Problem set for Unit 7.
Compute the Stefan-Boltzmann luminosity for Sirius A (T_eff = 9940 K, R = 1.711 R⊙) and for Sirius B (T_eff = 25000 K, R = 0.008098 R⊙), and compare each to its published luminosity (25.4 L⊙ and 0.0245 L⊙ respectively).
Using your Problem Set 04 result for the Sirius AB total mass from Kepler's third law (3.079 M⊙), restate the percent agreement with the independently measured mass sum (3.081 M⊙) found there.
Compute the Eddington luminosity for Sirius A and for Sirius B using their individually measured masses, and express each star's actual (published) luminosity as a percentage of its own Eddington luminosity.
Write a 250-400 word synthesis addressing: (a) which of your radiative or dynamical cross-checks (Problems 1-2) shows the closer agreement and why that might be, (b) whether Sirius B's white-dwarf structure makes the Stefan-Boltzmann cross-check in Problem 1 any less valid than for an ordinary main-sequence star like Sirius A, and (c) what your Problem 3 result implies about whether radiation pressure plays any role in either star's hydrostatic balance.
Submit a complete derivation with equations, units, labeled quantities, and a short narrative interpretation for each problem. Show every step; a correct final number without a visible derivation receives partial credit at most, and quoting a lecture number without adapting it to this problem's specific inputs receives no credit for that step.
OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 18 and Chapter 3 (read together, as in Lecture 14).
materials/ASTR310/data/ where referenced above.