where \(r\) is the radius of the sun and the sun is treated as a black body where \(e=1.\)

The radiant power per unit area received by the surface at a distance \(R\) from the center of the sun is given by

\(S = \frac{P}{{4\pi {R^2}}} = \frac{{\sigma 4\pi {r^2}{{\left( {t + 273} \right)}^4}}}{{4\pi {R^2}}} = \frac{{{r^2}\sigma {{\left( {t + 273} \right)}^4}}}{{{R^2}}}.\)