Question

When the Sun was a protostar, it had a maximum luminosity about 1000 times its present luminosity and a surface temperature about 1000K. What was its radius? Assume that the star radiates like a blackbody.

Answer 1

$$L=4\pi R^2\sigma T^4\\\frac{L'}{L}=\frac{R'^2T^4}{R^2T'^4}\\1000=\frac{R'^2(5800)^4}{(696 340\cdot10^3)^2(1000)^4}\\R'=2.22\cdot10^8\ m$$