Radiative Equilibrium Temperature · BPhO 2021 #3

Physics · heat-transfer

Problem

A small black sphere of radius

r

is placed at distance

d

from the Sun (luminosity

L_\odot = 3.85 \times 10^{26}\;\text{W}

). Assuming radiative equilibrium (absorbed solar power = emitted thermal power), find the equilibrium temperature. Use

\sigma = 5.67 \times 10^{-8}\;\text{W/(m}^2\text{K}^4)

. Take

d = 1\;\text{AU} = 1.50 \times 10^{11}\;\text{m}