 Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2016/s29/1/1/solution

Radiative equilibrium balances absorbed solar power against emitted thermal power, with no net energy accumulation. A spherical body's projected area absorbs

π r^{2} F_{S} (1 - A) / R_{A U}^{2}

; its full area emits

4 π r^{2} ϵ σ T^{4}

. Hence

T_{e q} = [\frac{F _{S} ( 1 - A )}{4 ϵ σ R _{A U}^{2}}]^{1/4} .

Here

A

is bolometric Bond albedo, not a geometric albedo measured at one phase or wavelength. The radius cancels because the absorption and emission areas scale together.

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