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 σT^{4}.

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 X σT^{4}

so, **E = 4πr ^{2} **X

**σT**… …. (1)

^{4}Let imagine a sphere with Sun at the centre and the distance between the Sun and Earth R as the 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 = 4πr^{2} S … … … (2)

By definition, equations (1) & (2) are equal.

so, **4πr ^{2} σT^{4} = 4πr^{2} S**

then, T^{4} = R^{2}S/σr^{2}

so, T = [R^{2}S/σr^{2}]^{1/4}

or, T = (R/r)^{1/2} (S/σ)^{1/4}

Knowing the value of R, r, S and σ the surface temperature of the Sun can be calculated.

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