Chapter 7

A Planetary Overview

Courtesy of T

he International Astronom

ical Union/M

artin Kornm

esser

1. In 2006, the IAU defined a planet to be a celestial body that

(a) orbits the Sun,

(b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a nearly-round shape, and

(c) has cleared the neighborhood around its orbit.

2. Pluto has been demoted to a dwarf planet, an example of an object in the Kuiper belt (a disk-shaped region beyond Neptune’s orbit, 30 to 1000 AU from the Sun).

Courtesy of NASA, ESA, and A. Feild (STScI)

7-1 Sizes and Distances in the Solar System

Astronomical Unit: A unit of distance equal to the average distance between the Earth and the Sun.

1. Diameter of Sun (1.39 106 km) is about 110 times that of Earth (1.3 104 km).

2. Jupiter’s diameter is about 11 times that of Earth.

3. Pluto’s diameter is about 1/5 that of Earth.

Figure 7.01: The Sun, planets, and a few of the large moons drawn to scale.

Measuring Distances in the Solar System

1. Copernicus used geometry to determine relative distances to the planets, while today we measure them using radar.

2. An outgoing radar signal is usually a burst of 400 kilowatts (4 105 watts), but the returning signal is only 10-21 watt.

3. Though Mars is about 1.5 AU from the Sun, the distance from Earth to Mars varies from about 0.5 AU to 2.5 AU.

Advancing the Model: The Titius-Bode Law

The Titius-Bode “law” is an empirical relationship that allows us to approximate the distances to the planets. It is not based on any theoretical framework.

7-2 Measuring Mass and Average Density

1. Newton reformulated Kepler’s third law to include masses:

a3/P2 = K (m1 + m2), where K = G/(42)

 

2. If one of the objects is the Sun and the other is a planet, the sum of their two masses is essentially equal to the mass of the Sun: therefore,

a3/P 2 = K MSun

3. Newton’s reformulation of Kepler’s third law allows us to calculate the Sun’s mass.

4. The masses of 7 of the 9 known planets can be calculated based on the distances and periods of revolution of these planets’ natural satellites.

 

5. For Mercury and Venus, which do not possess any natural satellites, accurate determinations of their respective masses had to await orbiting or flyby space probes.

 

6. The Sun contains 99.85% of the mass of the solar system. The nine planets and their satellites account for about 0.135% of the total solar system mass.

Calculating Average Density

 

1. In calculating average density, we assume that the object approximately spherical: average density = mass/volume.

 

2. If we know the average density of an object we can gain reasonable insights into its makeup.

7-4 Planetary Motions

1. All planetary orbits are ellipses, but all (except Pluto’s) are nearly circular.

 

2. Each of the planets revolves around the Sun in a counterclockwise direction as viewed from far above the Earth’s North Pole.

 

3. All planets—except Venus, Uranus, and Pluto—rotate in a counterclockwise direction, as viewed from far above the Earth’s North Pole.

4. Most of the satellites revolving around planets also move in a counterclockwise direction as viewed from far above the Earth’s North Pole, though there are some exceptions.

5. The elliptical paths of all the planets are very nearly in the same plane, though Mercury’s orbit is inclined at 7° and Pluto’s at 17°.

 

6. The inclination of a planet’s orbit is the angle between the plane of a planet’s orbit and the ecliptic plane.

Figure 7.04

7-4 Classifying the Planets

The eight planets fit into two groups: the inner (terrestrial) planets and the outer (Jovian) planets.

Size, Mass, and Density

 1. The Jovian planets have much bigger diameters and even larger masses than the terrestrial planets.

 

2. The terrestrial planets are denser than the Jovian planets.

Satellites and Rings

 

1. The Jovian planets have more satellites than the terrestrial planets. The four Jovian planets have a total of 150 satellites compared to only 3 satellites for the four terrestrial planets.

 

2. Pluto has 3 satellite.

 

3. Each Jovian planet has a ring or ring system. None of the terrestrial planets do.

Rotations

 1. Solar day is the amount of time that elapses between successive passages of the Sun across the meridian.

 

2. Meridian is an imaginary line that runs from north to south, passing through the observer’s zenith.

3. Sidereal day is the amount of time that passes between successive passages of a given star across the meridian.

4. The Earth’s solar day and sidereal day differ by about 4 minutes.

 

5. All the Jovian planets rotate faster than any of the terrestrial planets.

Figure 7.05: The tilt between a planet’s axis of rotation and its orbital plane varies among the planets in our solar system.

7-5 Planetary Atmospheres

1. Escape velocity is the minimum velocity an object must have in order to escape the gravitational attraction of an object such as a planet.

 

2. The escape velocity from the Earth’s surface is 11 km/s (24,600 mi/hr). The escape velocity from the Moon’s surface is only 2.4 km/s (5370 mi/hr).

 

3. Phobos (a moon of Mars) is so small that its escape velocity is about 50 km/hr (30 mi/hr).  

© P

hotodisc

Gases and Escape Velocity

 

1. There are three states of matter in our normal experience: solid, liquid, gas. The fourth state of matter is the plasma state.

2. Properties of a gas:

(a) As gas molecules interact, different molecules have different speeds.

(b) The average speed of the molecules depends on the temperature of the gas.

(c) At the same temperature, less massive molecules have greater speed.

3. The temperature of a substance is defined by the average energy of its molecules.

 

4. There is little free hydrogen in Earth’s atmosphere because low-mass hydrogen molecules can achieve escape velocity at the temperatures of the upper atmosphere.

 

5. On the sunlit side of the Moon even molecules of oxygen and nitrogen—so prevalent in Earth’s atmosphere—can achieve escape velocity in the Moon’s low gravity.

The Atmospheres of the Planets

1. Ten times the average speed of molecules at a particular temperature provides a good measure of whether a planetary body will retain a gas for billions of years.

 

2. Because of their size (and mass) the Jovian planets have retained almost all of their gases.

 

3. Using spectroscopy we can accurately find the composition of an object’s atmosphere.

Figure 7.08: The speed of gases depends on their temperature.

• The dashed line represents 10 times the average speeds.

• All of the planets, Pluto, and some planetary satellits are indicated at their corresponding temperatures and escape velocities.

7-6 The Formation of the Solar System

1. There are two main categories of competing theories to explain the origin of our solar system:

the evolutionary theories

the catastrophe theories.

Evidential Clues from the Data

A successful theory must be able to explain the following data:

(a) All the planets revolve around the Sun in the same direction, and all planetary orbits are nearly circular (except for Pluto).

(b) All of the planets lie in nearly the same plane of revolution.

(c) Most of the planets rotate in the same direction as they orbit the Sun, except for Venus, Uranus, and Pluto.

(d) The majority of planetary satellites revolve around their parent planet in the same direction as the planets revolve around the Sun.

(e) There is a pattern in the spacing of the planets as one moves out from the Sun.

(f) Similarities of chemical composition exist among the planets, but there are also differences.

The outer planets contain more volatile elements and are less dense than the inner.

(g) All planets and moons that have a solid surface show evidence of craters.

(h) All Jovian planets have ring systems.

(i) Asteroids, comets, and meteoroids populate the solar system along with the planets, and each category of objects has its own pattern of motion and location.

(j) The planets have more total angular momentum than does the Sun, even though the Sun has most of the mass.

(k) Recent evidence indicates that planetary systems in various stages of development exist around other stars.

Evolutionary Theories

 

1. All evolutionary theories have their start with Descartes’s whirlpool or vortex theory proposed in 1644.

 2. Using Newtonian mechanics, Kant (1755) introduced the idea of a rotating cloud of gas contracting under gravity and forming a disk. Laplace (1796) showed that such a disk will break up into rings.

 3. Such a rotating, contracting disk of gas should speed up

according to the law of conservation of angular momentum.

Figure 7.09

4. Angular momentum is a measure of the tendency of a rotating or revolving object to continue its motion.

 

5. Conservation of angular momentum is a law that states:

the angular momentum of a system will not change unless a net outside influence is exerted on the system, producing a twist around some axis.

 

6. The Sun—the center of the former rotating cloud—should be rotating much faster than it is observed to be.

The total angular momentum of the planets is known to be greater than that of the Sun, which should not occur according to Newton’s laws.

This contradiction caused the evolutionary theory to lose favor early in the 20th century.

Catastrophe Theories

1. A catastrophe theory is a theory of the formation of the solar system that involves an unusual incident such as the collision of the Sun with another star.

 

2. The first catastrophe theory—that a comet pulled material from the Sun to form the planets—was proposed by Georges de Buffon in 1745.

 

3. More recently, it was proposed that the Sun was a part of a triple star system that gave birth to the solar system through tidal disruption.

4. Such theories were discredited in the 1930s when it was shown that material pulled from the Sun would have been too hot to condense to form planets and would have subsequently dissipated into space.

 

5. Recent discoveries of planetary systems orbiting other nearby stars further discredit catastrophe theories, because catastrophic origins for such systems should be quite rare due to the unusual nature of the incident.

 

6. Finally, a solution for the angular momentum problem has been found, so catastrophe theories have been abandoned.

Present Evolutionary Theories

 

1. In the 1940s Weizsäcker showed that eddies would form in a disk-shaped rotating gas cloud and that the eddies nearer the center would be smaller.

 

2. Eddies condense to form small collections of particles that over time grow to become planetesimals, which in turn sweep up smaller particles through collision and gravitational attraction.

Figure 7.11: Eddies in a gas cloud

3. An object shrinking under the force of gravity heats up.

High temperatures near the newly formed Sun (protosun) will prevent the condensation of more volatile elements.

Planets forming there will thus be made of nonvolatile, dense material.

 

4. Farther out, the eddies are larger and the temperatures cooler so large planets can form that are composed of volatile elements (light gases).

Courtesy of Doctors Claude and Francois Roddier

Figure 7.13: Development of a solar system—planetesimals have formed and large eddies of gas and dust remain

5. As the young Sun heated up, it ionized the gas of the inner solar system.

The Sun’s magnetic field exerted a force on the ions in the inner solar system sweeping them around with it, causing the ions to speed up.

As per Newton’s third law, this transfer of energy to the ions caused the Sun to slow its rate of rotation.

 

6. Stellar wind is the flow of particles from a star.

7. Some young stars exhibit strong stellar winds.

If the early Sun went through such a period, the resulting intense solar wind would have swept the inner solar system clear of volatile elements.

The giant planets of the outer solar system would then have collected these outflowing gases.

Explaining Other Clues

1. Over millions of years the remaining planetesimals fell onto the moons and planets causing the cratering we see today.

2. Comets are thought to be material that coalesced in the outer solar system from the remnants of small eddies.

3. The formation of Jupiter and its moons must have resembled the formation of the solar system.

As we move outward from Jupiter, its moons decrease in density and increase in volatile elements.

4. Catastrophes probably played a minor, more localized role in the formation of the solar system, but the overall origin of our solar system was evolutionary in nature.

7-7 Planetary Systems Around Other Stars

Is it common for stars to have planets?

Different categories of evidence can help answer this question.

1. Direct observation/Infrared companions, such as is seen with the brown dwarf 2M1207 and the star T Tauri, can be evidence of possible planetary bodies.

Figure 7.14a

Courtesy of Doctors Claude and Francois Roddier

Figure 7.14b

2. Dust disks such as discovered around Pictoris and AU Microscopii provide evidence that conditions for planet formation exist around many Sun-like stars.

Courtesy of Mark McCaughrean and Mark Morten Andersen of the Astrophysical Institute Potsdam (AIP) and ESO

Figure 7.15a: An infrared photo of Beta Pictoris Figure 7.15b: AU Microscopii dust disk

Courtesy of Michael Liu, IFA-Hawaii/W.M. Keck Observatory

3. Pulsar companions discovered around pulsars as a result of the variations in the rate of the received signals from the pulsar.

4. A binary system is a pair of objects that are gravitationally linked so that they orbit one another.

A discernable visual wobble exhibited by a star would suggest the existence of an unseen companion— such as a large planet or group of planets.

Figure 7.16a

5. In the Doppler (radial-velocity) method the wobble observed in the Doppler shift of a star’s spectrum suggests the existence of one or more planets around the star.

Since 1995 this method resulted in the discovery of most of the 100 or so exoplanets known to date.

Figure 7.16b

6. When a stellar occultation occurs (i.e., one celestial object passes in front of another), the total amount of light received decreases.

During a transit (when a planet passes in front of its star), the star will dim.

Such dimming can confirm the existence of an exoplanet or lead to an exoplanet’s detection.

Figure 7.16c

7. When a planet passes between the observer and a distant star, the planet’s gravity acts like a lens and produces a brief enhancement to the star’s brightness.

It is possible to detect exoplanets using this gravitational microlensing method.

Figure 7.16d

The Formation of Planetary Systems

1. According to the core-accretion model of planetary formation:

planets start as small chunks of rock, dust, and debris and grow through accretion and collisions.

however, planets like Jupiter would take longer to form than the lifespan of the accretion disk around the star.

2. According to the disk-instability model, dense regions forming in the disk accrete more material and suddenly collapse to form one or more planets. However, such instabilities require massive disks, which are not commonly observed.

3. Observations also suggest that the size of the largest planet formed around a star is directly related to the star’s size.

4. Theoretical work supports observations suggesting that 25% of Sun-like stars have planetary systems.

5. It is too early for us to reach conclusions on the possibility of life existing on one or more exoplanets.

Future missions might be able to detect Earth-like planets and use spectroscopy to determine the chemical composition of their atmospheres and surfaces.