This question looks more closely at solar energy incident on a spherical celestial object of radius, R, orbiting the Sun at a mean distance of d . Suppose that the Sun radiates energy at a rate of P .
a. a At a distance, d, from the Sun, how much solar energy arrives per second per unit area? Call this quantity, S .
b. b So how much solar energy will be incident on the celestial object per second?
c. c Hence give an expression, in terms of S, for the mean power incident on the total surface of the celestial object per unit area.
d. d Now suppose that the albedo of the celestial object is α . Give an expression for the mean power per unit area absorbed by the celestial object.
e. e Now let us apply this to the case of the Earth. For the Earth. S≈1400 W .
f. i If the average albedo of the Earth is 0.3, show that the Earth would have to radiate 245 Wm−2 if it is to be in thermal equilibrium.
g. ii At what temperature would a black body have to be if it were to radiate at 245 Wm−2 ?
h. iii In fact, the globally averaged surface temperature of the Earth is 288 K. For the Earth to maintain thermal equilibrium with its surroundings how much more power per unit area must the Earth's surface absorb? You should consider the Earth to radiate as a black body for the sake of this question.
i. iv Since the Earth is in thermal equilibrium with its surroundings, where is this extra power coming from?
j. v By what name is this phenomenon usually known?