of making the computer do the work, I couldn’t face the hand laborover again. The dilemma long prevented me from getting on with a new edition. Mysolution is to keep the little drawings that are like gestures in the margins, and programthe charts and the sphere pictures. (Changing, incidentally, from parsecs—loved onlyby the mathematically-minded—to light-years.) It’s taken six months longer than Iexpected to rediscover how on earth I managed to make some of these plots. And I can’tunderstand how I managed to learn so much during that one year when I made theCompanion as an offshoot from the Calendar.

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Some other publications by Guy Ottewell from the Universal Workshop:

Astronomical Calendar 2011Events throughout the year; many charts; same page-size as the Companion

Albedo to ZodiacGlossary of astronomical names and terms, with pronunciation, origin, and meaning

To Know the StarsChildren’s introduction to astronomy

The Thousand-Yard Model, or, The Earth as a Peppercorn Instructions for a walk making vivid the scale of the solar system

The Under-Standing of Eclipses The geometry, history, and beauty of eclipses

Berenice’s HairNovel: what really happened to the stolen tress that became a constellation?

The Troy Town TaleNovel: the whole legend of Troy, the “collective dream of the Western world”

Portrait of a MillionPoster conveying the concept of a million, with selected million-facts

American Indian Map, and Navajo MapThe large map is colored by language-families, also shown in a table

The Arithmetic of VotingA fairer system, getting rid of the “voter’s dilemma”

The Spiral LibraryAn amusingly miraculous solution for libraries running out of space

Plurry: a musical instrumentwhose structure leads to an understanding of scales, keys, and modes

Stripe Latin: a grammar gameTen-Minute History of the World; and, Queen Guinevere’s RulesThink Like a Mother: a photo book of human rightsTurkey, A Very Short HistoryThe Winged Velocipede; or, how to f ly overseas with your bicyclePembrokeshire printsLanguage (poems)And prints of paintings

THE ASTRONOMICAL COMPANION

Copyright © 2010 by Guy Ottewell. Printed in the United States of America. All rightsreserved. Parts may be reproduced with prior permission and with acknowledgment.

ISBN 0-93456-60-7

PrefaceThis is a book to look in for explanations, for reference, or for mere enjoyment. I think itis for those who already enjoy either astronomy itself or the idea of it.

The book may be used to guide or supplement a short non-mathematical course inastronomy. Sections such as POSITION and EVOLUTION would be required reading,while others such as NAMES and CALENDARS can be left to catch the eye of the interest-ed student.

The book also functions as a companion volume to my annual Astronomical Calendar insimilar format. The Companion was born from the non-year-dependent supplementarymaterial that had begun to swell the bulk of the Calendar.

Douglas Roosa, my helper in several issues of the Astronomical Calendar, made at myspecification the physical model of the nearest stars (referred to in the note on the frontcover illustration), and did the drawing (now superseded) for the Hertzsprung-Russell dia-gram.

Few changes were made in most of the hurried reprintings. In the 2000 printing I intro-duced computer-programmed versions of the first few sphere-pictures.

Universal WorkshopP.O. Box 102, Raynham, MA 02767-0102, U.S.A.

800-533-5083 (toll-free) 508-802-5660 fax 508-967-2702customerservice@UniversalWorkshop.com author: guy@universalworkshop.com

www.UniversalWorkshop.com

First edition, October 1979Reprinted with revisions and corrections, January 1981, July 1983; reprinted July 1984,February 1985, February 1986, November 1987, December 1988, December 1989, May1991, August 1992, July 1993, November 1994, December 1995, December 1997, August2000, October 2001, November 2002, February 2008Second edition, October 2010

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Contentssections large illustrations______________________________________________________________________________

12 light-years (very nearest stars) front cover4 OVERVIEW OF ASTRONOMY Logarithmic Universe 56 POSITION Equatorial system 67 FOUR PLANES Four planes 78 HORIZON SYSTEM Horizon system 8

10 ORIENTING TO THE SKY Orienting to the sky 1012 CONSTELLATIONS Constellations 1214 NAMES Star names, Ophiuchus half of the sky 14

Star names, Orion half of the sky 1517 DESIGNATIONS 18 EARTH’S ORBIT Earth’s orbit 1719 ZODIAC

SOLAR SYSTEM 21 PLANETS Solar system, inner 2021 BODE’S LAW Solar system, outer 2122 TIME23 TIME-UNITS

JULIAN DATES24 SEASONS Seasons 2427 PRECESSION Precession 2830 CALENDARS31 CHRISTMAS32 MOON’S ORBIT Moon’s orbit 3334 PHASES Phases 3536 MOONLIGHT

EARTHLIGHT37 MOON’S ATTITUDE

MOON AS SIGNPOST38 ECLIPSE SEASONS

SAROS Pattern of eclipses 3940 ASTEROIDS Asteroids, inner 40

Asteroids, outer 4142 COMETS Comets 4244 METEORS Meteor-shower orbits 4546 DISTANCE 1.6 light-years (Oort cloud) 4648 NEAREST STARS 16 light-years (nearest stars) 4850 BRIGHTEST STARS 100 light-years (bright stars) 5053 SPECTRAL TYPES Hertzsprung-Russell diagram 52

HERTZSPRUNG-RUSSELL DIAGRAMEVOLUTION

56 DOUBLE STARS57 VARIABLE STARS58 OUTRUSH 600 light-years (clusters) 58

1,600 light-years (Orion) 593,300 light-years (Deneb, Gould Belt) 60

10,000 light-years (spiral arms) 6130,000 light-years (edge of Milky Way) 62

80,000 light-years (all of Milky Way) 63300,000 light-years (satellite galaxies) 64

3 million light-years (Local Group) 6530 million light-years (nearby groups) 66150 million light-years (Virgo Cloud) 67

1,500 million light-years (superclusters) 6813,700 million light-years (quasars, universe) 69

72 SPACE EXPLORATIONa chronology by Alastair McBeath

The four solar-system-escaping spacecraft 7274 INDEX

Hertzsprung-Russell aurora back cover

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ANDROME DA

ANT L I A

APUS

AQUARIUS

AQUILA

ARA

AR I E S

AUR I GA

BOÖTES

CAE L UM

CAME L OP ARDAL I S

CANCE R

CANES

VENATICI

CAN I SMA J OR

CAN I S

M I NOR

CAPRICORNUS

CAR I NA

CAS S I OP E I A

CENT

AURU

S

CE PHEUS

CE T US

CHAMAE

L E ON

CIRCINUS

COL UMBA

CORONA

AUSTRALIS

CORVUS

CRAT E R

CRUX

DORADO

DRACO

E R I DANUS

F ORNAX

GE M I N IGRUS

HOROL OGI UM

HY

DR

A

HYDRUS

INDUS

L ACE RTA

L E O

L E OM I NOR

L E P US

LIBRA

L YNX

LYRA

ME NS A MICROSCOPIUM

MONOCE ROSMU

SCA

NORMA

OCTANS

OR I ON

PAVO

PEGASUS

P E RS E US

PHOE N I X

P I CT OR

P I S CE S

PISCISAUSTRINUS

P UP P I SPYX I S

RE T I CUL UM

S CUL PT OR

S E XT ANS

T AURUS

TELESCOPIUM

T R I ANGUL UM

TRIANGULUM

AUSTRALE

TUCANA

UR S AMAJ OR

URSAMINOR

VE L A

VOL ANS

Earth

CORONABOREALIS

HERCULES

SCUTUMSAGITTARIUS

VI

RG

O

SERPENS

(CAPUT)OPHIUCHUS

DELPHINUS

EQUULEUS

CYGNUS

VULPECULA

SAGITTA

SERPENS (CAUDA)

SCORPIUSLUPUS

BERENICESCOMA

ah o r i z on

e c l i p t i c

e q u a t o r

Mi l

ky

Wa

y

12 The Astronomical Companion

Andromeda

Antlia

Apus

AquariusAquila

Ara

Aries

Auriga

Boötes

Camelopardalis

Cancer

CanesVenatici

CanisMajor

CanisMinor

Carina

Cassiopeia

Centaurus

Cepheus

Cetus

Chamaeleon

Coma

Corona

Crux

Cygnus

Dorado

Draco

Eridanus

Fornax

Gemini

Grus

Hercules

Horologium

Hydra

Hydra

Hydrus

Indus

Leo

LeoMinor

LepusLibra

Lupus

Lynx

Lyra

Mensa

Monoceros

Musca

Octans

Orion

Pavo

Pegasus

Perseus

PhoenixPictor

Pisces

Pisces

Piscis

PuppisPyxis

Sagittarius

Scorpius Sculptor

Serp

ens

Taurus

Telescopium

TriangulumAustrale

Tucana

UrsaMajor

UrsaMinor

Vela

Virgo

Volans

Vulpecula

CorvusCrater

Serpens

Ophi- uchus

Equuleus

SagittaDelphinus

Microscopium

Capricornus

Austrinus

AustralisNorma

Cepheus

Columba

Caelum

Circinus

A R G O

Reticulum

TriangulumCoronaBorealis

Lacerta

Berenices

Sextans

Tucana

Sculp-tor

Cas.

And.

Pho

enix

Scutum

post-Ptolemaic constellations zodiacal constellations bold conspicuous constellations

CONSTELLATIONS“Constellation” (Latin “together-star-ness,” from stella, “star”)meant originally a group of prominent stars apparently near eachother in the sky, so that they could be perceived as a geometricalform or a picture. Since individual stars appear as featureless points,their mutual arrangement was the only means of recognizing them

Some constellations, or parts of them, happen to be real group-ings in space: thus most of the stars in Coma Berenices belong to acertain star-cluster; 5 of the 6 stars in the “face” of Taurus belong toanother; 6 of the 7 bright stars in Orion to another; and 5 of the 7bright stars in Ursa Major to another. But, mostly, the stars we per-ceive as a constellation merely lie along roughly the same line ofsight from us, at greatly different distances. If we could travel toother viewpoints the constellations would dissolve.

Each culture has had its own way of dividing and pictorializingthe sky. Our system is basically that which originated in ancientMesopotamia and was elaborated by the Greeks.

Till recently, the traditional pictures were in real use and wereincluded in star atlases. The way of identifying a particular star was“in the crook of the Ram’s right foreleg” and the like. The mostprominent star in a constellation was its lucida. The dim or disre-garded stars between constellations were amorphôtoi or informes,“unformed.”

Later, so tha]t any star could be named and catalogued, everypart of the sky had to be assigned to a constellation; therefore bound-aries had to be drawn. Thus the constellations became essentiallydirections from us in space, or, rather, wedges of space outward fromus.

The boundaries as at first drawn were informal curves. As final-ly fixed, they became straight lines, which, however, turn a crazy

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APUS

AQUARIUSAQUILA

ARA

BOÖTES

CANES

VENATICI

CAPRICORNUS

CENTAURUS

CEPHEUS

CIRCINUS

COMA

BERENICES

CORONAAUSTRALIS

CORONABOREALIS

CORVUS

CYGNUS

DELPHINUS

DRACO

EQUULEUS

GRUS

HERCULES

HYDRA

INDUS

LACERTA

LIBRA

LUPUS

LYRA

MICROSCOPIUM

MU

SCA

NORMA

OCTANS

OPHIUCHUS

PAVO

PEGASUS

PISCES

PISCIS

AUSTRINUS

SAGITTA

SAGITTARIUS

SCORPIUS

SCUTUM

SERPENS(CAPUT)

SERPENS(CAUDA)

TELESCOPIUM

TRIANGULUMAUSTRALE

TUCAN

A

URSA

MINOR

VIRGO

VULPECULA

Great Squareof Pegasus

Little Dipper

the Circlet

the Teapot

the Teaspoon

Keystone

the Urn

bCaph

gAlgenib

aAnkaa

aShedir

bda or Deneb Kait

hAchird

gTsihd

Ruchbah

aA

cher

nar

eSegin

b Mer

aka Dub

he

dZos

Chor

x

Alula A

ustra

lisn

Alula B

orea

lis

lG

iauz

ar

bDenebola

b

g

aAlchiba

eMinkar

dMeg

rez

gGienah

hZaniah

aAcrux

dAlgorab

gGacrux

bChara

bKraz

g

Muhlifain

gPorrima

bM

imosa

eAlio

th

d Auva

a

Cor Caroli

eVindemiatrix

zMizar

aSpica

Alcor

zHeze

hAlka

id or Benetnash

hMuphrid

bHadar

or Agena

a Thuban

qMenkent

aArcturus

i Syrma

g Seginus

aRigilkent

eIzar or Pulcherrima

b Kokab

aZubenelgenubi

bNakkar

bZubeneshamali

g

Pherkad

m Alkalurops

iEdasich

b NusakanaGemma

or Alphecca

aUnukalhai

dDschubba

bGraffias

nJabbah

dYed Prior e

Yed Posterior

w Cujam

aAntares

bKornephoros

lMarfik

aAtria

mArrakis

hSabik

a Rasalgethi

d Sarin

b Rastaban

lMaasym

u Lesath

nKuma

dYildun

l Shaula

aRasalhague

yDziban

bCelbalrai

xGrumium

gEltanin

gAlnasl

dKaus Media

eKaus Australis

l Kaus Borealis

aVega

bShelyak

sNunki

qAlya

gSulafat

z

Ascella

d Altaisor Nodus Secundus

bArkab

aRukbat

bAlbireo

sAlsafi

g Tarazed

eTyl

a Altairb

Alshain

a Giedib Dabih

g Sadr

aPeacock Star

e Deneb

bRotanev

aSualocin

aDeneb

eGienah

eAlbali

a Kitalpha

a

Alderamin

bAlfirk

b Sadalsuud

gNashira

p1 Azelfafage

eEnif

dDeneb Algedi

xKurhah

aSadalmelik

aAlnair

qBaham

q Ancha

gSadachbia

z Homam

hMatar

m Sadalbari

d Skat

a

Fomalhaut

b Scheat

aMarkab

gErrai

CRU

X

URS

A

MAJO

R

Big

Dip

per

14 The Astronomical Companion

The oldest star-names still used in our culture are three that havecome all the way from the pre-scientific Greeks: Sirius, Arcturus,and Canopus. The words seem to be respectively a plain adjective,a dubious reference to position, and the name of a minor legendarypersonage—but there is something insecure about the explanationsof all three.

At least as old is the idea of a certain star’s wide-ruling charac-ter; so it was called in the different languages “king” (Basileus,Rex), “royal” (Basilica, Regia), even, strangely, “little king”(Basiliscus, Regulus), which, stranger yet, means also the cocka-trice, the lizard that poisons you with its eye. The form used byCopernicus is that which happens to have survived other earlier andlater ones.

The Greek astronomers ending with Ptolemy, and the Greek(Hesiod, Aratus) and Roman (Ovid, Manilius) poets, recorded namesthat presumably were in use before their time. Meanwhile other cul-tures had their own networks of star-names. For instance the Arabsof the jâhiliyya (the “ignorance,” as they later called their pre-Islamic stage) regarded a certain pair of stars as Kalb ar-Râ‘i, “dogof the shepherd”; and two other chains of stars as biers with mourn-

ers bearing them, so that the star leading one chain was Qâ’id Banâtan-Na‘sh al-Kubrâ, “chief of the daughters of the greater bier.”Civilization passed to the Islamic world, and its scholars preservedthe Greek works in Arabic and added encyclopaedias of their own.They accepted Ptolemy’s constellations, and thus redescribed thetwo adjacent stars in phrases (ra’s al-jâthi and ra’s al-h ≥awwâ’) thatmean “head of Hercules” and “head of Ophiuchus.” In Arabic thereare no capital letters; by inventing them we have forced ourselves todecide whether everything is a name or not. When Europe reawoke,and translated the Arabic works and the Arabic translations of Greekworks, the star-labels were not translated but transliterated, and thustook the appearance of names: Rasalgethi, Rasalhague. (A few ofthe native Arab names survived rejection by the later city-dwellingscholars: though for us the biers are Bears, the star at the end of thebear’s tail, having been at the front of one of the biers, receives thetwo apparently unconnected names Alkaid and Benetnash.) Thebulk of our names are neither Greek in form nor Arab in origin, butare fragments of Arabic descriptions of parts of Greek constellations.Copied by writers who did not understand them, they were corrupt-ed and re-corrupted: ra’s al-h ≥awwâ’, reasonably accurate asRasalhague, appeared as Rasalauge, Ras Alhagus, Rasalhagh, Rasal-Hangue, Azalange, Alangue, Ras al Hayro . . . Most of theseweeds withered, but we are left with variant names, variant

spellings, variant pronunciations, and it is a matter of taste which tochoose.

This has been the main stream of our star-name inheritance.Without feeling free to abuse the tradition, we do not need to regardit as sacred, certainly not as official; there is no clear demarcationaround it; it is a lake with wide channels to the lakes of other cul-tures. Whatever part the populace played in generating the firstnames, litterateurs early took a controlling position, and they havechanged and added. They did so unintentionally by corrupting, andintentionally by borrowing and inventing. Even now, someone whowants to offer a list of the “names” of stars in, say, Fornax will ran-sack a book and give some Chinese syllables—or some Sumerianones. (The Sumerian civilization may have been ancestral to all oth-ers, but it was utterly lost and only recently dug up, so there can beno pretence here of traditional flow.) As for invention, the mostdelightful story is that of Piazzi (discoverer of the first asteroid) whoin his observatory had an assistant and eventual successor calledNiccolo Cacciatore (“Nick Hunter”); Latinizing these names asNicolaus Venator and reversing them as Sualocin and Rotanev,Piazzi in his Palermo Catalogue of 1814 smoothly attached them totwo stars of the little Dolphin constellation. The secret eluded evenhis friends; authors solemnly puzzled out the etymology of thenames with ludicrous results; and the old process of corruption set in

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NAMES

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Ròtanev (b Del): Lat. Venator, “hunter,” reversed.Rúkbah (d Cas): Ar. ar-rukbah, “the knee.”Rúkbat (a Sgr), same.Sàbik (J Oph): Ar. as-sâbiq, “the preceding.”Sadáchbia (g Aqr): Ar. sa‘d al-akhbi’ah, “lucky [star] of the

tents”—plural of khibâ’ as in Alchiba. The root s-‘-d carriesthe meaning of “happiness, fortune” and appears in the namesSaudi, Sadat, Assad (as‘ad).

Sadalbàri (m Peg): Ar. sa‘d al-bâri‘, “lucky [star] of the excellentone.”

Sadalmélik (a Aqr): Ar. sa‘d al-malik, “lucky [star] of the king.”Sadalsùud (b Aqr): Ar. sa‘d as-su‘ûd, “luck of lucks”—very

lucky.Sádr (g Cyg): Ar. as≥-s≥adr, “the breast.” Cf. Shedir.Sàiph (k Ori): Ar. as-saif, “the sword.”Sàrin (d Her), given in some catalogues; I don’t know origin.Schèat (b Peg): Ar. as-sa‘q, “the leg.”Scùtulum (i Car): Lat., “little shield,” diminutive of scutum; see

Aspidiske.Ségin (e Cas) and Segìnus (g Boo): I don’t think anybody knows the

origin.Shàula (l Sco): Ar. ash-shaulah, “the raised [tail].”Shédir or Schédar (a Cas): Ar. as≥-s≥adr, “the breast.” Cf. Sadr.Shélyak or Sheliak (b Lyr): Per. shalyâq, “tortoise” (from whose

shell the lyre was made). Cf. Sulafat.Shératan (b Ari): Ar. ash-sharat≥ain, “the two signs” (Pisces and

Aries).Sírius (a CMa): Gk. seirios, “scorching.”Sírrah (a And): see Alpheratz.

Skat (d Aqr): Ar. as-sa‘q, “the leg,” like Scheat, and rather similarlycorrupted.

Spìca (a Vir): Lat., “ear of wheat” held in the hand of the maiden.Stérope (21 Tau): Gk., one of the 7 Pleiades sisters.Suálocin (a Del): Lat. Nicolaus reversed; see Rotanev.Suheil: the Arabic word sahl means “smooth” and a “plain” (as in

the Sahel across Africa south of the Sahara); the diminutivesuhail is a boy’s name and the name for Canopus; and it isapplied to many other stars low on the southern horizon—Alsuhail is only one of them—in combination with the wordswazn and muhlifain.

Sùlafat or Sulaphat (g Lyr): Ar. as-sulah≥fah, “the tortoise”; Cf.Shelyak.

Sy"rma (i Vir): Gk., “train.”Tània Austràlis and Boreàlis (m and l UMa) and Tàlitha A. and B.

(k and i UMa): Ar. ath-thâniyah and ath-thâlithah, “the second”and “third,” with Lat. words for “south” and “north.” See Alula;and Kaus. iUMa is also called Dnoces. The root th-l-th, “three,”is also in Mothallah.

Tárazed (g Aql): Per. shâhin-e-tarâzad, “plundering falcon,”applied to the constellation; see Alshain, which preserves the“falcon” part, with Arabic al- prefixed. Actually I do not knowtarâzad; the -zad part means “striking.”

Tarf (b Cnc): Ar. at≥-t≥araf, “the tip.” Contrast Alterf.Taýgeta (19 Tau): Gk., one of the 7 Pleiades sisters.Tégmine (m Cnc): ablative case (for some reason) of Lat. tegmen,

“cover.”Téjat (m Gem): I don’t know origin. Actually this star is Tejat

Posterior; Tejat Prior is the one that also has the name of Propus.

Thùban (a Dra): Ar. ath-thu’bân, “the snake.” Cf. Rastaban,Eltanin.

Tsih or Cih (g Cas): Chinese, said to mean “whip.” I can’t vouch forit. Also called Navi.

Tyl (e Dra), given in some catalogues; origin undisclosed.Unukalhai (a Ser): Ar. ‘unuq al-h≥ayyah, “neck of the snake.”Véga (a Lyr): Ar. al-wâqi‘, “the stooping” eagle. Nothing to do with

Spanish vega, “meadow.” See Altair. Vindemìatrix (e Vir): Lat., “vine-harvestress.”Wásat (d Gem): Ar. wasat≥ as-samâ’, “middle of the sky,” i.e. the

ecliptic, to which it is near.Wazn (b Col): Ar. al-wazn, “the weight.”Wézen (d CMa): same.Yed Prior and Posterior (d and e Oph): Ar. al-yad, “the hand,” and

Lat. Cf. Tejat. A more westerly star “precedes” an easterly onebecause it moves before it across the sky, reaching the meridianfirst.

Yíldun (d UMi): apparently Turkish yÈldÈz, “star.” Cf. Kokab.Zàniah (e Vir): Ar. az-zâwiyah, “the corner.” Cf. Zavijava.Zàurac (g Eri): Ar. az-zauraq, “the boat.”Zavíjava (b Vir): Ar. zâwiyat al-‘awwâ’, “corner of the barker.” Cf.

Zaniah and Auva. Also called Alaraph.Zósma (d Leo): Gk. zôsma, “enzonement, loincloth.”Zùbenelgenùbi and Zùbeneshamàli (or -sch-) (a and b Lib): Ar. az-

zubân al-janubi and ash-shamâli, “the southern claw” and “thenorthern claw” of the Scorpion (to which they once belonged).See Acubens.

Referring to stars as “Mirfak (the one in Hercules, not the one inPerseus)” or “the second of the ten lashes of the whip in the hand ofthe Charioteer” remained practicable only as long as one command-ed plenty of time and not many stars. There have to be briefer andmore extensible designations. But many different systems havebeen started, no one of them good for all purposes.

Bayer letters, principally Greek letters, were mainly intro-duced by Johann Bayer on the maps in his Uranometria of 1603.But the idea dates to earlier; Bayer’s letters were not generally usedtill the next century; he applied them only in the 48 ancient constel-lations, not in the 12 new ones that he invented, and only after histime were letters assigned in these and other new constellations.

In some constellations all 24 Greek letters are used; in Lynx andVulpecula only a, and in Leo Minor only b and o! One Greek-lettersequence serves the three constellations into which Argo was bro-ken—Carina, Puppis, and Vela—so the latter two also have no a.If there is an outstanding lucida star it is usually a, but the order ofthe other letters only very roughly corresponds with their brightness:it is more like an order of importance in the constellation figure.Thus in Cygnus Bayer first lettered the principal 2nd- and 3rd-mag-nitude stars that form the cross shape, then worked with decreasingsystematicness around the 4th- and 5th-magnitude stars till the let-ters were used up. Orion and Gemini each have two outstandingstars, and in each case Bayer awarded a to the one that is in fact lessbright—Betelgeuse perhaps because it is conspicuous by its red-ness and because its rival Rigel is lower in the sky and more liableto dimming by the atmosphere; Castor probably because he is cus-tomarily named before his twin Pollux. The Big Dipper stars are let-tered west-to-east along the Dipper. In west-to-east order bothCassiopeia and Corona Borealis happen to be b a g d e. The most

perverse order is in Sagittarius, where a and b are minor stars off ina southeastern corner, while the brightest star at the center of the fig-ure is no higher than s.

In designating a star, the letter is followed by the constellationname in the genitive—which is the reason why astronomers haveto learn Latin genitives if they learn no other grammar! ThusAldebaran is Alpha Tauri, “Alpha of Taurus,” which we can writethat way, or as a Tauri, or a Tau.

Only the lower-case forms are used as Bayer letters (we showthe capitals in case you want to know). The vowels eta and omegawere (in ancient Greek) longer and with lower tongue-positions thanepsilon and omicron.

Bayer gave alternative Greek letters to a few stars that belong totwo constellation figures: b Tau (El Nath) = g Aur, a And = d Peg, sLib = g Sco. Now only the first in each pair is official.

A letter may be spread to more than one star by means of sub-script numerals (sometimes written superscript). Thus a1 and a2Capricorni and a1 and a2 Librae are wide double stars (in each ofwhich a2 is the brighter); but o1 and o2 Eridani are a degree apartand at very different distances. p1-6 Orionis and t1-9 Eridani areloose chains of stars; and 19 stars spread over an area of Auriga (the“Lashes” of the Charioteer’s whip) are all called y.

Where the 24 Greek letters ran out, Bayer resorted to lower-caseroman letters (such as s Carinae) and finally to upper-case ones (GScorpii).

Flamsteed numbers (1, 2 . . . ) were actually instroduced byHalley and Newton in a 1712 prepublication of Flamsteed’s cata-logue unauthorized by Flamsteed himself, did not appear inFlamsteed’s own version (published posthumously in 1725), andgained currency with Lalande’s 1783 version of Flamsteed’s cata-logue. The numbers are assigned more systematically than Bayerletters, through each constellation in order of right ascension (westto east); they include all stars down to about magnitude 6. For starsthat also have Bayer letters those tend to be preferred. The numbersreach as high as 141 Tauri. By Lalande’s time all 88 of our constel-lations were in existence, so he might have given us a uniform sys-tem; but he carried it down only to declination —35°. So Eridanus,Puppis, Centaurus, and Scorpius are only partly numbered, and allthe more southerly constellations not at all.

Then came many more kinds of designation, in many of whichthe first few symbols refer to somebody’s catalogue, and the remain-ing numbers are sequential or else are a brief form of a map position(thus 1653+40) means right ascension 16h53m, declination +40°).

alphabeta

gammadelta

epsilonzetaeta

thetaiota

kappalambda

nuxi

omicronpi

rhosigma

tauupsilon

phichipsi

A aB bG gD dE eZ zH hQ qI iK kL lM m

N nX xO oP pR rS sT tU uF fC cY yW w

DESIGNATIONSExamples of designations from star catalogues:

Grb 1830: Groombridge’s catalogue of circumpolar stars, 1838.BD 2579: Bonner Durchmusterung, by Argelander, 1859.DM —52°12220: Cordoba Durchmusterung (of southern stars),1892.HD 245770: the Henry Draper Catalog, actually by Annie JumpCannon and E.C. Pickering, 1918-1924.GC 5605: Boss’s General Catalogue, 1936.ZC 3539: Zodiacal Catalogue, by Robertson, 1940.SAO 122731: Smithsonian Astrophysical Observatory catalog,1966.LSI +61°303: Luminous Stars in the Northern Milky Way, I, 1959.GJ 1061: Catalogue of Nearby Stars by Gliese and Jahreiss, 1991.GSC 9537 380: the Guide Star Catalog, 1989 and versions to 2009.HIP 118218 and TYC 9537 380 1: Hipparcos Catalogue and evenlarger Tycho Catalogue of stars measured by the Hipparcos satellitein 1989-93.

Double stars:ADS 17020: Aitken’s catalogue.S 3001: published by Friedrich Struve.OS 507: published by Otto Struve.

Variable stars (see the section on them):R Sagittarii, AQ Sagittarii, V356 Sagittarii, etc.

Clusters, nebulae, and galaxies:M44, the famous Messier list of objects that might be mistaken forcomets, compiled by Charles Messier and published 1771-86.H IV 37: Sir William Herschel’s nebula no. 37, of class IV (plane-tary nebulae).NGC 2632: Dreyer’s New General Catalogue, 1888 (based on SirJohn Herschel’s).IC 1954: Index Catalogue, one of the supplements to the NGC.III Zw 2: Zwicky’s third list of galaxies.

Most rapidly proliferating now are the objects of the newbranches of astronomy:Circinus Z-1: first X-ray source in the constellation Circinus.SMC X-2: second X-ray source in the Small Magellanic Cloud.ESO 113-IG45: European Southern Observatory southern sky sur-vey in blue light, field 113, interacting galaxy 45.3C 231: Third Cambridge Catalogue of Radio Sources.PSR 1913+15: a pulsar.MXB 1730-335: Massachusetts Institute of Technology Z-ray burstsources.OAO 1653-40: objects discovered by the Orbiting AstrophysicalObservatory (the Copernicus satellite).

One object may bear several different designations in its aspectsas double star and variable star, as nova and nova remnant, as opti-cal and non-optical source.

476 - 550? Aryabhata476 - 550? Aryabhata founder of Indian astronomyfounder of Indian astronomy598 - 668 Brahmagupta598 - 668 Brahmagupta invented zeroinvented zero

787 - 886 Abu Ma`shar al-Balkhi (Albumasar)787 - 886 Abu Ma`shar al-Balkhi (Albumasar) preserved Aristotelian theory for Europepreserved Aristotelian theory for Europe800? - 870? al-Farghani (Alfraganus)800? - 870? al-Farghani (Alfraganus) measured the Earth, translated Ptolemymeasured the Earth, translated Ptolemy803 - 873 Muhammad ibn Musa ibn Shakir803 - 873 Muhammad ibn Musa ibn Shakir one of 3 astronomical "Sons of Musa"one of 3 astronomical "Sons of Musa"

903 - 986 Abd ar-Rahman as-Sufi (Azophi)903 - 986 Abd ar-Rahman as-Sufi (Azophi) first noted Andromeda and Large "Magellanic" Cloudfirst noted Andromeda and Large "Magellanic" Cloud940? -1000 Abu Mahmud Khujandi940? -1000 Abu Mahmud Khujandimural sextant, obliquity of Earthmural sextant, obliquity of Earth946? -1003 Gerbert d'Aurillac (Pope Sylvester II)946? -1003 Gerbert d'Aurillac (Pope Sylvester II) brought Muslim astronomy to Europebrought Muslim astronomy to Europe

965 -1040? Ibn al-Haytham (Alhazen)965 -1040? Ibn al-Haytham (Alhazen) all-round scientistall-round scientist988? -1061? Ali ibn Ridwan988? -1061? Ali ibn Ridwan described the supernova of 1006described the supernova of 1006

1029 -1087 Az-Zarqali (Arzachel)1029 -1087 Az-Zarqali (Arzachel) astronomical instruments and tablesastronomical instruments and tables1031 -1095 Shen Kuo1031 -1095 Shen Kuo eclipses, improved instrumentseclipses, improved instruments

1048 -1131 Omar Khayyam1048 -1131 Omar Khayyam observatory; calendar more accurate than oursobservatory; calendar more accurate than ours1114 -1185 Bhaskara II1114 -1185 Bhaskara II mathematical astronomermathematical astronomer

1149 -1209 Fakhr ad-Din ar-Razi1149 -1209 Fakhr ad-Din ar-Razi suggested many worlds, many universessuggested many worlds, many universes1195? -1256? John of Sacrobosco1195? -1256? John of Sacrobosco "Tractatus de Sphaera", textbook for 4 centuries"Tractatus de Sphaera", textbook for 4 centuries1201 -1274 Nasir ad-Din Tusi1201 -1274 Nasir ad-Din Tusi got the Mongols to build his observatorygot the Mongols to build his observatory

1221 -1284 Alfonso X of Castile1221 -1284 Alfonso X of Castile the Alfonsine Tablesthe Alfonsine Tables1304 -1375 Ibn ash-Shatir1304 -1375 Ibn ash-Shatir brought Ptolemy closer to realitybrought Ptolemy closer to reality

1323? -1382 Nicole Oresme1323? -1382 Nicole Oresme the Earth rotatesthe Earth rotates1394 -1449 Ulugh Beg1394 -1449 Ulugh Beg great observatory at Samarkandgreat observatory at Samarkand

1401 -1464 Nicholas of Cusa1401 -1464 Nicholas of Cusa anticipated Copernicus, Galileo, Kepleranticipated Copernicus, Galileo, Kepler1403 -1474 Ali Qushji1403 -1474 Ali Qushji science free from religionscience free from religion

1460? -1528 Al-Birjandi1460? -1528 Al-Birjandi thought-experiments like Galileo'sthought-experiments like Galileo's

Some medieval astronomers.

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After the March equinox, the Sun moves to ecliptic longitude 1°, 2°,3° . . . Since there are 360° in the circle and 365¼ days in the year, it gainsa little under a degree a day. It moves through the rest of Pisces toAries . . . Always on the ecliptic, it moves north of the Earth’s equatorialplane; its declination changes from 0° to +1°, +2°, more slowly than thegain in longitude. (The Earth’s equatorial plane, moving with the Earth, isdropping south of the Sun.) The Sun’s rising-point moves north along thehorizon. It moves slowest if you live on the equator, faster farther north,till at the pole it moves at infinite speed—that is, it instantly leaves thehorizon.

Everywhere at sunrise shadows point south at least slightly (since theSun is rising north of east). In the north hemisphere, this lasts only till theSun has slid up to where it is east from you. Still the only place for whichthe Sun rises vertically is the equator, but it does not rise toward the zenith(being now on a “small circle” of the sphere). For a place just north of theequator, the Sun, though climbing at a slight slope, reaches the zenith atnoon.

The Sun sets a little north of west. Like any star in the north celestialhemisphere, it has spent slightly more than 12 hours in the sky for placesin the north hemisphere of the Earth—days are getting longer thannights—and slightly less for the south.

The north hemisphere of the Earth is starting to tilt toward the Sun, andwill remain so till the other equinox. As seen from the Sun, the north polehas crept inward of the limb: it is nearer than the center of the Earth is, andremains permanently in view till the other equinox; the other pole has dis-appeared till the other equinox. The terminator, since it does not passthrough the poles, slants across the map. The people for whom the Sun isrising at the same time as for you are those north and slightly west of you,and south and slightly east. (And the opposite at sunset.) The lines of lat-itude as seen from the Sun begin to appear curved. Those in the southhemisphere are shorter, and some at the south end disappear; some aroundthe north pole come completely in view as narrow ellipses. But of theequator always half remains in view. The “top” of the Earth remains apoint on the Arctic Circle (though appearing closer to the pole); but thetrailing and leading points of the Earth move inward from the two tropicstoward the equator, while the points where the two tropics touch the eclip-tic plane move around toward the subsolar point (Cancer) and the antiso-lar point (Capricorn).

The rate at which the Sun’s rising- and setting-points creep northwardalong the horizon is fastest at the equinox; toward the June solstice itbecomes imperceptible. The same happens with the northward movementof the latitude at which the Sun is overhead; and the lengthening and rais-ing of the Sun’s trajectory in the sky and the lengthening of the daylight;and the tilting of the north hemisphere toward the Sun and the shorteningof the distance of the north pole from the Sun; and the northward gain inthe Sun’s declination.

At the June solstice, the Sun reaches geocentric longitude 90°, on theTaurus-Gemini border (the Earth being at 270° heliocentrically). The Sunis at its northernmost declination of 23½° in the map of the sky. (The equa-torial plane, centered in the Earth, is dipping farthest south of the Sun.) TheSun’s rising- and setting-points are farthest north around the horizon. Forplaces on the equator this is just 23½° north of the east and west points.For places farther north it increases; till at 66½° N. (the Arctic Circle) it is90°: that is, the rising- and setting-points are the same, the north point; theSun on this one day just touches the horizon and does not set. For theAntarctic Circle the Sun comes up from below and touches the horizon andgoes down again. For the north pole, the Sun’s rightward circle around thesky (parallel to the horizon as always) is highest—23½°—above thehorizon.

The Sun seems to pass overhead at noon many days in a row for peo-ple in the Sahara and Mexico and other places along the Tropic of Cancer.(This may be a reason why they, and the Australian and Kalahari andAtacama deserts on the other tropic, are more scorched than the equator,where the Sun is overhead twice a year but moves away more quickly.)Outside the two tropics, the Sun is never overhead (nor is it ever overheadfor anyone except at noon). Shadows (north of the Tropic of Cancer),pointing north at noon as always, are at their shortest. Students, likeancient men, can mark the tip of a pole’s shadow and thus determine thetime of noon; mark it each noon and thus determine the date of solstice.

Days are longest for the north hemisphere, nights for the south, andthey are still essentially equal at the equator. The north hemisphere is mosttilted toward the Sun (and the south away) by the maximum angle of 23½°.As seen from the Sun, the north pole is on the north-south meridian of theEarth; it is at its minimum distance from the Sun (as compared with thecenter of the Earth). The “top” of the Earth, still on the Arctic Circle, isnow also on the central meridian, all the Arctic Circle being in view fromthe Sun; the “bottom” of the Earth is on the Antarctic Circle which, but forthis one point, is out of view on the night side; the bow and trailing pointsof the Earth are both on the equator; the subsolar point, center of the diskas seen from the Sun, is on the Tropic of Cancer which here dips to touchthe ecliptic plane, while the other tropic rises to touch that plane at the anti-solar point on the night side.

All these geometrical rhythms can be filled in by analogy for the otherthree quadrants of the year.

There are some modifications for more fastidious accuracy:—Atmospheric refraction curves the path of light by more than half

a degree (34´) at the horizon. So the Sun appears on the horizon when geo-metrically it is this much below. This lengthens every day by about 2¼minutes at either end for places on the equator, where the Sun is risingstraight up; by longer times for places at higher latitudes. For the poles itmeans that on each equinox day the Sun appears not exactly on the hori-

zon, but more than half a degree above; so the polar “day” is not exactlyhalf the year, from equinox to equinox, but 1.445 days longer at each end.

—The Sun is not a point but a disk with angular width of about halfa degree (32´). It is so bright that daylight begins as soon as the merestpoint of it shows, without waiting for its center. So day begins at the equa-tor about another minute earlier (the time it takes for the center to climbvertically half the Sun’s width), more at other latitudes where the Sunclimbs slantingly. At the north pole the upper limb of the Sun creeps intoview .68 of a day before the center does. So the combined effect is thatthe Sun comes into view here 2.125 days before the March equinox andstays in view for as long past the September equinox; at the south pole theconverse, so the two polar “days” overlap each other by 4¼ days. Seenfrom a “real” point of view: the Sun is huge, and there is a time when lightfrom the northern part of it is shining on (and a little past) the north poleof little Earth while light from the south of it is shining on our south pole.

—The equinoxes and solstices are strictly instants, not days. So it isnot really true that at the March equinox, for example, the Sun for allplaces rises at the exact east point. It does so only for those places (alonga north-south line of longitude) where the instant of sunrise coincides withthe instant of equinox. For the next band of places, the Sun as it rises isalready a fraction of a degree farther along the ecliptic and a hair farthernorth along the horizon. And the band of places for which it was settingat the instant of equinox is on the opposite side of the globe.

—The Earth’s orbit is elliptical. So for example the north pole isnearest to the Sun at the June solstice only as compared with the center ofthe Earth, a difference of a mere 6,000 kilometers. The whole Earth is2,500,000 kilometers nearer in January and farther in July.

—Also because of the ellipticity of its orbit, the Earth’s speed alongthe orbit varies, while it rotates at a constant rate; this causes a variation inthe length of the day, so that it is not quite true that, for example, day andnight remain of equal length all year at the equator.

We might expect our changing distance from the Sun to be the reason whywe get hotter and colder. Since perihelion brings us 2,500,000 kilometersnearer than average in January and aphelion as much farther out in July(whereas the axial tilt only ever makes a 400th of this difference), wemight think that the whole Earth would have summer in January and win-ter in July; or at least that northern winter and southern summer would bewarmer, and northern summer and southern winter colder—in otherwords, for the north hemisphere to have moderate seasons and the southextreme ones. But it is the other way around! The extreme temperaturesare recorded in the continents of the north hemisphere. This is because ofthe greater amount of ocean in the south. Water gains and loses heat moreslowly than land. (The exceptions which indeed prove the rule are the capsof the two hemispheres, water for the north and land for the south:Antarctica has more extreme temperatures than the Arctic Ocean.) So notonly is Earth’s climate kept steady by the comparative smallness of itsorbit’s eccentricity, but it is kept even steadier because the oceans work inopposition to the eccentricity.

For some other planets, which have more eccentric orbits and do nothave oceans at all, this is a season-causing factor more equal with rota-tional tilt. We can see it on Mars. The north hemisphere of Mars leansSunward on the more distant side of its orbit (around aphelion). So on thisside of the orbit the north has a not very warm summer, with the northpolar icecap not shrinking much, while the south has a terrible winter, itsicecap spreading greatly. On the other side of the orbit, the north has a rel-atively mild winter, with its icecap not spreading much, while the southhas (for Mars) a hot summer, in which its icecap may disappear altogeth-er.

What most greatly affects our temperature is not the changing distancefrom the Sun, nor the changing length of daytime: it is the angle at whichsunlight strikes. Looked at from where we are, this is the altitude of theSun.

If the Sun is at or below the horizon, If the Sun is at or below thehorizon, you are getting no heat from it. As it climbs, the amount of heatyou receive from it rapidly goes up; the growth slows as the Sun reachesits highest. This suggests a sine curve, and in fact the amount of radiationhitting the atmosphere is proportional to the sine of the Sun’s altitude.

Then add the effect of the atmosphere, which reduces the radiationreceived, and is, say, 1000 kilometers thick. As the Sun’s altitude lowers,its light is coming more slantingly through the atmosphere, till at altitude0 it is traversing about 3700 kilometers of it. Thus the atmosphere exag-gerates the difference caused by altitude. But it also scatters sunlight andthus brings it to us by routes other than the direct; so that for instance theamount is not zero when the Sun’s altitude is zero—we are receivingsome glow after and even before dawn. Then add, of course, the clouds inthe atmosphere and other variations of weather.

In general, though, the most radiation per unit area is reaching Earthat the subsolar point, the center of the disk as seen from the Sun, and itdecreases from there to the limb, where the Sun appears on the horizon.Some places, in the tropics, move from the limb to the center; others tra-verse shorter arcs across the Sunlit face and do not reach the center. As thesubsolar point moves to its northernmost in June, all places north of theTropic of Cancer have their longest times in the sunlight and come their

Sun

June

March

December

September

---Capricorn---Arctic

---Cancer

A view with the ecliptic plane level, and from alower angle (ecliptic latitude 7.5°, longitude 190°).Sun enlarged 5 times, Earth 2000 times.

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32 The Astronomical Companion

MOON’S ORBITThe Earth is a planet, revolving around the Sun in a year, and theMoon is a satellite, revolving around the Earth in about a month—this picture is now familiar to almost everyone, and is approximate-ly true, but can be misleading.

Suppose you are on some comet high above the solar system.You might see the third planet, far out from the Sun, as a tiny speckof light, or you might be able to resolve it into two specks, one 4 or5 magnitudes fainter than the other. Together they pursue their vastyearly cycle.

As they go, you may notice them gradually changing places.Sometimes the smaller speck is in the lead, then it slows slightly,thus falling back to the inside position, and then to a position in therear. Then it speeds up again—slightly—till it overtakes on theoutside, and continues forging slowly ahead till it is again in thelead.

The familiar picture tends to make us imagine that the Moon’scourse through space must describe loops or perhaps cycloid cusps:

But, in fact, it does not even include convex waves:It is everywhere concave toward the Sun!This statement amazes people, but from the true-scale diagram itbecomes easy to accept. The distance the Moon oscillates in and outis only ¼ of 1 percent of the radius of the huge circle. And it per-forms this tiny oscillation only about 12 times in going around thecircle. In the large diagram, about 1/12 of the circle is drawn, con-necting the positions of the Earth. If you draw a curve connectingthe positions of the Moon, it is almost the same circle. The curva-ture just decreases slightly around the time of new Moon.

A truer picture still is that both Moon and Earth revolve aroundthe barycenter (center of mass) of the Earth-Moon system; and it isthis barycenter that revolves in a smooth orbit around the Sun. TheEarth has 81.3 times as much mass as the Moon. So their barycen-ter is 1/81.3 of the distance from the center of the Earth to the cen-ter of the Moon. This proves to be inside the Earth, 4728 km fromthe center and 1650 km (1025 miles) below the surface. There is noone particle that is the barycenter: the Earth rotates, so the barycen-ter keeps traveling (at an average speed of 1196 km/hr) through theEarth’s mantle, staying always below the Moon. If you happen to bein a tropical country, then at some time in the month the Moon willpass over your head, and at that moment you can tell yourself thatthe barycenter of the Earth-Moon system is a thousand miles underyour feet, gliding through the rock at the speed of a fast jet plane.

The Earth, then, sways around the barycenter, but slowly, with aperiod of about a month: the main mass of the Earth keeps on theopposite side to the Moon, but has a much shorter circle to travel.When astronomers, standing on the Earth’s surface, measure theapparent position of some other planet, they are not measuring froma smoothly traveling station, so they find that, for instance, Marswhen at its nearest appears displaced up to 17″ ahead of where itshould be (when Earth is swinging behind the barycenter) or 17″behind (when Earth is ahead of the barycenter). Indeed this provid-ed the experimental, as opposed to theoretical, way of calculatingwhere the barycenter is, and of determining the relative mass ofEarth and Moon.

Having first become clear about the true almost-circular orbitsof barycenter, Earth, and Moon around the Sun, let’s revert to themore familiar picture in which we imagine the Earth (or barycenter)standing still and the Moon therefore in a far smaller almost-circularorbit around it. This, after all, is convenient in thinking about therelations of these two little planets.

Periods of the Moon in its orbit around the Earth are also called“months.”

The Moon’s mass (1/81.3 of the Earth’s) and average distancefrom the Earth determine its averaqge period around the Earth,27.32166 days. This is the sidereal month; that is, in relation to thestars, to space in general. If at a certain instant the Moon is crossingthe line in space that leads from us to the star Omega Piscium, thena sidereal month later it will again be in that same direction.

However, the map position of Omega Piscium will not be quitethe same: because of the Earth’s precession, the star will have moveda small distance (about 3.76”) eastward; or, more truly, the mapframework will have moved westward. Suppose, at the first pass,the star was on the R.A. 0 line: then, the next timearound, the Moonwill reach this position about 7 seconds of time before it reaches thestar. So this tropical month, or period in relation to our sky-mapcoordinates, is 7 seconds shorter, or 27.32158 days.

Suppose also that on the first pass the Sun was in the same direc-tion as Omega Piscium; in other words, this was the moment of newMoon. A sidereal month later, when the Moon comes round to thedirection of Omega Piscium, the Earth-Moon system has moved26.929 of its curved orbit around the Sun (360 × siderealmonth/sidereal year); so the direction to the Sun is now that muchdifferent. So the Moon has to travel on considerably farther beforeagain reaching the Sunward line. So this synodic (or synodical)month is 29.53059 days. It is the period from new Moon to newMoon, during which the Moon goes through its cycle of “phases” orapparent shapes to us, caused by the angle at which we see the Sunlitside of it.

This cycle is most conspicuous to mankind, so the calendarmonth originated from it.

The synodic month is a sliding measure of time; one can also saythat two full Moons, or first quarters, or any other phases, are a syn-odic month apart. A word for the anchored unit of time, from a cer-tain new Moon to the next new Moon, is lunation. Lunations arenumbered in a series begun by E. W. Brown from 1923 Jan. 16; thuslunation 953 began with the new Moon of 2000 Jan. 6.

Eccentricity. The Moon’s orbit around the Earth is not quite a cir-cle, but an ellipse, with an eccentricity of .054900, the Earth (or,

strictly, the barycenter) being at one focus of the ellipse. In otherwords, the Moon’s distance from the Earth varies by about 5.49%more or less than its average distance. This is not greatly eccentric:about 3 times more so than the Earth’s (or, strictly, the barycenter’s)orbit around the Sun, and almost exactly the same as Saturn’s.

(The orbit of the Earth’s center around the barycenter must,then, be a tiny ellipse of the same shape. Thus the depth of thebarycenter beneath Earth’s surface varies between about 1900 and1400 km. When the Moon is at perigee, the barycenter is deepestbelow Earth’s surface.)

At perigee the Moon looks larger, and brighter, and appears tomove faster through the sky, both because it is nearer and because itactually is moving faster in its orbit. From these observationsHipparchus discovered its varying distance from Earth, though hethought it could be accounted for by a circular orbit with the Earthplaced eccentrically. And this did fit well enough for many cen-turies, till the observations became more exact.

The ellipticity varies. Roughly, at the times when the ellipse hasits axis pointing toward the Sun, it is stretched to a longer shape;when it is broadside to the Sun, it is pulled more toward the circular.Thus if the Moon is at perigee at the time of new or full Moon, itsposition is nearer in—at its closest to the Earth, in fact—and ifperigee coincides with first or last quarter, it is farther out. Thesevarying distances of course affect the apparent size of the Moon.

Nor does the ellipse remain oriented the same way in space: itsaxis precesses, forward. This, too, is due mainly to the pull of theSun. It takes 3236.2 days (about 8 years and 10 months) for theperigee to precess all the way around. Each time the Moon comesaround to where the perigee was before, the perigee has movedabout 3° onward, so the Moon has to travel on for another quarter ofa day to catch up with it. So the period from perigee to perigee isthis much longer than the sidereal month; it is 27.55455 days, and iscalled the anomalistic month.

Inclination. Satellites, at leat those rather close to their planets asthe Moon is, generally revolve in their planets’ equatorial planes.Look at Jupiter’s flock, obediently circling their master’s middle asif on leading-strings from his belt. The Moon does not do this. Itasserts its independence by ignoring the Earth’s equator and swim-ming along in the same plane around the Sun as the Earth does, theecliptic plane.

This is not fully accurate. The ecliptic plane is, most truly, theplane in which the barycenter of the Earth-Moon system moves,with Earth and Moon revolving around it. The chances are againstthe Earth and Moon themselves revolving in exactly the same plane.In fact they revolve in a plane inclined to it by 5°8´43″ (5.145°).Thus they rise and fall slightly through the ecliptic plane. The Mooncan get up to 37,000 km north or south of the plane (11 times its owndiameter), the Earth’s center only 456 km (1/28 of the Earth’s diam-eter). So the Earth’s body is always floating in the ecliptic plane,even if a little high or low; whereas the Moon does not stay in aplane at all, but rides a gentle roller-coaster around the Sun. (TheEarth bobs like a floating ball with the surface (the ecliptic) alwaysaround its waist; the Moon, like a dolphin, curving over and under.)

The inclination or tilt (just like the eccentricity or shape) of theMoon’s orbit varies in amount, and precesses in direction; again, themain cause is the pull of the Sun; and, again, the speed of the pre-cession is remarkbly rapid. However, the direction of the precessionis backward (retrograde, westward).

The variation is ±9´ (0.15°), with a period of 173 days (justunder half a year). Thus the tilt to the ecliptic is at a maximum of5.295°, and then 3 months later it is at a minimum of 4.995°.

The direction of tilt regresses around the orbit at a rate of 0.053°a day, so that it goes all the way around in 18.6 years (6793.5 days).This is called the nutation-period. If it is hard to visualize a “plane’sdirection of tilt precessing,” recall the sight of a dropped plate, spin-ning not quite flat to the floor (before settling flat).

At a certain point the Moon is at its ascending node, where itcuts upward through the ecliptic plane. It goes around its orbit, cut-ting downward again half way around, and after a sidereal month itwould reach the same point again. But meanwhile the ascendingnode has moved 1.44° backward to meet it. It therefore reaches the

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Astronomical Companion 45

The Lyrid and Perseid orbits are far the largest for any of the major showers, and happen to be almostidentical in size and shape. They extend out to 57 a.u. from the Sun (as against 35 for Halley’s Cometand 49 for Pluto); only about ¼ of each of them appears in our picture. Their planes are almost perpen-dicular to each other. Most of the Lyrid orbit is north of the ecliptic plane, most of the Perseid orbitsouth. Yet they are so arranged that in both cases the meteors descend steeply across our orbit, at pointswe pass in April and August. The Lyrids have the very steep inclination of 79°; the Perseids are almostas steep, at 67° (technically 113°, since they are moving in retrograde direction around the Sun). ThePerseids were the dominant steady stream of the 20th century. The Lyrids were observed in China in 687B.C.; showed 90 per hour in 1982. The Draconids are an example of a youthful swarm still movingaround their orbit in irregular huge clumps. Notice that the Lyrid ascending node is just outside the orbitof Saturn, while the Draconid comet similarly was captured by Jupiter.

Two July showers. The lines of nodes for the Capricornid and Delta Aquarid orbits almost coincide.But the nodes are at opposite ends of the line: the Capricornids descend where the Delta Aquarids ascend.To be exact, we meet the Delta Aquarids slightly earlier, at our orbital longitude 305° (measured fromthe equinox point, �), and the Caricornids at 307°; that is why the date usually given for the Capricornidmaximum is July 28 and for the Delta Aquarids, July 30. Actually, the showers spread over many days,since the meteor streams are really broad bundles of orbits of which the one we show is the central one.Both Capricornids and Delta Aquarids move directly (counterclockwise) around the Sun, and have shal-low inclinations (7° and 27°), so that they appear to us rather slow (especially the Capricornids) andcome from near the ecliptic (the Capricornids just north of it, the Delta Aquarids just south). The orbitof the Delta Aquarids is the very eccentric (elongated), and has its perihelion point the nearest to the Sun(only 0.069 a.u. or 10 million km). It looks as though we ought to see meteors from another part of theCapricornid stream about January 28 (appearing to come from Pisces or Cetus).

Three winter showers. All have “direct” motion (counterclockwise as seen from the north, like theplanets). But the Quadrantid and Ursid orbital planes are tilted steeply to the ecliptic plane, theGeminids much less so. The three descend into the part of our orbit that we traverse in December andJanuary. The ascending node of the Quadrantids (where they pass northward through the ecliptic plane)is just inside the orbit of Jupiter. The Geminid orbit, unlike the other two, passes very close to the Sun;the orbit, smaller than any comet’s, was puzzling until it was realized that the parent body is an Apolloasteroid, 3200 Phaethon. The line along the middle of each orbit is its “major axis,” also called “line ofapsides” because it connects the perihelion and aphelion points. All these lines intersect at the Sun.

A comet and its meteors. Halley’s Comet itself misses the Earth by many million kilometers: itsascending node is well outside our orbit, its descending node well inside. But the particles that separatefrom it, mainly at its perihelion passages, follow various diverging orbits (which, barring other influ-ences, will reconverge at the point of separation, though at different times according to the lengths oftheir new orbits). Thus the particles collectively form a huge bundle of orbits in space, vastly wider thanthe comet. Within this great “bundle,” those “threads” that happen to intersect the Earth’s orbit are seenby us as meteor streams. Since the Halley orbit is fairly flat to the ecliptic plane (18°), it passes rela-tively near to our orbit twice, and two of the other threads in the bundle are able to strike us, one on theway in (at the October part of our orbit) and the other on the way out (at the May part). In looking atthis model, realize that (1) the particles that encounter us in May as Eta Aquarid meteors are not reallythe “same” as the Orionids in the sense that they could have hit the Earth in October: they would havepassed a few million kilometers above. (2) Other “threads” of the bundle must surround the comet’sorbit in all directions, so that if we were not on the Earth but riding ten million kilometers above wewould still see Halley-derived meteors in May and October.

Three showers of November. The Andromedids are catching up with the Earth and hence appear tous as slow meteors; the Leonids are meeting us head-on and so appear extremely swift. The inclinationof the Andromedids is only 13°; that of the Leonids, 164°—which is to say, they have retrogrademotion, and are inclined 16° to the ecliptic plane the other way. A 16° triangle of cardboard is visiblesupporting the Leonid plane in the model. The Andromedid and Leonid planes intersect rather close tothe Earth’s orbit. Adding the Taurid orbit would make a situation too tangled to picture this way (it isinclined only 5°, and would be mostly hidden by the other two planes). Mentally slide it in along thedashed line till its focus (the dot) is at the Sun. Unlike the other two, the Taurids are coming up fromjust under the ecliptic plane; that is, we see them at their ascending node. They then pass only 0.375 a.u.from the Sun. They are following (approximately) the shortest cometary orbit, that of Comet 2P Encke.

Orbits of the major showers(Cardboard models!)

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56 The Astronomical Companion

DOUBLE STARS AND OTHER MULTIPLE STARS

A star which, on examination, proves to be two or more stars is a“double star.” This term is in familiar use though the subjectincludes triple and other multiple stars. A star system is any natur-al group of one, two, or more stars.

Till 1803 (when William Herschel showed otherwise) it wasassumed that doubles are merely optical: stars that happen to be inthe same line of sight and have no real connection, one (probablythe fainter) being farther away. There are some such: Sarin (dHerculis) is two stars whose paths happen to be crossing). But wenow know that at least 60% are true binaries. This term, too, isunsatisfactory (seeming to refer to no more than two stars); so isphysically connected (suggesting that there is some kind of bridgebetween them). What is meant is that the two or more stars aregravitationally bound to each other, and travel together throughspace, orbiting around their common center of mass or barycenter.

(There is a third conceivable case between the opticals and the

binaries: stars that are actually passing very near each other, andmay even be bent into temporary hyperbolic orbits around theircommon barycenter, but are destined to separate forever, unless,very improbably, they collide.)

Some companion stars such as Proxima Centauri, 36 OphiuchiC, Van Biesbroeck’s, and Alcor, though they appear close to theirprimaries, are really hundreds of solar-system widths away, so thatit is not quite sure that they are physically connected.

Over 100,000 visual binaries are known. If we add non-visualbinaries, and future discoveries, it seems that half the stars in theuniverse may belong to binary systems. If we take the nearest starsto us as a typical sample, it seems that an even higher proportionmay have faint companions, undetectable if farther away. If wetake the very nearest stars as typical, it seems that a further propor-tion may have unseen companions, like Jupiter, slightly too smallto have become luminous as stars. If we take our own star as typ-

ical, it may be that even single stars are non-simple in the sense ofhaving systems of smaller companions, grading from planets all theway down to dust. And a distant small companion of the Sun mayyet be discovered against the starry background.

Many members of double systems are themselves closer dou-bles; the large multiples grade into small clusters; a cluster mayhave doubles within it, or a multiple system as its core. This musthave to do with the way stars form, as centers of contraction in neb-ulae that are irregular in size and density.

On maps, double stars are often distinguished by a line throughthe symbols.

Binaries break down into the following types according to howthey are detected or their physical connectedness is shown (and,roughly, this typology also arranges them in order of discovery andof increasing closeness to each other):

Visual doubles (either optical or binary) are those that can be resolved into separate images. First, thereare the naked-eye ones, presumably known of old: Mizar and Alcor (z and 80 Ursae Majoris, 12´ of arcapart); a Capricorni (6´); to keen eyes, a Librae (4´) and e Lyrae (3´). Others, such as q1 and 2 Tauriin the Hyades and q1 and 2 in Orion’s sword, are considered too far apart to count as doubles.

The first telescopic multiples were among Galileo’s discoveries in 1617: Mizar itself; and a triple,q2 inside the Orion Nebula, later found to be quadruple and called the Trapezium; it is now known tohave at least 7 other members and is perhaps the heart of a cluster.

For some visual doubles the evidence that they are binary is only that they are at a common dis-tance, or show common radial velocity (speed toward or away from us, deduced from the blueward orredward shifting of lines in their spectra), or common proper motion (they travel parallel to each otherover the years). Thus the two stars of Albireo, being at least 100 times as far apart as the Sun andNeptune, must be orbiting each other so slowly that it could be thousands of years before we detect evenwhich direction they are taking. These pairs are also known as “relfixes” (“relatively fixed,” where theword “relative” is pleasantly ambiguous).

Others are close enough to each other that their orbital motion around each other is detectable.These include most of the close doubles that challenge the telescopic observer.

Non-visual types:If refined measurements of the proper motion of a star show it moving from year to year in a slight-

ly wavy line, it is probably, as it travels, revolving around the barycenter of itself and a companion toofaint to see. Sirius was the classic case of such an astrometric binary from 1844 till 1862 when its com-panion was found visually.

There may also be irregularities in the orbital curves of two stars in a visual pair, meaning that oneof them has a closer companion, perhaps planet-sized.

New doubles in the zodiacal band of the sky are continually being discovered by amateurs fromstepwise occultations by the Moon: a star’s light is seen (or photoelectrically measured) to be cut offgradually or in two or more quick steps instead of one.

The spectrum of a star’s light can reveal its duplicity in two ways: First, the lines in the spectrummay shift to and fro, indicating that the star’s radial velocity is rhythmically altering. It must be revolv-ing swiftly around its barycenter with an unseen companion, and the orbit must be roughly edge-on tous. Or the lines may keep dividing in two and then coming together again: the observed light is fromboth stars and when one is approaching the other is receding. (One component of, again, Mizar was thefirst example discovered.) The term for this type is spectroscopic binary, but sometimes it loosely cov-ers also the second type: spectrum binary, in which the spectrum is composite, and must contain lightfrom different types of stars.

If two stars happen to revolve in a plane edge-on to us (it must be almost exactly so, or the starsmust be close together), they periodically eclipse each other, wholly or partially, as can be seen fromsharp or sloping drops in their combined light-curve. These eclipsing binaries therefore are treated asa class of both double and variable stars.

Some of these latter types are thought to be so close that they tidally distort each other or are actu-ally touching (contact binaries), and matter is flowing between them. An example is b Lyrae. In manyclose systems one star is a nova or other variable, its instability being the effect on it of the other. Orone may be a black hole or other strange body, detectable through its effect on the light of the visiblestar.

The brighter star of a pair is called the primary. The other may be called secondary, companion, orcomes (Latin for “companion”; plural comites).

Their apparent relative position is given by two figures: angular separa-tion (usually in seconds), and position angle of the secondary (measuredcounterclockwise from the north).

Since the stars are orbiting, both these quantities keep changing. If theorbit is counterclockwise (position angle increasing) it is called direct; ifclockwise (position angle decreasing), it is a retrograde orbit. This followsthe use of these terms for the solar system, where almost everything movescounterclockwise (as seen from the north). The change in position is rapid forstars physically close together, with short orbital periods, so that printed infor-mation a couple of decades old cannot be relied on. Orbit diagrams are moresatisfactory in that they show, and explain, the situation for a span of many years.

The true situation is that each star ofa pair moves in its own ellipse, around abarycenter which is at one focus of bothellipses. The more massive star has thesmaller orbit. More truly still, eachorbit slowly precesses, and thus is arosette rather than an ellipse.

For simplicity we ignore not only precession but the orbital movement of one of the stars (thebrighter—which is not always the more massive). We use a frame of reference in which it is held still,and draw the other star’s relative orbit around it (which will be larger than the true ellipse around thebarycenter).

The line of apsides is also the major axis of theellipse. The star moves fastest at periastron and slow-est at apastron.

This orbit may be tilted any way to our line ofsight, so the apparent orbit usually looks quite dif-ferent. It may be rounder or more elongated; the pri-mary star appears to be no longer at the focus; the lineof apsides is foreshortened and no longer runs alongthe major axis. Minimum angular separation nolonger coincides with periastron nor maximum withapastron; there are often (not always) two minima andtwo maxima. The only thing always in the same placeis the center of the ellipse (half way along both majoraxis and line of apsides); and the proportion betweenperiastron and apastron distances remains the same.The line of nodes, running through the primary star,divides the part of the orbit farther from us than theprimary star (dashed) from the part nearer (solid). In practice, we do not know which is which unlessradial-velocity studies of the star have been made.

To find the combined magnitude of two stars, the formula is:

—log(2.512 to the power of —mag1 + 2.512 to the power of —mag2) / —0.4

2.512 is the factor between magnitudes and is the 5th root of 100; 0.4 is the logarithm of it. An easiermethod (suggested by Kenneth Rose of Bryn Athyn, Pennsylvania), giving a good enough answer inmost cases, is:

if difference between mags. is this or more: 0 .1 .3 .5 .8 1.1 1.5 2.1 3.4then subtract this from smaller mag. (brighter star): .8 .7 .6 .5 .4 .3 .2 .1 .0

Binary stars are important for science because determining their orbits, from many observations,enables measurement of their masses and hence much else about them.

And double stars make good telescopic targets for city-dwellers, because sky brightness does notwash them out as it does nebulous objects or planetary details. Also, the most systematic way to trainyour eye and test your telescope’s resolving-power is to see which doubles it will “split.” Start withwide pairs, move to closer ones till you find the limit. Just above the limit, you see a definite waist orminimum of light between the stars; just below, you see one elongated image. From such observationsW.R. Dawes found the Dawes limit, an empirical formula for the closest double a telescope shouldsplit. It is 4.56 seconds divided by the aperture in inches. Thus, a

However: (1) Dawes worked in the 19th century and used refracting telescopes; modern reflectorsshould do slightly better. (2) Dawes was a seasoned observer; it may take you a while to catch up withhim! (3) Blue stars are easier to separate than red ones. (4) The brighter the star, and the larger the tele-scope, the more the image spreads by irradiation (on eye retina or film); strictly, Dawes’s formulaapplies to a pair of stars of magnitude

—brighter stars being more difficult, and fainter ones easier (so long as they can be seen at all). (5)The greater the magnitude contrast, the more difficult: thus d Cygni is difficult though not very close;and Sirius and Procyon are very difficult, the glare of the primaries drowning the faint companions.

To learn that stars have color may come as a slight surprise. They tend to appear just white, by contrastwith surrounding darkness. Fainter ones, especially, seem without color because fainter light stimulatesonly the rods of the retina, which do not discriminate color. However, if two of these pale spots of lighthappen to be close together, the slight tints in each become more noticeable. Thus double stars offerthe strongest sensations of color in the night sky (other than auroras, the eclipsed Moon, some fireballs,and scintillation of stars low in the atmosphere; the spectacular colors that photographs, or printing, canbring out in nebulae are far below the limit of vision in any telescope).

But “color” is not a simple objective measurement: it is a judgment made in the brain, and is affect-ed not only by the mixture of wavelengths in light falling on the cones of the retina, but also by lightthat fell just before (fatigue), by light falling on neighboring cones (contrast), and by expectations, evenby language. Thus the contrast between two stars may not merely heighten the color in each, but mayseem to push them apart to strange places in the spectrum. Of two yellows, the more redward may seemamber or purple, the more blueward turquoise or gray . . . For reasons like this, double stars cause notonly relatively strong color-impressions but an endless variety of human responses and descriptions.

So if you take up the pleasures of double-star observing you will be led to curiosity about the “real”color of each star. And this is bound up with the questions of its distance, size, and physical nature. Theanswer is best summed up by the short descriptive formula such as K5 III, where III means that it is agiant, and K5, the spectral class, means that it probably has a certain surface temperature that makes itglow orange. Thus spectral type gives an idea of the color the star would display if we were near to it.Still, the only star we have seen in such a way is our G2 Sun; when we travel far enough toward otherstars to see their surfaces we may be in for some surprises!

1-inch telescope 4.56″2 should split 2.28″3 2 stars of 1.52″4 separation 1.14″

5-inch telescope 0.91″6 should split 0.76″7 2 stars of 0.65″8 separation 0.57″

9-inch telescope 0.51″10 should split 0.46″12.5 2 stars of 0.36″16 separation 0.29″

4.5 seen in a 3-inch telescope6 66.6 8

7.1 seen in a 10-inch telescope7.6 12.58.2 16

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Sphere radius 13,700,000,000 light-years,or about 4,200 megaparsecs.Radius of inner sphere 1,500,000,000 light-years.Grid lines on equatorial plane 5.000,000,0000 light-years apart.

can only become a larger and larger fraction of that distance,approaching it as a limit. Also, the number of light-years of distanceis the number of years the light has been traveling to reach us; if thedistance could become greater than the universe is old, we would beseeing objects before the beginning of the universe of which they arepart.

The redshift, however, can increase indefinitely. No matter howdistant they get and how close to the speed of light away from us, thelight of the quasars still reaches us with the usual speed of light. Butwe cannot observe it: longer wavelength is the same as lower ener-gy, and it has been shifted off the end of the spectrum, where it hasno energy.

The quasars pile up, as it seems to us, just inside the limiting dis-tance which they cannot reach. It would seem from our point ofview—or, put another way, if space were not curved—that theymust be ever closer together just inside that skin. On the contrary,they are drawing apart from each other at the same increasing rate asfrom us. From the point of view of each one of them (or whateverhas by now evolved out of them) they are the centers; the limitingdistance is equally far away all around them, and we are among theobjects vanishing toward it.

This Hubble distance, as it is called, is found by dividing thespeed of light c (299,792 kilometers per second) by the Hubble con-stant (or parameter) of recession H (in kilometers per second permegaparsec). This is a number that matters: the size, age, and fateof the universe depend on it. Edwin Hubble estimated it as 550.That is, if H is 550, then for each megaparsec of distance from us agalaxy cluster or quasar is receding from us 550 kilometers per sec-ond faster. If H is smaller the Hubble distance is larger. And theestimates for H gradually came down. Around 1970 there was dis-pute (with public debates) between those who favored values

around 100 and around 50. In 1979 a likely value seemed to be 55.Recent studies, using various methods, have found values between77 and 70, still with uncertainties of up to 15%. So it is with uncer-tainty that we now pick 71, giving a Hubble distance of about 4,200megaparsecs, or 13,700 million light-years.

Only figuratively is it the “edge of the universe.” The universe,though finite, has no edge (just as, two-dimensionally, the surface ofa balloon is finite but has no edge). It is perhaps the “distance wheregalaxies would be if they could be moving away from us at the speedof light,” but, as they cannot, it is a distance slightly greater than anyactual distance can be—until the universe grows older.

Objects at the largest possible distances from us in oppositedirections are twice as far from each other, right? No. They areclose to each other, in the sense that they were—at the time whenthe light now reaching us started from them—near the beginningof the universe, which was then small. In this sense the outermostsphere, with seemingly the vastest area of all, is a point.

But the Hubble distance is not really the radius of the universeat present: the expanding universe is more than 3 times larger.Objects whose light left them, on its way to us, nearly 13.7 billionyears ago have been carried away from us all that time by the uni-versal expansion, and are now at the “co-moving distance” of per-haps 47 billion light-years.

And now it has been found (from the otherwise unexplaineddimness of distant supernovas) that the speed of expansion, insteadof gradually slowing, must, after half the universe’s present age,have gone over to acceleration. And this in turn requires somethingelse that, being as yet unobserved, is called “dark”: dark energy. Ofthe whole content of the universe, 73 percent is dark energy, 23 per-cent dark matter, 4 percent the ordinary matter and energy that weknow.

The Big Bang 13.7 billion years ago created space, which expandswith the universe; there is no space outside it, and that is why thoughfinite in size the universe has no edge. Nor does it have a center,though what our picture shows as its edge is in another sense its cen-ter, since it is where, for us, its beginning is located.

This is unpicturable: a space which has no center; every point init seems to be the center, surrounded by a different sphere of pointsthat are the most remote. It is unpicturable by our brains becausethese evolved to survive in a certain small environment.

Since we cannot in any way see as far as this distance—norcould we be situated outside it, since there is no outside—it is para-doxical to make a picture in which we are outside it and can see intoit, all the way to the Earth and as far again on the other side. So Ihave suggested the strangeness by the distorted projection that aris-es when I bring my eye close to the skin of our universal bubble andpeer in.

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2004 Jan 2: The Stardust craft passed within 140 miles of comet Wild 2, collecting samples forEarth return.

Jan 4: A U.S. rover named Spirit landed on Mars.Jan 25: Another U.S. rover, Opportunity, landed on Mars.Mar 2: Rosetta was launched by Europe. It is slated to orbit a comet in 2014.Jun 21: For the first time a private space vehicle, SpaceShipOne, reached space.Jun 30: Cassini, launched in 1997, went into orbit around Saturn, first craft ever to do so.Aug 3: Messenger was launched on a seven-year journey to the planet Mercury.Aug 9: The first deployment of solar sails in space was achieved by Japan.Aug 31: The 63rd and last Atlas II rocket was launched.Sep 8: The Genesis craft, loaded with solar wind particles, crashed on reentry.Nov 8: A new Soyuz 2-1a rocket, the first major upgrade since the 1960s, had its maiden

launch.Dec 21: A Delta IV heavy rocket, twice as powerful as a standard Delta IV, made its maiden

flight.

2005 Jan 14: Europe’s Huygens probe landed on Saturn’s moon Titan.Feb 12: The heavy-lift version of Ariane 5 made its first successful launch.Jul 4: Deep Impact made a successful collision with comet Tempel 1.Jul 26: America’s manned spaceflight program resumed after more than two years.Sep 12: A Japanese spacecraft, Hayabusa, orbited asteroid 25143 Itokawa.Oct 11: Cosmonaut Krikalev set a record for cumulative days in space: 803.Oct 12: China sent its second manned mission into orbit.Oct 19: The 368th and last Titan rocket was launched. The first flew in 1959.

2006 Jan 15: After seven years in space, Stardust landed on Earth with samples from a comet.Jan 19: New Horizons was launched. It will reach the dwarf planet Pluto in 2015.Mar 10: Mars Reconnaissance Orbiter went into Martian orbit.Apr 11: Europe’s Venus Express craft went into orbit around Venus.

Aug 15: Voyager 1 became the first craft to reach a distance of 100 AU from the Sun.

2007 Jan 11: A Chinese weapon shot down a satellite, creating 35,000 pieces of junk.May 14: China entered the commercial space arena with a launch for Nigeria.Sep 27: Dawn was launched to study the asteroids 4 Vesta (in 2011) and 1 Ceres (in 2015).Oct 29: A Chinese satellite orbited the Moon.

2008 Jan 14: The Ulysses craft, launched in 1990, flew over the north pole of the Sun.Feb 11: The European-built Columbus module was attached to the ISS.Mar 9: Europe launched its first space freighter, the ATV, to resupply the ISS.May 25: A U.S. probe named Phoenix landed on Mars.Jun 4: The Japanese module Kibo was attached to the ISS.Jul 26: The first Soyuz 2-1b rocket was launched.Sep 25: China launched its first 3-person crew into orbit.Sep 26: China performed its first spacewalk, a feat first performed by Russia in 1965.Sep 28: Falcon 1 became the first privately-built liquid-fueled rocket to reach orbit.Nov 8: A craft launched by India went into lunar orbit.

2009 Feb 10: The first collision of two intact satellites occurred as Cosmos 2251 hit Iridium 33.Mar 6: The Kepler telescope was launched to search for Earth-like planets in deep space.May 14: Europe launched two space observatories, Herschel and Planck.May 18: Shuttle astronauts repaired the Hubble space telescope for the last time.Jun 23: The U.S. craft Lunar Recon Orbiter went into orbit around the Moon.Jul 1: The heaviest comsat ever built (15,233 pounds) was launched on an Ariane 5.Jul 17: The ISS crew complement reached 13 people, the most ever in space at one time.

2010 Feb 1: The U.S. canceled plans to return astronauts to the Moon.Apr 22: The first robotic spaceplane, the X-37B, was launched by the U.S. Air Force.Jul 10: Rosetta made a fly-by of the asteroid 21 Lutetia, the largest asteroid yet seen close up.

INDEX2012 scare: 303C 273 quasar: 6847 Tucanae: 6161 Cygni: 49; 58

A.A.V.S.O.: see AmericanAssociation of Variable StarObservers

a.u.: see astronomical unitabsolute magnitude: 50-51; 53absorption lines: 53Acamar: 27acceleration of expansion: 69accretion disks: 68Achelis, Elizabeth: 31Achernar: 27active galaxies: 68Adhara: 50-51Adonis (asteroid): 40age of Moon: 35age of universe: 69Akkadians: 30albedo: 36Alcor: 56Alexander the Great: 30Algol: 11; 57alien beings: 49Alkaid: 11; 14; 58All Fools’ Day: 26All Saints’ Day: 26Alpha Centauri: inside front cover;

48-49; 50-51alphabet: 29Altair: 49altazimuth: 8-9altitude: 11Aludra (Eta Canis Majoris): 60American Association of Variable

Star Observers: 57Amor asteroids: 41amorphôtoi: see unformedAndromeda Galaxy: 65; 67Andromedid meteors: 43; 44angular measurement: 46angular momentum: 19Annunciation: 26; 31anomalistic month: 32; 38-39anomalistic month and year: 23antapex of the Sun’s way: 58Antarctic Circle: 24 ff.ante meridiem: 22antihelion source: 44apex of the Sun’s way: 58aphelion: 18; 25Apollo asteroids: 41; 45apparent magnitude: 50-51apparent time: 22apparent vs. real: 4; 18apparitions: 43Aquarius, Age of: 29Arabic: 9; 14; 16Aratus: 14Arctic Circle: 24 ff.Arcturus: 63Argelander, Friedrich: 57Argo: 17; 62Aries: 19; 29Arietid meteors: 43Aristotle: 42; 43ascending node: see nodesasssociations of stars: 59Assyrian calendar: 30asterisms: 12asteroid designations: 43

asteroids: 4; 19; 40-41Astraea (asteroid): 40astrology: 19; 29; 30astrometric binary stars: 56Astronomical Almanac, The: 22; 41;

50Astronomical Calendar, The: inside

front cover; 22; 30; 31; 37; 50astronomical unit: 18-19; 47Aten asteroids: 41atomic second: 23Attila: 43attractor: 67Augustus: 31autumn: 26azimuth: 7

Babylonia: 29; 30; 38Backlund, Oskar: 43bar of Milky Way galaxy: 62Barnard, Edward Emerson: 49Barnard’s Star: 49barred spiral galaxies: 62; 65barycenter: 35barycenter of Earth-Moon system: 32barycenter of star system: 56Bayer letters: 17; 57Bayer, Johann : 12Bayeux Tapestry: 43bearing: 9Beehive Cluster: see PraesepeBeltane: 26Benetnash: see AlkaidBessel, Friedrich: 49Besselian year: 23Betelgeuse: 10; 22; 51; 57; 58; 60Betulia (asteroid): 41Biela’s Comet: 43; 44Big Bang: 69Big Dipper: 11; 12; 22; 58binary stars: 56birds, migration: 29Birkat Ha-H ≥ammah: 26black hole: 54; 67; 68blackbody radiation: 53Bode, Johann: 21Bode’s Law: 21; 40Bok globules: 53Bolton, John: 68Bopp, Thomas: 43Brahe, Tycho: 42brightest stars: 50-51Brigid, Saint: 26Brocchi’s Cluster: 12brown dwarfs: 49bulge, central, of galaxy: 62; 63Bunton, George: 31Burnham, Robert, Jr.: 50Burnham’s Celestial Handbook: 50

Cacciatore, Niccolo: 14-15calendar month: 32calendars: 30-31Caligula: 31Candlemas: 26Canis Major: 59Cannon, Annie Jump: 53Canopus: 11; 50-51Capella: 27Caph (Beta Cassiopeiae): 22carbon cycle: 54Castor: 50-51Catalogue of Nearby Stars: 49Cat’s Eye Nebula: 19

celestial equator: see equatorcelestial sphere: 4; 19celestial sphere, area of: 12Cepheid stars: 54; 57; 64Ceplecha, Zdenek: 44Ceres: 40Chaffee, Roger: 15Chandrasekhar limit: 54Chi Orionis: 61Chicago asteroids: 41China: 42Chinese calendar: 30Christian calendar: 31Christmas: 26; 31Cidenas (Kidinnu): 29Ciotti, Joseph: 31Circlet of Pisces: 12circumpolar: 11; 12civil time: 22Clavius, Christopher: 31Clement of Alexandria: 31clock time: 22clusters of galaxies: 67; 68; 68; 69clusters of stars: 56; 58; 60; 63Coathanger: 12cocoon nebula: 53colliding galaxies: 65Collinder 399: 12color index: 53color of stars: 56color-luminosity graph: 53Coma Berenices: 12Coma Cluster of stars: 58coma of comets: 42-43comets: 4; 19; 31; 42-43; 44; 46comets, objects mistaken for: 59co-moving distance: 69companion stars: 56conjunction, triple of Jupiter and

Saturn: 31constellations: 12-13; 19contact binaries: 56coronagraph: 43Costsworth, Moses: 31crescent Moon: 34Cronia festival: 31cross-quarter days: 26Crux-Scutum Arm: 62culminating: 9; 12; 22Curtis, Heber: 65

dark energy: 69dark matter: 68; 69Dawes limit: 56Dawes, William Rutter: 56day, kinds of: 23day, length of: 25daylight-saving time: 22day-night cycle: 30decans: 19declination: 6; 19; 27-29deep-sky objects: 17degenerate matter: 53Deimos: 40Delphinus: 29Delporte, Eugène: 12Delta-T: 22Deneb: 50-51; 58; 59; 60Denebola: 22density waves: 62descending node: see nodesdesignations of asteroids: 40designations of comets: 43

designations of stars and deep-skyobjects: 17

designations of variable stars: 57Dio Cassius: 31Diocletian: 31Dionysius Exiguus: 31Diphda (Beta Ceti): 59disk of Milky Way galaxy: 60; 63distance: 46-47distance, ultimate: 69distances between stars vs. galaxies:

65diurnal motion: 10diurnal parallax: 47Domitian: 31Double Cluster in Perseus: 61double stars: 50; 56Draco: 24draconic month: 33Dreyer, J.L.E.: 59Dubhe: 58dust clouds: 62dwarf galaxies: 64dwarf planets: 40dwarf stars: 53Dynamical Time: 22

early-type stars: 53Earth: 20earthlight: 36Earth’s orbit: 18-19earthshine: 35; 36Easter: 26eccentricity of Moon’s orbit: 32eccentricity of orbit: 18eclipse year: 30; 38-39eclipses: 35; 38-39; 43eclipses of Moon: 36eclipsing binaries: 56; 57ecliptic: 4; 7; 18-19; 32-33; 63ecliptic poles: 19Edgeworth, Kenneth: 19Edwards Perpetual Calendar: 31effective temperature: 53Egyptian calendar: 30Einstein, Albert: 53ellipse, elliptical orbit: 18ellipsoid, triaxial: 37ellipsoidal stars: 57elliptical galaxies: 65; 67elongation: 34Emiliani, Cesare: 31emission lines: 53; 68Encke, Johann Franz: 40Encke’s Comet: 43Ephemeris Time: 22Ephorus: 43epoch: 29equation of time: 22equator: 4; 9; 27equatorial system: 6; 7; 19equinox points: 6equinoxes: 19; 24 ff.; 27-29Equitable Calendar: 31era: 30Eros (asteroid)F: 41escape velocity: 54Eta Aquarid meteors: 43evolution of stars: 53=55expansion of space: 67; 69extra-solar planets: 49

facing south: 10figured area of sky: 27

fireballs: 44First Point of Aries: 19; 29First Point of Libra: 29first-magnitude stars: 15; 50-51Fish, Age of the: 29fixed objects: 4Flamsteed numbers: 17Flamsteed, John: 17flare stars: 57Fleming, Williamina: 53Flying Wedge: 12Fomalhaut: 27Franklin, Benjamin: 22full Moon: 19

galactic equator: 27galactic plane: 59; 66galactic system: 7; 60galactic year: 62galaxies: 60; 66; 67; 68; 69galaxy clusters: 67galaxy groups: 67genitive: 12; 17giant stars: 49; 53gibbous Moon: 34Giotto: 43Gliese, Wilhelm: 49globular clusters: 61; 63; 64; 65; 67goddesses: 40gods, Greek and Roman: 21Gould, Benjamin Apthorp: 12Gould’s Belt: 60Great Attractor: 67great circle: 10Great Square of Pegasus: 22Greek: 12; 14; 16; 19; 20; 34; 40Greek calendars: 30-31Greek letters: 17; 57Greeks: 12; 38Greenwich: 22Gregorian calendar: 23; 26; 31Grissom, Virgil “Ivan”: 15Groundhog Day: 26groups of galaxies: 67; 68guest-stars: 42Guy Fawkes Day: 26

Hale, Alan: 43Hale-Bopp, comet: 43half-wave of eclipses: 38-39half-year: 38-39Halley, Edmond: 17; 43Halley’s Comet: 42-43; 45Hallowe’en: 26halo of galaxy: 63handspan: 37Hardy, Thomas: 26Harvard classification: 53Heaven’s Gate cult: 43hegira: see hijraHelin, Eleanor: 41Hencke, Karl: 40Henderson, Thomas: 49Henry Draper Catalogue: 53Herbig-Haro objects: 53Hercules: 29Herod I: 31Herschel, John: 36Herschel, William: 56; 58Hertzsprung gap: 54Hertzsprung, Ejnar: 53Hertzsprung-Russell diagram: 49; 52-

55; 57Hesiod: 14

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Hevelius (Hoevelke), Johannes : 12Hidalgo (asteroid): 41hijra: 30Hilaria festival: 26Hilda asteroids: 41Hill, Betty and Barney: 49Hipparchus: 29; 32; 33Hipparcos: 17; 47; 49; 50-51; 53Hirayama families: 41horizon system: inside front cover; 7;

8-9horns of the Moon: 34Horsehead Nebula: 53hour of right ascension: 6hour of time: 23houses, zodiacal: 19Hubble constant of recession: 66; 69Hubble distance: 47; 69Hubble, Edwin: 65; 69Hudson, George: 22Huli festival: 26Hungaria asteroids: 41Hyades: 58Hyakutake, comet: 43hyperbolic orbit: 43; 56

I.A.U.: see InternationalAstronomical Union

I.C.: see Index CatalogueIbex: 19ice ages: 63Ides of March: 26; 31Iliad: 41illuminated fraction: 34-35Imholc festival: 26In Defense of Variety: 29inclination of meteor orbits: 45inclination of Moon’s orbit: 32; 38inclination of the ecliptic: see

obliquity; 24 ff.Index Catalogue: 59Indian calendar: 30informes: see unformedInnes, Robert: 49insolation: 26intercalation: 30intergalactic medium: 68International Astronomical Union:

12; 22; 43International Fixed Calendar: 31International Meteor Organization:

44interstellar medium: 60invariant plane of the solar system:

19Iranian calendar: 30irregular galaxies: 65

jâhiliyya (“time of ignorance”): 14Jahreiss, Hartmut: 49Janus (god): 31Jerusalem: 31; 43Jesus: 31jets: 67; 68Jewish calendar: 30Josephus, Flavius: 31Julian calendar: 23; 31Julian Dates: 23Julius Caesar: 31Juno: 40Jupiter: 20; 40; 41; 42-43Jupiter and the invariant plane: 19Jupiter-family comets: 43Jupiter-masses: 49

Kant, Immanuel: 65Kepler, Johannes: 31Kepler. Johannes: 43Kidinnu (Cidenas): 29kiloparsec: 47Kirkwood gaps: 41Kleszcz, Evarist: 31Kokab: 27Kreutz, Heinrich: 43Kuiper Belt: 19Kuiper, Gerard: 19

Labor Day: 26Lacaille: 12Lady Day: 26Lagoon Nebula: 27; 60Lagrangian points: 41Lalande, Jérome: 17Lammas: 26Lashes of Auriga’s whip: 17late-type stars: 53Latin: 12; 16; 17latitude: 6; 29latitude, ecliptic: 19latitude, terrestrial: 10; 24 ff.leap week: 31leap year: 23leap-days and years: 31Leonardo da Vinci: 36Levy, David: 43libration: 37light curves: 57light, speed of: 47; 68; 69light-time: 47light-year: 47; 69limb of Sun: 25

line of apsides of Moon’s orbit: 38line of nodes: 38Little Dipper: 12Local Bubble: 60Local Group of galaxies: 65; 66; 67local time: 22logarithmic universe: 5Long Count: 30longitude: 6; 29longitude of the Moon: 34longitude, ecliptic: 19longitude, terrestrial: 24 ff.lucida: 12Lugnasad: 26luminosity of stars: 53luna incognita: 37lunar mansions: 19lunation: 23; 32; 38Lyttleton: 42

M31: 65M33: 65M35: 27; 60M35 cluster: 62M87: 67; 68Machholz, Don: 43Maffei 1 and 2 galaxies: 66Maffei, Paolo: 66Magellan, Ferdinand: 64Magellanic Cloud, Large: 19Magellanic Clouds: 64

magnitude: 56; 57magnitude of Moon: 36magnitude, apparent and absolute:

50-51main belt: 40main sequence: 53; 59major planets: 19map symbols for double stars: 56map symbols for variable stars: 57March equinox: 29maria on the Moon: 36Marius (Mayr), Simon: 65Mars: 20; 40Mars, seasons on: 25Marsden, Brian: 43Martinmas: 26mass of stars: 53Maury, Antonia: 53May Eve: 26Maya calendar: 30Mazapil meteorite: 43mean Sun: 22Méchain, Pierre: 43megaparsec: 47Mercury: 20merging galaxies: 65meridian: 9; 22meridians of longitude: 22Mesopotamia: 12Mesopotamian calendar: 30Messier numbers: 59

Messier objects: 67Messier, Charles: 43; 59meteorites: 40; 44meteoroids: 44meteors: 4; 19; 43; 44-45

Metonic cycle: 23; 31metric calendar: 31micrometeorites: 44Milky Way: 4; 7; 27; 59; 65; 67Milky Way, center: 62Milky Way, disk: 60Milky Way, rotation: 62Milton, John: 44minor planets: 19; 40Mintaka: 10; 27minute of right ascension: 6minute of time: 23Mira: 51; 57Molineux, Emerie : 12month: 30month, kinds of: 23; 32month, sidereal: 32Moon: 4; 32-37

Moon, declination: 33Moon, interfering with meteor obser-

vation: 44Moon, shape: 37moonlight: 36moons: 19motion of star star: 58motion, diurnal: 10Muh≥ammad: 30multipe stars: 56Muslim calendar: 30

N.G.C.: see New General Cataloguenadir: 9names: see also designationsnames of stars: 14-17; 51near-Earth objects (N.E.O.s): 41nearest stars: 48-49

nebulae: 59; 59; 62; 63; 65nebulae, pre-stellar: 53Neptune: 21; 42; 43neutron star: 54New General Catalogue: 59New Year’s Eve: 26Newton, Isaac: 17; 33; 43NGC2158: 27

NGC2158 cluster: 62Niyazov, Saparmurad: 31nodes of Moon’s orbit: 32-33; 38nodes, ascending and descending: 19nodical month: 23; 33; 38-39nomenclature: see designationsnon-gravitational effect: 43noon: 22Norma Arm: 62Norma Cluster of galaxies: 67Northern Cross: 12nova: 31; 57Nubecula Major and Minor: 64nuclear fusion: 49; 53; 68nucleogenesis: 54nucleus of comets: 43nutation: 32

obliquity: 18; 27occultations: 36; 56; 68Olympiad: 31Omar, caliph: 30Omega Centauri: 11; 61Omega Piscium: 6; 22; 32Oort Cloud: 42; 46Ophiuchus: 19Öpik, Ernst: 44

optical double stars: 56optical doubles: 50orbits of double stars: 56orienting: 10-11Orion: 12; 59Orion Arm: 60; 61Orion association: 60Orionid meteors: 43Outer Arm: 62overview of astronomy: 4Ovid: 14

Palisa, Johann: 40Palitzsch, Johann Georg: 43Pallas: 40parabolic orbit: 42-43parallax: 47; 49parsec: 47Paschal Moon: 26Patrick, Saint: 26Pazmino’s Cluster: 61peculiar galaxies: 65perihelion: 18; 25periodic vs. long-period comets: 43Perseus Arm: 61Perseus Cluster of stars: 58Perseus Double Cluster: 61Persian: 16Phaethon (asteroid): 45phase angle: 34phases of Moon: 34-35; 37; 38phases of Moon and Earth: 36Phobos: 40Piazzi, Giuseppe: 14; 40; 49Pickering, William Henry: 53Pinwheel Galaxy: 66Pioneer spacecraft: 70-71Pisces: 31Plancius, Petrus : 12planes: inside front cover; 9planetoids: 40planets: 19; 20

planets, extra-solar: 49planets, viewing: 27Pleiades: 58; 60Pluto: 19; 21Polaris: 6; 11; 27; 59; 60poles: 9Pons, Jean-Louis: 43Pope, Alexander: 18population I and II: 54; 63; 65post meridiem: 22Praesepe or Beehive Cluster: 58precession: 19; 27-29; 32precession of double-star orbits: 56precession of Moon’s axis: 37precession of Moon’s orbit: 32precessional amounts: 29prime vertical: 9; 11projections: inside front cover; 19pronunciation of constellation names:

12pronunciation of star names: 16proper motion: 12; 49; 56Propus (Eta Geminorum): 27proton-proton cycle: 53proto-stars: 53Provençal (“Quan li jor sont lonc en

mai”): 29Proxima Centauri: inside front cover;

49; 56Ptolemy: 12; 14pulsar: 54pyramids: 27

Quadrantid meteors: 43quarter-days: 26quasars: 40; 68; 69

rabbits: 10radial velocity: 56radian: 12; 46radiants: 44

radio source Sagittarius A*: 62radio sources: 67; 68Rasalgethi: 14Rasalhague: 14real vs. apparent: 4; 18Realm of Galaxies: 66recession: 66; 67; 68red dwarfs: 49; 54red giants: 53; 57reddened light on Moon: 36redshift: 68; 69reformed calendars: 31refraction: 25; 36regression of Moon’s orbit: 38Regulus: 14; 50-51Reinmuth, Karl: 40relativistic speed: 68Research Consortium on Nearby

Stars: 49rift in Milky Way: 27; 62right ascension: 6; 19; 22; 27-29rings: 19rising and setting: 10; 24 ff.; 35Roman calendar: 31Rose, Kenneth: 56Rotanev (Beta Delphini): 14-15rotation of Moon: 37royal stars: 19Royer, Augustin : 12Russell, Henry Norris: 53

Sagittarius: 62; 63Sagittarius A*: 62Sagittarius Arm: 61Saint John’s Eve: 26Saint Lucy’s Day: 26Samhain (festival): 26San Juan Capistrano: 26São Paulo: 26Sarin (Delta Herculis): inside front

cover; 50; 56saros: 38-39satellite galaxies: 64; 65satellites, natural: 19Saturn: 21Saturnalia: 26; 31Scaliger, Joseph: 23Scancalendar, The: 31scattered disk: 19Schiaparelli, Giovanni: 44Schmidt, Maarten: 68Scorpius-Centaurus association: 60Sculptor Group of galaxies: 66season, eclipse: 38-39seasons: 4; 24 ff.

seasons, words for: 26Secchi, Angelo: 53second of right ascension: 6second of time: 23semimajor axis: 18Seneca,Lucius Annaeus: 42setting: see risingShapley, Harlow: 63; 65Shetland Islands: 31Shoemaker, Eugene: 41Shoemaker-Levy 9, comet: 43shooting stars: 44Sickle: 12sidereal time: 6; 9; 22; 27sidereal year: 29Sigma Octantis: 6; 27signs of the zodiac: 19; 29Silvester’s Day: 26Sinus Medii: 37Sirius: 50-51; 58Sky Catalogue 2000: 50small circle: 10Solar and Heliospheric Observatory

(SOHO): 43solar system: 4; 19; 68solar time: 22Solar Walk: 18solstices: 24 ff.

Sombrero Galaxy: 67Sosigenes: 31south: 10Southern Cross: 12; 27space: 69space exploration: 70-71Spanish: 12spectral type: 53-54; 56spectroscopic binaries: 56sphere pictures: inside front coverspiral arms: 60; 61; 62spiral galaxies: 65; 66; 67spring: 26standard time: 22star: 53stars, nearest: inside front cover; 48-

49Sualocin (Alpha Delphini): 14-15subsolar point: 24-25Sumerians: 14; 30summer: 26summer time: 22; 26Summer Triangle: 12Sun, altitude: 25Sun, angular width: 25Sun, motion: 58; 62Sun, position in galaxy: 59; 62Sun, variation: 57

sundial time: 22Sun-grazing comets: 43Sun’s quit: 58superclusters of galaxies: 67; 68supergiant stars: 53supernova: 31; 54; 57; 67; 69surface of Milky Way disk: 60swallows: 26symbols for the zodiac: 19synodic month: 23; 32; 38-39systems of stars: 56syzygy: 34; 38

T Tauri stars: 53Table Mountain: 36Tara: 26Taurid meteors: 43Taurus: 12Taurus and the Alphabet: 29Teapot: 12Teegarden, Bonnard: 49terminator: 24 ff.terminator of Moon: 36Thales: 27Theodor, Pieter : 12Thuban (Alpha Draconis): 27time: 22-23

time signals: 22time zones: 22-23time-units: 30Titius, Johann: 21transit: 9transneptunians: 19; 43Triangulum Galaxy: 65triaxial ellipsoid: 37Trifid Nebula: 27; 60Trojan asteroids: 41tropical year: 23; 29tropics of Cancer and Capricorn: 24

ff.tughra (Turkish monogram): 47Tunguska event: 43Turkish: 27Türkmenistan: 31Tycho catalogue: 49

U.T.: see Universal TimeUlysses spacecraft: 43Under-Standing of Eclipses, The: 38unformed stars: 12Unicorn: 19Universal Time: 22universe, age of: 69universe, “edge” of: 69Uranus: 21; 40Ursa Major: 12Ursa Major galaxy cluster: 66Ursa Major Group: 58

Van de Kamp, Peter: 49variable stars: 50; 53; 57

veering and backing: 9Vega: 11; 27; 58Venus: 20vernal: 26vernal equinox: see equinoxes; 24 ff.Vesta: 40Veterans’ Day: 26Virgo Cluster of galaxies: 67Virgo Supercluster: 67; 68visual double stars: 56Vogel: 53voids among galaxies: 68Voyager spacecraft: 70-71

walls of galaxies: 68waning Moon: 34watches of day and night: 30waxing Moon: 34weeks: 30Wells, H.G.: 36Whipple, Fred: 42Whirlpool Galaxy: 66white dwarfs: 53; 54White, Edward H., II: 15Willett, William: 22winter: 26Wolf, Max: 40Working List of Meteor Streams: 44World Calendar: 31Wright, Thomas: 65

X-ray bursters: 54

year: 4; 18-19year, kinds of: 23Yildun: 27Yule: 26; 31

zenith: 9; 24 ff.; 29zenithal hourly rate: 44zero-age main sequence: 53Zeta Reticuli: 49Zeta Tauri: 27zodiac: 19

zodiacal constellations: 12; 29zone of avoidance: 66zones, time: 22Zulu Time: 22

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Hertzsprung-Russell Aurora. This picture (first used on the cover of Astronomical Calendar 2007) pre-tends that the stars have miraculously f litted to positions in your sky such that the intrinsicallybrighter ones are higher, and the hotter ones are to the left. It is thus a colored version of theHertzsprung-Russell diagram (see page 52 of this book), the famous graph that is a tool for under-standing the nature and evolution of the of stars.

The upright dimension is absolute magnitude (the Moon happens to mark level 0); the horizontaldimension is spectral class, from hot blue O at the left through B, A, F, G, K, to red M at the right.

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