Apparatus and Setup
This lab computes the classical (conservative) habitable-zone boundaries for the Sun and for TRAPPIST-1 from their real luminosities (Lecture 09), censuses every TRAPPIST-1 planet against its own star's boundaries, and qualitatively evaluates Venus's and Mars's real climate outcomes against the same framework (Lecture 10).
Materials and Data
Sun: L=1 Lsun, HZ = 0.953-1.768 AU. TRAPPIST-1: L=5.660e-04 Lsun (live-verified), HZ = 0.0227-0.0421 AU.
| Planet | a (AU) | T_eq (K, zero albedo) | HZ status |
|---|---|---|---|
| TRAPPIST-1b | 0.0115 | 400 | inside inner edge (too hot) |
| TRAPPIST-1c | 0.0158 | 342 | inside inner edge (too hot) |
| TRAPPIST-1d | 0.0223 | 287 | inside inner edge (too hot) |
| TRAPPIST-1e | 0.0293 | 251 | inside HZ |
| TRAPPIST-1f | 0.0385 | 219 | inside HZ |
| TRAPPIST-1g | 0.0469 | 198 | outside outer edge (too cold) |
| TRAPPIST-1h | 0.0619 | 173 | outside outer edge (too cold) |
Procedure
- Reproduce the Sun's and TRAPPIST-1's habitable-zone inner/outer boundaries from their real luminosities using the flux-boundary equation.
- Reproduce the HZ-status classification for all seven TRAPPIST-1 planets shown in the table.
- Compute Venus's and Mars's real insolation (from their real orbital distances) in units of Earth's insolation, and check each against the Sun's computed habitable-zone boundaries.
- State, using Lecture 10's climate-feedback reasoning, why Venus's and Mars's real observed climates (a runaway greenhouse and a frozen, dry surface, respectively) are or are not fully explained by the classical habitable-zone boundaries alone.
Analysis and Uncertainty
State explicitly that the classical habitable-zone boundaries used here assume an Earth-like atmosphere and zero-albedo radiative equilibrium; a specific planet's real climate depends on its actual atmospheric composition, albedo, and geological activity (Lecture 10), which this lab's insolation-only calculation does not capture.
Deliverables
- Reproduced HZ boundary calculations for the Sun and TRAPPIST-1.
- Completed HZ-status table for all seven TRAPPIST-1 planets.
- Venus/Mars insolation check with a climate-feedback discussion.
Assessment Criteria
- Correct sqrt(L)-scaling arithmetic for both stars' HZ boundaries.
- Correctly classified HZ status for all seven TRAPPIST-1 planets.
- Explicit statement of the classical-HZ-versus-actual-climate distinction from Lecture 10.
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.
- Habitable-zone flux boundaries: Kasting, Whitmire & Reynolds (1993), standard published, level 2. TRAPPIST-1 luminosity: reused from ASTR320's live verification.