Solar constant is the amount of energy received from the sun per second per unit area by a perfect black body on the earth, the area being placed normal to the direction of radiation.

Let S be the solar constant r be the distance of the earth from the sun and R be the radius of the sun.

Total energy radiated by the sun per second is \sigma T^4 \times 4 \pi R^2

Here T is the temperature of the sun and \sigma is the Stefan’s constant.

Energy received per second per unit are on the surface of the earth is

= \dfrac{\sigma T^4 \times 4 \pi R^2}{4 \pi r^2} = \dfrac{\sigma T^4 R^2}{r^2}

According to the definition of the solar constant, this is the solar constant.

S = \dfrac{\sigma T^4 R^2}{r^2}

T^4 = \dfrac{Sr^2}{\sigma R^2}

T = \left(\dfrac{Sr^2}{\sigma R^2}\right)^\frac{1}{4}

Hence by knowing the value of S, the temperature of the sun can be estimated.