= Solution
The solar <flux> at <Earth> is $\sigma T_\odot^4R_\odot^2/L^2$. A spherical <Earth> intercepts sunlight over its cross section but radiates over its whole surface, giving
$$
\pi R_E^2\sigma T_\odot^4\frac{R_\odot^2}{L^2}=4\pi R_E^2\sigma T_E^4,
\qquad
\boxed{T_E=T_\odot\sqrt{\frac{R_\odot}{2L}}=275\,\mathrm K.}
$$
This is \b[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.<Climate and Earth's Energy Budget by NASA Earth Observatory>[Sections The Natural Greenhouse Effect and Effect on Surface Temperature]{ref}
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