Worked Solutions and Rubric Notes
1. Claim Audit: Exoplanet Habitability
Earth-like could mean Earth-sized, rocky density, Earth-like insolation/orbit, atmosphere with certain gases, liquid-water conditions, or biosignature evidence. Each requires different measurements: transit radius, radial velocity or TTV mass, density, stellar luminosity and orbital period, atmospheric spectra, and repeated biosignature/context checks.
Rubric: Award credit for setup, physical reasoning, units, calculation or evidence, and interpretation. Distinguish arithmetic slips from conceptual errors.
2. Evidence Chain Across the Course
Answers vary. Example for expansion: spectra show redshift; line IDs give z; distances are estimated independently; redshift correlates with distance; expansion model explains pattern. Weak links might include distance calibration, peculiar velocities, or selection effects.
Rubric: Award credit for setup, physical reasoning, units, calculation or evidence, and interpretation. Distinguish arithmetic slips from conceptual errors.
3. Order-of-Magnitude Sanity Check
At 100 Mpc, 1 degree corresponds to about 0.0175 x 100 Mpc = 1.75 Mpc of transverse motion in one year, many millions of light-years per year, far faster than light. The claim is physically impossible.
Rubric: Award credit for setup, physical reasoning, units, calculation or evidence, and interpretation. Distinguish arithmetic slips from conceptual errors.
4. Final Reflection with Quantitative Evidence
Examples: parallax gives distance but only for small measurable angles; Doppler shift gives radial velocity but not transverse motion; inverse-square law gives luminosity if distance is known; Hubble law gives approximate distance/recession relation at low redshift but has scatter and cosmological limits.
Rubric: Award credit for setup, physical reasoning, units, calculation or evidence, and interpretation. Distinguish arithmetic slips from conceptual errors.