Apparatus and Setup
This lab applies the mass-luminosity relation and main-sequence lifetime scaling (Lecture 07) to four real, precisely measured stars: the Sun, Alpha Centauri A and B, and Sirius A (all carried forward with established provenance from ASTR 230/ASTR 310).
Materials and Data
| Star | Mass (M⊙) | Measured L (L⊙) |
|---|---|---|
| Sun | 1.000 | 1.000 |
| Alpha Centauri A | 1.0788 | 1.5059 |
| Alpha Centauri B | 0.9092 | 0.4981 |
| Sirius A | 2.063 | 25.4 |
Procedure
- For each of the three non-solar stars, compute the mass-luminosity prediction L ≈ M^3.5 and the percent agreement with the measured luminosity in the data table.
- For each of the four stars, compute the main-sequence lifetime estimate t_MS = 10 Gyr × (M/M⊙)/(L/L⊙) using the measured (not predicted) luminosity.
- Rank the four stars by main-sequence lifetime, and state which single input (mass or luminosity) is most responsible for Sirius A having by far the shortest lifetime of the four.
- The Sun's actual age is about 4.57 Gyr. Compare this to your computed solar main-sequence lifetime, and state what fraction of its total main-sequence lifetime the Sun has completed so far.
Analysis and Uncertainty
Sirius A's percent agreement (step 1) is expected to be noticeably worse than Alpha Centauri A/B's; state explicitly why a single fixed mass-luminosity exponent (3.5) is not expected to fit equally well across a wide range of stellar masses.
Deliverables
- Completed mass-luminosity prediction table with percent agreements.
- Completed main-sequence lifetime table for all four stars.
- Written ranking and explanation of Sirius A's short lifetime.
- Solar age-versus-lifetime comparison with the completed-fraction calculation.
Assessment Criteria
- Correct mass-luminosity and percent-agreement arithmetic for all three stars.
- Correct lifetime arithmetic for all four stars.
- Correct identification of luminosity (not mass alone) as the dominant driver of Sirius A's short lifetime.
- Correct solar age-completed-fraction arithmetic.
References and Provenance
- OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 19.3.
- All four stars' masses and luminosities: carried forward with established provenance from ASTR 230/ASTR 310 (see
materials/ASTR330/reference-log.md). - Generated by
materials/ASTR330/src/generate_astr330_content.py.