 Solution

ID: past-exam-of-the-physics-course-of-the-year-4-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-1/a1/solution

The solar flux at Earth is

σ T_{⊙}^{4} R_{⊙}^{2} / L^{2}

. A spherical Earth intercepts sunlight over its cross section but radiates over its whole surface, giving

π R_{E}^{2} σ T_{⊙}^{4} \frac{R _{⊙}^{2}}{L ^{2}} = 4 π R_{E}^{2} σ T_{E}^{4}, T_{E} = T_{⊙} \frac{R _{⊙}}{2 L} = 275 K .

This is below the observed mean surface temperature. Atmospheric infrared absorption and emission produce a greenhouse effect that raises the surface temperature relative to the effective radiating temperature. Including reflected sunlight alone would lower the estimate further; albedo does not explain a warmer surface.^[ref]

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