The solar constant for a planet is `S`. The surface temperature of the sun is `T.K`. The sun subtends an angle `theta` at the planet . Find `S`.

Explanation

Solar constant `(S)` is defined the rate at which radiations are received from sun per unit surface area.

`tan(theta//2)=(Rs)/(R )`
`tan(theta//2) ~= theta//2=(Rs)/(R )`
`[(Rs)/(R )=theta//2]`
Solar constant `(S)=("Power received")/("Surface Area")`
`S=(sigma(4piRs^(2))T^(4))/(4piR^(2))=sigma((Rs)/(R ))^(2)T^(4)`
Using small angle approximation we get
`S=sigma((theta^(2))/(4))T^(4)`
`S=(sigmaT^(4)theta^(2))/(4)`