Problem set for Unit 1.
Sirius A has T_eff = 9940 K (a standard published value; see reference-log.md). Using b = 2.8971e-03 m·K, compute Sirius A's peak emission wavelength in nanometers and state which part of the spectrum it falls in.
Sirius A has a measured radius of 1.711 R⊙. Compute its Stefan-Boltzmann luminosity in solar units, showing the full unit conversion from R⊙ to meters.
The independently published luminosity of Sirius A is about 25.4 L⊙. Compute the percent agreement between your Problem 2 answer and this value, and state one physical reason a small residual disagreement might remain (e.g., measurement uncertainty in R or T_eff, or a departure from a perfect blackbody spectrum).
Sirius A (T_eff = 9940 K, R = 1.711 R⊙) and Alpha Centauri A (T_eff = 5748 K, R = 1.223 R⊙, from Lecture 02) have similar radii but very different temperatures. Using the R²T⁴ scaling, explain quantitatively (with a computed ratio, not just words) why Sirius A is roughly 17 times more luminous than Alpha Centauri A despite only a factor of 1.73 difference in temperature.
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 5.4 and Chapter 18.1.
materials/ASTR310/data/ where referenced above.