1445 Introductory Astronomy 5a-1

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1445 Introductory Astronomy I

Chapter 5a

Planetary Systems

R. S. Rubins Fall, 2010


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Five Essential Things to do in Space 1

In an article published in Scientific American in 2007,

George Musser lists the following goals for NASA.

1. Monitor Earths Climate (from Space).

2. Prepare an Asteroid Defense.

3. Seek Out New Life.

4. Explain the Genesis of the Planets.

5. Break out of the Solar System He asks whether NASA is about understanding the Earth,

the space shuttle and station, human exploration, exploring

the solar system, exploring the outer universe and space,

or science in general? 2


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1. Monitor Earths Climate

Program has been underfunded for over a decade.

New orbiting measuring instruments are needed to be in

place before the older satellites die.

2. Prepare an Asteroid Defense

Asteroids 10 km across (dinosaur killers) hit about every 100

million years.

Asteroids 50 meters across (city destroyers) hit about onceper millenium.

To deflect an asteroid by one Earth radius, its velocity should

be reduced by 1 mm/s, a decade in advance.

This program is also underfunded. 3


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3. Seek Out New Life

Here NASA is taking a follow the water approach, by studying

Mars, Jupiters moon, Europa, and Saturns moons, Titan and

Enceladus.

Many experiments are being made on Mars, but there is a needto dig at least 2 meters below its toxic surface, and also to bring

samples back for study.

4. Explain the Genesis of the Planets

There is a special need to understand Jupiter, the first-born and

largest planet, which probably influenced the formation of the

rest.

Comets, which were the collectors of the early solar system

material, are also in need of much more detailed study. 4


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5. Break out of the Solar System

This has been achieved by the Voyager 1 and2spacecraft,

launched in 1977, which are now over 100 AU from the

Earth, having crossed a major boundary of the solar system

the termination shock roughly 8 billion miles from theSun, in 2004 and 2006 respectively.

There are now European and American proposals for much

faster and more efficient systems using ion drive

propulsion, rather than rocket propulsion of earlier space

vehicles..

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Solar System: Significant Data 1

A theory of the solar system should explain the following.

1. The planets orbit in planes close to the ecliptic.

2. The planets revolve about the Sun in the same direction as

the Suns rotation.

3. With the exceptions of Venus, Uranus and Pluto, the planetsrotate in the same direction as their orbits about the Sun

4. With the exceptions of Mercury and Pluto, the planetary

orbits are almost circular.

5. The smaller rocky planets (the terrestrial planets) are nearer

to the Sun, and the larger gaseous planets (the gas giants

or Jovian planets) are further from it.

6. Gas giants have ring systems.


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The Solar System: Significant Data 2

7. The spacings between neighboring planets between Venus

and Neptune increase with distance from the Sun.

8. Planets with solid surfaces (terrestrial planets) show

evidence of craters.

9. The terrestrial planets contain less than 0.2% of the lightestelements, hydrogen and helium, which constitute over 99%

of the Sun.

10. The gas giants are primarily composed of volatile gases,

particularly H and He.

11. The existence of asteroids, meteoroids and comets.

12. Data from the Sun and planets are consistent with the solar

system having been formed about 4.5 billion years ago.


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Radioactive Dating

Radioactive datingmeasures the time at which rockssolidified, since radioactive products prior to that time wouldhave escaped.

Such measurements give an age of close to 4.5 billion yearsfor the oldest rocks on the Earth (the Jack Hills Zircons inAustralia), as well as for samples obtained from the Moon andmeteorites.

In the example shown above, the isotope 40K (potassium)decays into Ca and Ar with a half-life of 1.28 billion years.


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Origin of the Solar System 1

Stars and planetary systems are formed from gigantic gas

clouds, containing about 74% H and 25% He by weight, withthe remaining 1% consisting of heavier elements.

Our solar system probably evolved from a gigantic rotatingcloud of gas and dust, perhaps several light years (10-20

trillion miles) across. The elements between Li (lithium) and (iron) were created

in the thermonuclear fusion process by which stars producetheir energy, while elements heavier than Fe were createdin massive supernovae explosions.

The fact that heavier elements are present in abundance onthe Earth means that the solar system was not among thevery early generations of stars.


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A gas cloud collapses if it is at

i. a sufficiently low temperature, so that the outward

thermal pressure is small;

ii. a sufficiently high density, so that the gravitational pressure

causes the cloud to collapse inwards.

The cloud collapses into a disk if it is rotating, because the

rotation creates an effective outward force, balancing gravity.


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The heavier elements in the solar systemwere created in processes occurring inearlier generations of stars. Theseelements, and their compounds, make upthe dust contained in the gas cloud.

Just as an ice-skater spins faster as she

brings her arms inwards, so does a rotatingmass spin faster as it collapses inwards.

The star is formed at the center of the disk,while planets condense throughout thedisk, at regions where the matter is

densest.


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Iron and silicates vapors condense to form dust particles when

the temperature drops below 1200 K.

The condensation of easily vaporized compounds, such as

water and methane, occurs only in the outer region of the disk.


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The heavier iron and silicate dust particles adhere together in

the inner region of the disk, formingplanetesimals, which are

objects from millimeters to kilometers in size.

Lighter, ice-rich planetesimals are produced in the outer regionof the disk.


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Ultimately, gravitational attractions cause the clumping of the

planetesimals in both regions of the solar disk.

Because H2

and He are by far the most abundant gases in the

solar disk, the cooler outer planets become surrounded by huge

envelopes of these gases.


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Formation of Solar System Summarized


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The Solar System

The solar system consists of the Sun and the objects orbiting it,

which are the planets, their moons, and asteroids, meteoroids

and comets, all of which shine in reflected sunlight.

The planet Jupiter is more than twice as massive as all of the

other satellites added together, but has a mass of only about(1/1000) M

Sun.

The inner or terrestrial planets are small rocky planets.

Their order from the Sun is Mercury, Venus, Earth and Mars.

The Jovian planets or gas giants are 15 to 320 more massive

than the Earth, and do not have distinct surfaces.

Their order from the Sun is Jupiter, Saturn, Uranus and Neptune.


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Terrestrial Planets versus Gas Giants

Terrestrials Gas Giants

Nearer the Sun Further from the Sun

Small LargeMostly solid Mostly fluid

Lower mass Higher mass

Slower rotation Faster rotation

Higher density Lower density

No rings Rings

Fewer moons Many moons


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The Terrestrial Planets


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The Gas Giants (or Jovian Planets)


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Planets Compared to the Sun 1


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Planets Compared to the Sun 2


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Comparative Planetary Data 1

Planet Diameter(Earth=1)

Mass(Earth=1)

Average Density(kg/m3)

Mercury 0.38 0.055 5400

Venus 0.95 0.82 5200Earth 1.00 1.00 5500

Mars 0.53 0.11 3900

Jupiter 11.21 318 1300

Saturn 9.45 95 700

Uranus 4.01 15 1300

Neptune 3.88 17 1600


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Comments on Diameter, Mass and Density

Planet sizes and masses fall into four groups as follows:

I (smallest):Mercury and Mars (5000 7000 km diameter);

II : Venus and Earth (12,000 13,000 km diameter);

III: Uranus and Neptune (50, 000 51,000 km diameter);

IV (largest):Jupiter and Saturn (120,000 140,000 km diameter).

[For comparison, Pluto has a diameter of roughly 2400 km.]

The average density = mass/volume.

The smaller terrestrial planets have higher densities, the Earthbeing the densest (5520 kg/m3).

The larger gas giants have the lowest densities, Saturn (690

kg/m

3

) being less dense than water (1000 kg/m

3

).


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Comparative Planetary Data 2

Planet Average

Distance fromSun

(AU)

Siderial Orbital

Period

(Earth years)

Siderial

RotationalPeriod

(Solar days)

Mercury 0.39 0.24 59Venus 0.72 0.62 243

Earth 1.00 1.00 1.00

Mars 1.5 1.9 1.03

Jupiter 5.2 11.9 0.41

Saturn 9.5 29.4 0.43

Uranus 19.2 84 0.69

Neptune 30.1 164 0.72


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Keplers Third Law of Planetary Motion

The square of the sidereal periodof a planetis proportional

to its (Mean distance from the Sun)3 ; i.e. P2 = a3.


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Titius-Bode Law

How the Titius-Bode Law,dn = (3n + 4)/10 AU, fits the data.

Planet Distance from Sun (AU)

n Bodes Law Measured

Mercury 0 0.4 0.39

Venus 1 0.7 0.72

Earth 2 1.0 (1.0)

Mars 4 1.6 1.5

Ceres 8 2.8 2.8

Jupiter 16 5.2 5.2

Saturn 32 10.0 9.5

Uranus 64 19.6 19.2

Neptune 128 38.8 30.1


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Comments on Orbits and Rotations

The Titius-Bode law is an empirical law, which fits the data

well, except for Neptune, probably because nearby Pluto.

It is not a fundamental law, which can be derived simply from

Newtons laws, although computer simulations using Newtons

laws show that some agreement with it.

The period of revolution (orbital period) of a planet about the

Sun is given by Keplers 3rd Law,P2 = a3.

The rotational periods of the planets (about 24 hours for the

Earth) are not connected to their distances from the Sun.

With the exceptions of Venus and Uranus (probably due to

early glancing collisions with asteroids), all the planets rotate

in the same as their orbital motion, so that the Sun appears to

rise in the East.


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Computer Simulation of Planet Formation

A computer simulation show how a solar system, originallycontaining 100 planetesimals, ultimately produces four planetsthrough accretion after a period of about 400 million years.

Time zero 30 million years 440 million years

100 planetesimals 22 planetesimals 4 planets


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A Note of Caution

The proposed origin of the solar system given here appears

logical, but studies of exoplanets associated with other starshave cast doubts on its correctness.

The observations of numerous Hot Jupiters, which are very

large planets, much closer to their star than Mercury is to

the Sun, suggests that these giant planets might have beenformed far from their star, but have moved much closer to it.

The inward migrations ofHot Jupiters may pull icy objects

into smaller rocky planets, giving rise to oceans on the

latter.

If this happened to Jupiter, it might have flicked lesser

planets out of its way as it moved to its present position.

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1445 Introductory Astronomy 5a-1