From Stefan's law, the rate at which energy is radiated by sun at its surface is $P=\sigma \times 4\pi R^2{T}^4$



[Sun is a perfect black body as it emits radiations of all wavelengths and so for it $e$=1]

The intensity of this power at earth's surface is

$I=\frac{P}{4\pi r^2}=\frac{\sigma \times 4\pi R^2{T}^4}{4\pi r^2}=\frac{\sigma R^2{T}^4}{r^2}$

The area of earth which receives this energy is only one-half of total surface area of earth, whose projection would be $\pi r_0^2$.

$\therefore$ Total radiant power as received by earth

$= \pi r_0^2\times I$

= $\frac{\pi r_0^2\times \sigma R^2{T}^4}{r^2}=\frac{\pi r_0^2{R}^2\sigma T^4}{r^2}$