Question

For two hypothetical planets, one that is located at an average distance that is twice the average distance of the Earth from the sun and one that is located at an average distance that is one half of the average distance of the Earth from the sun, how would their equilibrium temperatures compare with the equilibrium temperature of the Earth?

Answer 1

Let R = Average distance of a planet from Sun.

r = Radius of the planet

L = luminosity of Sun

Power received by the planet from the sun,

Let T = Equilibrium temperature of the planet,

Then power radiated by the planet

(assuming emissivity of the planet approximately equal to 1, as its value for earth is 0.96)

Where = Stefan's Boltzmann constant.

When thermal equilibrium is attained

Solar luminosity, L = 3.828*10^26 W

and = 5.67*10^-8 Wm^-2K^-4

For earth R = R_E = 1 AU = 1.496*10^11 m

From equation (1),

For Planet 1 having equilibrium temperature T₁, which is located at double the average distance of earth from sun, its distance from Sun, R₁ = 2R_E,

Therefore from (3) we get

Similarly for planet 2, for which average distance from Sun is R₂ = R_E/2, temperature