Apply the frost-line, condensation-sequence, and core-accretion concepts from Lectures 01-02 to real dwarf planets, satellites, and formation-timing arguments.
Pluto has mass 1.303e+22 kg and radius 1188.3 km, and orbits at a mean semimajor axis of 39.48 AU, far beyond the frost line. Compute Pluto's mean density and compare it to Ceres's and Vesta's densities from Lab 01 and to the icy-satellite density range from Lecture 01. State whether Pluto's density is consistent with the condensation-sequence prediction for a Kuiper Belt object.
Titan has mass 1.3452e+23 kg and radius 2574.7 km. Compute Titan's mean density. A pure water-ice body would have density ≈ 917 kg/m³; a pure rocky body would have density ≈ 3000 kg/m³ or higher. Estimate, using a simple linear mixing argument, what mass fraction of rock (versus ice) Titan's bulk density implies, and state one reason this simple estimate is only approximate.
Using the equilibrium-temperature-based frost-line method from Lecture 02 (setting T(r) = 150 K), compute the frost-line distance for a young star with (a) half the Sun's luminosity and (b) twice the Sun's luminosity. Compare both results to the Sun's own frost line (∼2.8 AU) and state, in one sentence, how frost-line distance scales with stellar luminosity.
In two to three sentences each, explain (a) why gravitational focusing makes runaway growth self-reinforcing for the largest body in a local planetesimal swarm, and (b) why oligarchic growth eventually slows this process down once a few embryos dominate their feeding zones. Your answer must reference the gravitational-focusing cross-section argument from Lecture 02, not just restate that 'bigger objects grow faster.'
Jupiter's core accretion is estimated to have reached the ∼5-10 Earth-mass critical core mass while the gas disk still had several Myr of lifetime remaining, while Uranus's and Neptune's cores are thought to have formed more slowly. Using the core-accretion argument from Lecture 02, explain quantitatively (with reference to the ∼90% hydrogen/helium mass fraction of Jupiter and Saturn versus the ∼10-20% hydrogen/helium mass fraction of Uranus and Neptune) why this timing difference alone is sufficient to explain the compositional gas-giant/ice-giant divide.
Submit a complete derivation with equations, units, labeled quantities, and a short narrative interpretation for each problem. Show every step; a correct final number without a visible derivation receives partial credit at most, and quoting a lecture number without adapting it to this problem's specific inputs receives no credit for that step.
OpenStax Astronomy 2e, Sections 7.2 and 8.5.
materials/ASTR320/src/generate_astr320_content.py where referenced above.