Lab 07: Capstone: A Complete Physical Characterization of Alpha Centauri AB

Apparatus and Setup

This capstone lab has students reproduce every calculation used in Lecture 14's synthesis from the raw measured orbital elements and stellar parameters, combining the radiative (Lectures 01-02) and dynamical (Lectures 07-09) toolkits developed across the entire course, and add a new radiation-pressure check (Lecture 13).

Materials and Data

Use ../data/alpha_centauri_ab.csv and ../data/alpha_centauri_orbit.csv for all inputs; do not use any number not present in, or directly derivable from, these files and the physical constants used throughout the course.

Procedure

1. Radiative chain: compute the Stefan-Boltzmann luminosity for Alpha Centauri A and for Alpha Centauri B from their measured radii and temperatures, and compare each to its independently measured luminosity (percent agreement).
2. Dynamical chain: compute the total system mass from Kepler's third law applied to the measured period and semimajor axis, and compare it to the independently measured sum of individual masses (percent agreement).
3. Radiation-pressure check: compute the Eddington luminosity for each star using its own mass, and express each star's actual luminosity as a fraction (in percent, using scientific notation) of its own Eddington luminosity, confirming that radiation pressure is negligible for both stars.
4. Synthesis: write a structured, 300-500 word synthesis addressing (a) which of your four percent-agreement checks in steps 1-2 is the strongest confirmation and why, (b) what shared assumption (if any) links the radiative and dynamical chains and therefore limits their mutual independence, and (c) what an astronomer would conclude if steps 1-2 had instead disagreed by, say, 25% rather than a few percent.

Analysis and Uncertainty

Both the radiative chain (which needs a physical radius, derived from angular diameter and distance) and the dynamical chain (which needs a physical semimajor axis, derived from angular separation and distance) depend on the same measured parallax/distance to Alpha Centauri. Explicitly identify this shared dependency in your synthesis paragraph (b) above.

Deliverables

• Completed radiative-chain, dynamical-chain, and Eddington-luminosity calculations for both stars, with all unit conversions shown.
• The 300-500 word structured synthesis paragraph.

Assessment Criteria

• Correct, fully shown arithmetic for all radiative, dynamical, and Eddington-luminosity calculations.
• Synthesis paragraph correctly identifies the shared parallax/distance dependency as a limitation on the independence of the two chains.
• Synthesis paragraph gives a physically sound account of what a large (25%) disagreement would imply (an error in one of the input measurements or an unmodeled physical effect, not simply "one method is right and one is wrong").

References and Provenance

• OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 18 and Chapter 3 (read together, as in Lecture 14).
• All Alpha Centauri AB data: live-verified this session.