The solar constant is the amount of radiant energy received per second per unit area by a perfect black body on the Earth with its surface perpendicular to the direction of radiation from the sun in the absence of atmosphere. It is denoted by S and its value is 1.388 ? 103 W m-2. Surface temperature of the Sun can be calculated from solar constant.
Surface temperature of the Sun
The Sun is a perfect black body of radius r and surface temperature T. According to Stefan?s law, the energy radiated by the Sun per second per unit area is equal to σT4.
Where σ is Stefan?s Constant.
Hence, the total energy radiated per second by the Sun will be given by
E = surface area of the Sun ? σT4
Let us imagine a sphere with Sun at the centre and the distance between the Sun and Earth R as radius (Fig.). The heat energy from the Sun will necessarily pass through this surface of the sphere.
If S is the solar constant, the amount of heat energy that falls on this sphere per unit time is E = 4πR2S ????.(2)
By definition, equations (1) & (2) are equal.
4πr2σT4. = 4πR2S
T4 = R2S/r2σ
T = (R/r)1/2(S/ σ)1/4
Knowing the values of R, r, S and σ the surface temperature of the Sun can be calculated.