The surface temperature of the sun is T0  and it is at average distance d from a planet. The radius of the sun is R. The temperature at which planet radiates the energy is

r = Radius of planetT1 = Temperature of planet at which energy is radiated Power radiated by Sun, P = 4πR2σT04Energy received by planet = P4πd2×πr2 = R2T04πr2σd2Energy radiated by planet = 4π2σT14For thermal equilibrium,R2T04π r2σd2 = 4πr2σT14R2T04 = 4d2T14T1 = ToR2d