Exam #2 - June 29, 2000 - Solutions

The Jovian Planet Systems, Small Bodies, and the Formation of the Solar System

Astronomy 1110

Dr. Henry Throop, University of Colorado

"In order for a scientific revolution to occur, most scientists have to be wrong." -- unknown

Formulas & Numbers

Kepler's 1st law: All planets move in ellipses, with the Sun at one focus.
Kepler's 2nd law: The orbit of each planet sweeps out equal area in equal time.
Kepler's 3rd law: (orbital period in yr)2 = (average distance in AU)3, for bodies orbiting the sun.
Kepler's 3rd law: (orbital period in s)2 = 4 pi2 (average distance in cm)3 / (G (M1 + M2))
Newton's law of gravity: F = G (Mass 1) (Mass 2)/(distance)2
1 AU = 150 million km (1.5 108 km = 1.5 1013 cm)
1 km = 103 m = 105 cm = 106 mm
Speed of light = c = 3 1010 cm/s
Light year = 1 1018 cm
Velocity = Distance / Time

Instructions: There are 20 questions. The first set should be done on the bubble form, and the second and third sets on the test itself. If you are unclear on anything, please talk to me or Rob. The exam is due at the end of class, 12:35 PM.

Multiple Choice (30 points @ 3 points each)

1. Jupiter's moon Io is the most actively volcanic body in the solar system. Why was this surprising when it was discovered?
a) Io is not fully differentiated.
b) Ganymede has a strong magnetic field, and is probably warm inside.
c) Jupiter is a long distance from the sun, and thus cold.
d) Galileo had not predicted this when he observed the moons of Jupiter.

2. The greenhouse effect
a) Affects the Jovian planets' upper atmospheres.
b) Only works for terrestrial planets, near the Sun.
c) Makes Jupiter's core much warmer.
d) Must be stopped!

3. Jupiter's core can reach temperatures over 20,000 K. What causes these high temperatures?
a) Tidal heating
b) Core dumping and unsuccessful rebooting
c) Radioactive decay
d) Differentiation

4. The Mars Climate Orbiter dramatically crashed into the planet's surface on September 23, 1999, due to a unit conversion error in a short software code that converted foot-pounds into newton-meters, English to Metric. This mission cost about $100 million. About how many such Mars missions could be launched to equal the cost of one launch of the Space Shuttle?
a) two
b) four
c) ten
d) forty

5. Compared with a planet made of purely ices, a planet made of equal parts ices, metals, and rocks is probably
a) less dense
b) more dense
c) depends on the mass
d) brighter

6. The process by which heat escapes from the Earth's interior is
a) Convection
b) Differentiation
c) Astigmatism
d) Tidal heating

7. The densest materials in the solar system condense from their gas to solid state at...
a) The highest temperatures
b) The lowest temperatures
c) Depends on their distance
d) Can't tell

8. Assuming Pluto formed at its current location, does the solar nebula model predict we would find metals in Pluto?
a) No - metals condense only in the inner solar system.
b) Yes - metals condense almost anywhere.
c) Any metals were probably brought in from elsewhere.
d) Pluto is icy, but Charon probably metallic.

9. Saturn's rings are primarily
a) Atmospheric gasses thrown off by the planet's rotation.
b) Destroyed lost spacecraft sucked away from Mars.
c) Broken up remains of comets, moons, and asteroids.
d) On highly elliptical orbits.

10. A recent headline in the National Enquirer proclaimed, "New Galaxy Shaped Like a Gigantic...
a) Pinwheel!"
b) Fetus!"
c) Rhinestone!"
d) Crucifix!"

Short Answer Questions (30 points @ 5 points each)

1. Jupiter can retain hydrogen in its atmosphere, but in our atmosphere, hydrogen rapidly escapes to space. What are two reasons why Jupiter can retain this gas?

2. Saturn is over 120,000 km across, but we've can see through less than 1% of it directly. List three ways we can figure out what's inside it.

  • Measure its mass and density by observing satellites orbiting it
  • Study impacts; e.g., Shoemaker-Levy/9 comet (1994)
  • Laboratory experiments
  • Magnetic field
  • Study how the planet is squished out - fatter at the equator than the poles
  • Look in other wavelengths besides visible light (radio, infrared, etc.)
  • The Galileo probe (1996)

3. Jupiter takes about 12 years to orbit the sun, and at one part of the asteroid belt, an asteroid takes 6 years to orbit. Describe (briefly) why this asteroid might be an interesting one to watch.

It's in a resonance!

4. Your friend Halley says that she was making flapjacks for breakfast last summer and saw a comet high overhead, with its tail pointed toward Denver (from Boulder). Do you believe her? Why or why not?

Can't be - the tail's pointing toward the sun! Comet tails always point away from the sun!

5. The Earth has a moon, but Venus doesn't. Propose a reason for this.

The Earth was randomly hit by an impactor, and Venus was not.

6. Extrasolar planets have been discovered orbiting nearly 50 stars, but we've never been able to directly image most of them. Why not?

The planets are not too faint or too far away. Rather, they are lost next to the overwhelmingly bright light from their stars - like looking for a bug in oncoming headlights.

Long Answer Questions (40 points @ 20/10/10 points each)

1. (20 points) Broadly summarize the differences between the terrestrial planets (TP's) and the Jovian planets (JP's). You should include aspects of their size, composition, formation history, heat sources, and satellites, as well as other things which could be considered important. You need not talk about individual planets (Earth, Saturn, etc.) unless you'd like to. Ignore Pluto, who is being difficult.

TP's: closer in (0.3-3 AU), warmer, rocky, some atmosphere, some satellites. Probably formed from collection of planetesimals, and then atmospheres delivered later by comets. Built of rocks & metals, and have mostly differentiated. They get a very small fraction (%) of their energy from differentiation and radioactive decay, but most of the energy at the surface comes from the Sun.

JP's: further out (5-30 AU), cooler at the outer edge, big dense cores of molten rock/metals and high-pressure, liquified hydrogen. They were formed by gravitational sweepup of gas by cores which formed from the solar nebula. They all have many, many satellites - some quite interesting - and as a result, many ring systems too. Being further form the Sun, internal heat such as differentiation is the dominant heat source.

2. (10 points) Let's say we were to point our telescopes up to the star Astro-1110, and were able to witness a solar system being formed in front of our eyes. We observe two things about Astro-1110: a) the nebula is much hotter than ours ever was (ices can't condense at its outer edge and never will, but rocks and metals can throughout) and b) its solar wind is much weaker than our Sun's, and always will be. If we assume everything else about the star and its nebula is the same as our own, describe the planetary system that will form. You can assume the positions and sizes of the rocky planetesimals formed are the same as in our system.

Because this system is hotter and ices can't condense, we won't have any icy planets, icy moons, or comets. The remaining rock & metals will condense like they did here, so the inner solar system will probably be roughly similar to that which we're familiar with. The TP's, however, will be left without atmospheres, if there's no ices (including water) that can condense.

In the outer solar system, cores for the Jovian planets will still be formed, although they might be slightly smaller. However, if the solar wind is weaker, the JP's will probably attract much much gas than our JP's did, since the gas will stick around much longer before it's all blown away.

The solar wind is not strong enough to move the position of anything other than gas and very small dust, so the actual positions of the planets could be similar to ours. Howver, since the positions are determined somewhat randomly (look at all the extrasolar planets!), they could also be quite different than ours.

3. (10 points) The four `Galilean Satellites' (or `Medicean Stars', as Galileo called them) are fascinating worlds. Pick two of them and write about them: what do they look like, what's happening on their surfaces, what's happening in their cores (why?), and what's a major question that you'd like to answer about them?

Io: The most actively volcanic body in the solar system. No impact craters - they're all covered in lava and `ash' from its volcanic activity. It has a very warm core, heated by tidal heating from Jupiter and its resonance with Ganymede and Callisto. No ices left here - it's very dense.

Europa: Europa appears to have been warm quite recently, as we can see by `icebergs' which are now frozen in place, but were probably floating on surface ocean water within the last several million years. This means that - even though it's far from the Sun - Europa too is warm, heated by its orbital resonances. There are some impact craters, but not many. We see a lot of strange ridges cross-crossing the surface, probably from water that has oozed up through cracks in the surface as Europa is squooshed tidally.

Ganymede: This is a somewhat older surface than Io & Europa. It has some ridges and mysterious patchy terrain. Largest satellite in the solar system. Like the others, it's in a tidal resonance, but doesn't appear to be warm right now.

Callisto: The oldest of the four satellites. Heavily cratered. Some very minor evidence for tectonics, but mostly less exciting than the other three moons. Not in a resonance, and as a result it's cooled off quite a bit.


Dr. Henry Throop, University of Colorado / throop@broccoli.colorado.edu

Last modified 30-Jun-2000