Celestial mechanics.
1. Consider how the tidal bulge raised
on Earth by the moon accelerates the moon forward (like a small rocket
pushing forward) and hence drives it slowly away from Earth. (a) Consider
a system (such as Neptune's) in which the planet rotates prograde but the
slowly orbiting large moon revolves retrograde. What is the result in terms
of orbital evolution of the satellite? (b) What is the result if the planet
rotates retrograde and the moon orbits retrograde? HINT: Think about
not only revolution and rotation directions but what effect orbital distance
also can play. [5 points]
2. Discuss the effectiveness and course
of tidal orbital evolution for the two moons of Mars, Phobos and Deimos.
In your answer, make comparisons to the Earth-Moon system.
[4 points]
3. Two asteroids in the asteroid belt collide.
They are on roughly circular orbits whose semi-major axes differ by 0.3
AU. At what speed do they collide? HINT: The main asteroid belt lies at
a distance of about 2.2-3.2 AU from the sun. Show calculations and units.
[5 points]
Cratering.
4. You are an astronaut traversing a 10-km-diameter
crater on Mercury. The crater sits in a ~50-m-deep flow of basaltic lava,
overlaying upland material of unknown composition X. You begin on the lava,
cross the ejecta blanket, descend into the crater; and climb the central
peak. (a) Draw a cross-section view of the crater showing the distribution
of subsurface materials in and around the crater, and labelling prominent
features, especially near the rim of the impact crater. (b) Describe some
of the rocky or soil-like materials (i.e. some combination of basalt or
X) you find during your traverse. HINT: Depth/diameter ratios for fresh
craters (simple and complex) are typically on the order of ~0.1. [5 points]
5. A volcanic plain on the moon is observed
to have about 10% as many craters per unit area as Mare Imbrium. What is
its absolute age? Explain your answer. [4 points]
Petrology & endogenic processes.
6. If the lunar (or other) magma oceans
solidified in the first 100 Ma or so of planetary history, why are 4.5-Ga-old
"genesis rocks" so rare on these worlds? [2 points]
7. (a) Compare the appearance of the surface
topography (especially the presence of heavily cratered areas and intercrater
plains) on two moonlike worlds if magma ocean activity or near-surface
melting lasted only until 4.4 Ga ago on one (case 1) but until 3.8 Ga ago
on the other (case 2). (b) Speculate on the relative timing of volcanism
and impact cratering on the Moon and Mercury and discuss how these objects
differ from the two cases outlined in (a). [4 points]
8. (a) What does the absence of large lunar
volcanic mountains and the presence of the maria imply about the fluidity
of lunar lavas? (b) Why are terrestrial-style maars unlikely on the moon?
(c) What does the morphology of lunar dark-halo craters imply about the
gas content of some lunar lavas? [6 points]
9. Smith and others (1979) discuss a 20-km-thick
crust of sulfur and silicates on Io, with perhaps a 1-km-deep layer of
liquid sulfur involved in the eruptions. Johnson and others (1979) used
the geometry of the erupting plumes to calculate an average resurfacing
rate over all Io of 3 x 10-4 to 0.1 cm/year. The radius of Io
is 1820 km. (a) If a layer roughly 10 km deep is assumed to cycle through
the eruptions, how long does it take for all this material to go through
the cycle of eruption, burial, remelting, and re-eruption? (That is, what
is the turnover time?) (b) If Io formed 4.55 billion years ago, calculate
the number of times that material has been through the cycle. Show work
and units. [7 points]