Apparatus and Setup
This is a data-analysis lab reproducing the two founding exoplanet-detection measurements of this course using the equations derived in Lectures 01-02: 51 Pegasi b's 1995 radial-velocity discovery and HD 209458 b's 1999 transit discovery. No telescope time is required; all inputs are real, live-verified system parameters.
Materials and Data
| Quantity | 51 Pegasi b | HD 209458 b |
|---|---|---|
| Period (d) | 4.2308 | 3.5247 |
| Eccentricity | 0.0063 | 0.0081 |
| Measured K (m/s) | 55.90 | 84.27 |
| Inclination (deg) | 49.8 | 86.71 |
| Host star mass (Msun) | 1.11 | 1.15 |
Both systems' parameters are live-verified this session (direct web fetch of Wikipedia's "51 Pegasi b" and "HD 209458 b" articles, 2026-09-24, citing Mayor & Queloz 1995 and Charbonneau et al. 2000/Henry et al. 2000 respectively). Note: the fetched 51 Pegasi b infobox listed K as "55.77 km/s," a units error caught by cross-checking against the article's own prose and the well-established published value of ≈55.9 m/s; this lab uses the corrected units throughout (see ../reference-log.md).
Procedure
- Using Kepler's third law, compute 51 Pegasi b's semimajor axis from its period and the (star+planet) total mass, and compare to the published value (0.0523 AU).
- Solve the radial-velocity mass function numerically for 51 Pegasi b's minimum mass Mp sin(i), given the measured K, and compare to the published minimum mass (0.469 MJup).
- Using the independently constrained inclination (49.8°), compute 51 Pegasi b's true mass and compare to the published value (0.61 MJup).
- Using HD 209458 b's published radius and its host star's radius, compute the predicted transit depth and compare to the measured 1.5% dip.
- Using HD 209458 b's period, semimajor axis, and stellar radius, compute the predicted transit duration and compare to the measured ≈3-hour transit.
- Using HD 209458 b's independently known mass and inclination (from the transit), predict its radial-velocity semi-amplitude K and compare to the measured value (84.27 m/s).
Analysis and Uncertainty
State explicitly, for each of the six computed quantities above, whether your computed value matches the published value to within the precision of the adopted stellar mass/radius inputs, and identify which single input parameter's uncertainty would most affect each computed result if it were revised.
Deliverables
- All six computed quantities with full derivations and unit tracking.
- A one-paragraph statement of which detection method (RV or transit) supplied which piece of information for each planet, and why combining both methods for HD 209458 b gives more information than either alone.
Assessment Criteria
- Correct Kepler's-third-law and mass-function arithmetic with correct SI units throughout.
- Correct transit depth/duration arithmetic with correctly identified stellar-radius input.
- Correctly identified units correction for 51 Pegasi b's K value, with a stated justification.
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.
- 51 Pegasi b and HD 209458 b system parameters: live-verified this session (Wikipedia, 2026-09-24); see
materials/ASTR350/reference-log.md. - Generated by
materials/ASTR350/src/generate_astr350_content.py.