Due and Scope
Due: [insert date]. Submit calculations, evidence tables, and short interpretations.
Learning objectives: compare giant planets using density, sunlight, heat flow, rotation, and magnetic fields; assess icy-ocean evidence; use orbital scaling for rings and moons.
Instructions: Keep units visible. State when values are rounded and when evidence is indirect. Revisions may be resubmitted with a change note.
Problems
1. Giant-Planet Density and Composition 25 points
Use this lecture table: Jupiter \(M=318M_E, R=11.2R_E\); Saturn \(M=95M_E, R=9.45R_E\); Uranus \(M=14.5M_E, R=4.01R_E\); Neptune \(M=17.1M_E, R=3.88R_E\). Use \(\rho/\rho_E=(M/M_E)/(R/R_E)^3\) and \(\rho_E=5.51\,\mathrm{g\ cm^{-3}}\).
- Compute each mean density.
- Identify which is less dense than water.
- Explain why low density does not mean the planet is physically small or low mass.
- Interpret Uranus and Neptune relative to Jupiter and Saturn in terms of H/He versus ice/rock enrichment.
Deliverables: density table and composition interpretation.
2. Sunlight and Internal Heat in the Outer Solar System 25 points
Solar flux scales as \(1/r^2\). Use distances 5.2, 9.5, 19.2, and 30.0 AU for Jupiter, Saturn, Uranus, and Neptune.
- Compute sunlight relative to Earth for each planet.
- If Neptune emits about 2.6 times as much energy as it absorbs from the Sun while Uranus emits roughly the same as it absorbs, explain what this implies about internal heat.
- Describe one observation that helps distinguish absorbed sunlight from internal heat.
Deliverables: relative-flux table and interpretation.
3. Europa Ocean Evidence Chain 25 points
A mission observes an induced magnetic signal, a young fractured surface with few craters, and possible plume material. Build an evidence chain for a subsurface ocean.
- For each observation, state the measurement and the ocean-related interpretation.
- Give one non-ocean ambiguity or systematic uncertainty for each observation.
- Rank the observations from most direct to least direct for a present ocean.
- Explain why tidal heating and resonance are relevant to keeping liquid water possible.
Deliverables: evidence chain table and ranked conclusion.
4. Ring-Particle Orbital Periods 25 points
For particles orbiting the same planet, \(P\propto r^{3/2}\). Saturn's main rings extend roughly from \(75,000\) km to \(137,000\) km from Saturn's center.
- Compute \(P_{outer}/P_{inner}\).
- If the inner edge period is 5.0 hours, estimate the outer edge period.
- Explain why different orbital periods cause shear and why narrow rings need confinement or replenishment.
Deliverables: period-ratio calculation and ring-dynamics explanation.
OpenStax Companion Practice
Recommended for additional practice: OpenStax Astronomy 2e, Chapter 11, Review Questions 10-16 and Figuring for Yourself 27-30; Chapter 12, Review Questions 3, 4, 8, 9, and 12; Thought Questions 16 and 19; Figuring for Yourself 24 and 26. Verify numbering against the adopted PDF before LMS release.