Apparatus and Setup
This lab builds a full mass-radius-density table and diagram from this course's real dataset (six solar-system planets, seven TRAPPIST-1 planets, and HD 209458 b) and classifies each world by bulk composition regime, applying Lecture 04's demographic reasoning.
Materials and Data
| Body | Mass (Mearth) | Radius (Rearth) | Density (kg/m³) |
|---|---|---|---|
| Mercury | 0.055 | 0.383 | 5427 |
| Venus | 0.815 | 0.949 | 5243 |
| Earth | 1.000 | 1.000 | 5514 |
| Mars | 0.107 | 0.532 | 3934 |
| Neptune | 17.150 | 3.880 | 1638 |
| Jupiter | 317.800 | 11.210 | 1326 |
| TRAPPIST-1b | 1.017 | 1.116 | 4034 |
| TRAPPIST-1c | 1.156 | 1.097 | 4828 |
| TRAPPIST-1d | 0.297 | 0.788 | 3346 |
| TRAPPIST-1e | 0.772 | 0.920 | 5466 |
| TRAPPIST-1f | 0.934 | 1.045 | 4512 |
| TRAPPIST-1g | 1.148 | 1.129 | 4398 |
| TRAPPIST-1h | 0.331 | 0.755 | 4240 |
| HD 209458 b | 216.8 | 14.91 | 360 |
Procedure
- Plot (by hand or with a simple script) mass versus radius on log-log axes for all 14 bodies in the table, and identify the rocky/gas-giant density branches visually.
- Compute the density ratio between the densest and least dense body in the table, and identify both bodies.
- Rank the seven TRAPPIST-1 planets by density and identify which one or two are most likely to carry a substantial water/ice mass fraction relative to the others (Lecture 06's composition-degeneracy reasoning).
- Using the occurrence-rate framing of Lecture 04, state (in one sentence, using this course's real dataset as an illustration, not as a statistically complete survey) why a demographic conclusion about "typical" planets cannot be drawn from this 14-body sample alone.
Analysis and Uncertainty
State explicitly that this lab's 14-body sample is illustrative, not survey-complete or selection-effect-corrected (Lecture 03); a genuine occurrence-rate statement requires a full, completeness-corrected survey sample, which this lab does not attempt to construct.
Deliverables
- Completed mass-radius-density table (already provided; verify/reproduce the TRAPPIST-1 and HD 209458 b density calculations from mass and radius).
- Mass-radius diagram (log-log) with rocky and gas-giant branches labeled.
- Density ranking and composition-degeneracy discussion for the TRAPPIST-1 planets.
Assessment Criteria
- Correctly reproduced density calculations for all seven TRAPPIST-1 planets and HD 209458 b.
- Correctly identified rocky/gas-giant branches and correctly ranked TRAPPIST-1 densities.
- Clearly stated selection-effect caveat about sample completeness.
References and Provenance
- 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.
- TRAPPIST-1 mass/radius values: standard published (Agol et al. 2021), reused from ASTR320's live verification; see
materials/ASTR350/reference-log.md. - Generated by
materials/ASTR350/src/generate_astr350_content.py.