ASTR 230 Problem Set 01: Stellar Properties, Spectra, and Classification

Problem set for Unit 1.

Problems

1. Stefan-Boltzmann for Rigel 15 points

Rigel has T_eff = 12100 K and radius 78.9 R☉. Using L = R²(T/5778)⁴ L☉, compute Rigel's luminosity in solar units. Show every step.

2. Inverse-square reasoning 15 points

Two stars have the same luminosity. Star A is 10 pc away and Star B is 40 pc away. Compute the ratio of their apparent brightness (flux), F_A/F_B, and state which star appears brighter and by what factor.

3. Spectral classification physics 15 points

Vega (A0V, T_eff = 9602 K) shows the strongest hydrogen Balmer lines of any common spectral type, while both hotter O/B stars and cooler K/M stars show weaker Balmer lines. Explain, in terms of hydrogen ionization and excitation fractions, why Balmer line strength peaks near A0 rather than at the hottest stars.

4. Textbook problem: Sirius system radii 15 points

OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 18, Figuring for Yourself, Exercise 18.41-18.43 (Sirius system radius comparison, using T_Sun = 5800 K and T_Sirius A = 10,000 K): work through the radius ratio derivation for Sirius A relative to the Sun, then state how your result compares to the radius given for Sirius A in this course's data table (1.71 R☉).

Due and Scope

Submit a clear solution with equations, units, labeled quantities, and a short narrative interpretation for each problem. Show every step; a correct final number without visible work receives partial credit at most.

OpenStax Companion Reading

OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 18.1-18.2 (brightness/radii of stars) and Chapter 17.1-17.4 (spectral classification).

References and Data Sources