Problems
1. Phobos and Mars's Roche Limit 15 points
Phobos (mass 1.0659e+16 kg, radius 11.27 km) orbits Mars at 9376 km, well outside Mars's Roche limit today, but is known to be spiraling slowly inward due to tidal dissipation inside Mars. Compute Phobos's own density from its mass and radius, then compute the fluid Roche limit for a body of that density orbiting Mars (mean density computed from Mars's mass and radius). Compare Phobos's current orbital radius to this Roche limit and state, in one sentence, what this comparison implies about Phobos's long-term fate.
2. Saturn versus Jupiter: Why Does Density Differ Despite Similar Composition? 15 points
Saturn's and Jupiter's mean densities differ substantially (ratio 0.518) despite both planets sharing a similar bulk hydrogen/helium-dominated composition. Using the self-compression argument introduced for terrestrial planets in Lecture 03 and revisited for giant planets in Lecture 11, explain in a short paragraph why Jupiter's much stronger self-gravity is sufficient to explain this density difference without requiring the two planets to have fundamentally different compositions.
3. Neptune's Ring Arcs 15 points
Neptune's rings include unusual partial arcs of clumped material rather than a uniformly distributed ring, maintained by resonant confinement with the nearby moon Galatea. Using the shepherd-moon concept from Lecture 12 (developed there for Saturn's F ring), explain in a short paragraph how a single nearby moon's resonant gravitational influence could concentrate ring material into discrete arcs rather than spreading it uniformly around the full ring circumference.
4. Jupiter's Zonal Wind Depth and Gravity Harmonics 15 points
Juno's gravity-field measurements indicate Jupiter's zonal winds persist to a depth of roughly 3000 km below the visible cloud tops before being damped out. Using the concept of increasing electrical conductivity with depth (Lecture 11), explain in a short paragraph why the winds should be expected to damp out at increasing depth, rather than persisting all the way to Jupiter's center.
5. Why Ice Giants Are Not Simply Small Gas Giants 15 points
Explain, in a short paragraph referencing both Lecture 02's core-accretion timing argument and Lecture 11's compositional data (∼90%+ hydrogen/helium for Jupiter/Saturn versus ∼10-20% for Uranus/Neptune), why classifying Uranus and Neptune as 'ice giants' rather than merely 'smaller gas giants' reflects a genuine compositional and formation-history distinction, not just an arbitrary size cutoff.