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 / 4

The Moon's mean equatorial temperature near 206 K is well below the approximately 270 K global effective radiative temperature. The surface has a large day-night range and finite thermal inertia; $⟨T^4{⟩}^{1/4}$ exceeds $⟨T⟩$, so comparing those two differently averaged quantities as though they were equal is invalid. The discrepancy need not imply a missing atmospheric greenhouse effect on an airless Moon.

Jupiter emits at about 130 K rather than the solar-only estimate around 111 K. Intrinsic heat contributes additional outgoing flux, so $\sigma T_{\mathrm{emit}}^4=F_{\mathrm{absorbed}}+F_{\mathrm{internal}}$. The difference of fourth powers is the relevant energy excess, not their direct temperature difference. Cooling and contraction of the interior provide the main physical motivation for including this extra term.