Extraterrestrial irradiation

Extraterrestrial radiation is the radiation that can be measured outside the Earth’s atmosphere. It fluctuates with the distance from earth to sun in the course of a year around the solar constant $E_0 = 1367 ~\text{W/m}^2$.

From the day of the year $d$ and the solar constant the extraterrestrial radiation $E_\text{extra}$ is calculated (according to Duffie/Beckman).

$E_\text{extra} = E_0 \cdot \big( 1 + 0.033 \cdot \cos \big( 2 \pi \cdot \frac { d }{365} \big) \big) $