Determining the sizes and physical parameters of stars
A star’s radius is hard to measure directly (only the nearest, largest stars show up with an interferometer, e.g. Betelgeuse, Michelson, 1920), so it is found from L = 4πR² σT⁴. Comparing with the Sun: R / R☉ = √(L / L☉) · (T☉ / T)². So at the same temperature a more luminous star is larger; at the same luminosity a cooler star is larger (red giants). Stellar radii cover a huge range: a neutron star ≈ 10–12 km, a white dwarf ≈ Earth-sized (≈ 0.01 R☉), the Sun 1 R☉, supergiants like Betelgeuse ≈ 700–900 R☉. Stellar masses cover a much narrower range – from ≈ 0.08 to ≈ 100–150 solar masses. Mean density ρ = M / (4/3 πR³): the Sun ≈ 1.4 g/cm³, a white dwarf ≈ 10⁶ g/cm³, a red supergiant ≈ 10⁻⁷ g/cm³ (much thinner than air).
In your notebook rank the radii of five stars (the Sun, Sirius B, Betelgeuse, a neutron star, Proxima) in decreasing order and compute their sizes on a scale where the Sun = 1 cm.