Intermediate

Radius of a red supergiant

Betelgeuse has a luminosity of $L = 1.2\times10^{5}\,L_\odot$ and its spectrum peaks at $\lambda_{\max} = 830$ nm. Estimate its effective temperature and radius, and compare the radius to the orbit of Mars ( $1.52$ AU).

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Reading resources

Material that covers the physics behind this problem.

An Introduction to Modern AstrophysicsCarroll & Ostlie
The standard reference for olympiad-level astrophysics. Chapters 1-3 cover the celestial sphere, orbits and the magnitude system.
Textbook
HyperPhysics. AstrophysicsGeorgia State University
Quick concept maps and formula references. Good for refreshing a relationship mid-problem.
Website
Crash Course AstronomyPhil Plait
46 short episodes. Useful for building intuition quickly before diving into the maths.
Video