Let \(R=\) radius of the sun, \(d=\) distance of the earth from the sun.

Power radiated by the sun \(=\left(4 \pi R^2\right) \sigma T^4=P\).

Energy received per unit area per second normally on the earth

\(= S =\frac{ P }{4 \pi d ^2}=\frac{4 \pi R ^2 \sigma T ^4}{4 \pi d ^2}=\left(\sigma T ^4\right)\left(\frac{ R }{ d }\right)^2=\frac{1}{4} \sigma T ^4\left(\frac{2 R }{ d }\right)^2\)

Angle subtended by the sun at the earth \(=\theta=\frac{2 R}{d}\).

\(\text { or, } S =\frac{\sigma}{4} T ^4 \theta^2\)