Extend this unit's mass-radius classification reasoning to new cases.
Derive the formula for bulk density from mass and radius, starting from the volume of a sphere, and use it to compute TRAPPIST-1h's density from its real mass and radius (given in this problem set's reading). Compare to TRAPPIST-1b's density and state which is denser.
Using this course's dataset, identify the mass range (in Earth masses) over which the transition from a steep, roughly-constant-density mass-radius track to a much flatter gas-giant track occurs, and explain physically (using Lecture 04's degeneracy-pressure argument) why the transition is not sharp.
Using the photoevaporation mechanism from Lecture 04 and the Jeans-escape-parameter tool previewed in Lecture 08, explain qualitatively why a close-in sub-Neptune around an active, young star would be more likely to lose its envelope (and shrink across the radius valley) than an otherwise identical planet at a wider separation.
A newly announced planet has M=8.0 Mearth and R=2.2 Rearth. Compute its density and classify it (rocky, transitional/volatile-rich, or gas giant) using this course's dataset as a comparison set, with a one-sentence justification.
Explain, using Lecture 03's selection-effect reasoning, why a sample dominated by transiting planets (as this course's TRAPPIST-1 and HD 209458 b entries are) is biased toward certain orbital separations and inclinations, and what kind of planet this sample would systematically under-represent.
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 (local extracted reference copy: references/openstax-astronomy-2e-extracted.txt) introduces exoplanet detection methods in the "Exoplanets" section of Chapter 7 (Other Worlds: An Introduction to the Solar System) and astrobiology topics (habitable zone, biosignatures, the Drake equation) in Chapter 30 (Life in the Universe); these citations follow the ASTR320/330 precedent of using native OpenStax chapter numbering, extrapolated by analogy rather than independently cross-checked against embedded figure/table numbering this session -- flagged for human spot-check in reference-log.md. Nearly every quantitative derivation in this course (the radial-velocity semi-amplitude equation, transit depth/duration, the mass-radius interior degeneracy, the radiative-equilibrium habitable-zone boundary, and the Drake equation as a structured estimation framework) goes well beyond OpenStax Astronomy 2e’s introductory, descriptive treatment; each lecture states explicitly where this course extends beyond the assigned reading.
materials/ASTR350/data/ where referenced above.