Question

. How far away (in A.U.) from the star Rigel (surface temperature T=12,000 K, radius R=35 solar radii) would we have to place a perfect copy of the Earth (same albedo, greenhouse, etc…) to reach the same equilibrium temperatures as our Earth.

Answer 1

(Stephens law) where I is the intensity due to the Rigel star, R and T be its radius and temperature respectively.

we know

where P_e is the power received by the earth which is at a distance r from the Rigel star. R_E and T_E are radius and temperature of Earth respectively.

Power lost by the earth

Now to get the equilibrium temperature, we equate power received and power lost

substituting the values in the above equation

Note I assumed T_E as 300K. and converted solar units to AU( 1 solar radii = 1/215 AU)