ASTR 101 Problem Set 04 Solutions

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Worked Solutions and Rubric Notes

1. Mean Density and Composition

rho_B/rho_E = 0.11/(0.53^3) = 0.11/0.149 = 0.74. Planet B's mean density is about 74% of Earth's, suggesting a different interior structure/composition or less compression. This resembles Mars-like comparison.

Rubric: Award credit for setup, physical reasoning, units, calculation or evidence, and interpretation. Distinguish arithmetic slips from conceptual errors.

2. Crater Counts and Surface Age

Region X is probably older because it accumulated more impacts. Assumption: impact rate and preservation conditions are comparable. Complications include resurfacing, lava flows, erosion by ejecta, secondary craters, or different target properties.

Rubric: Award credit for setup, physical reasoning, units, calculation or evidence, and interpretation. Distinguish arithmetic slips from conceptual errors.

3. Escape Velocity Reasoning

Small asteroids have low mass and small radius, producing low escape velocity; gas molecules can more easily exceed escape speed. Giant planets have much larger escape velocity and can retain light gases more effectively, though temperature and atmospheric chemistry also matter.

Rubric: Award credit for setup, physical reasoning, units, calculation or evidence, and interpretation. Distinguish arithmetic slips from conceptual errors.

4. Habitability Evidence Ranking

Answers may vary, but high-quality responses separate past/present liquid water, energy sources, chemistry, and evidence quality. Europa often ranks high for possible subsurface ocean plus tidal energy; Mars for past water and accessible geology; Titan for organic chemistry but very low surface temperature; typical asteroid lower unless hydrated minerals or subsurface ice are specified.

Rubric: Award credit for setup, physical reasoning, units, calculation or evidence, and interpretation. Distinguish arithmetic slips from conceptual errors.

Textbook Problem Rationale

OpenStax Astronomy 2e, Solar System formation exercises, Review Question 20, extracted index line 9381: solar nebula and why the Sun formed at its center.
OpenStax Astronomy 2e, Solar System formation exercises, Thought Question 21, extracted index line 9383: what other stars teach about solar-system formation.
OpenStax Astronomy 2e, terrestrial worlds exercises, Review Question 3, extracted index line 9340: requirements for retaining an atmosphere.
OpenStax Astronomy 2e, outer solar-system exercises, Review Question 3, extracted index line 15362: evidence for a liquid-water ocean on Europa and why it matters.
OpenStax Astronomy 2e, planetary evolution exercises, Review Question 8, extracted index line 17915: role of impacts in planetary evolution, including giant and modest impacts.

Use these recommendations for additional practice or adaptation. Confirm numbering against the final adopted edition before assigning.