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The solar constant

The average amount of energy that the Earth striking the top of the Earth's atmosphere from the Sun is about 1370 J m-2s-1 and this quantity is known as the solar constant.

The amount that actually reaches the ground can vary enormously and depends on:
(a) the angle of the Sun's rays
(b) the transparency of the atmosphere. This is altered by cloud over, rain, volcanic activity and emissions from industry.
The amount reaching the ground is called insolation and can be as much as two thirds of that striking the upper atmosphere. In poor conditions however as much as 70% may be reflected or absorbed by the atmosphere.

Assuming that the Sun is a black body, we can use this information to determine the temperature of the surface of the Sun.

Example problem
Assume that the Sun behaves like a perfect black body of temperature T and radius r calculate the temperature of the surface of the Sun.

Therefore energy emitted by the Sun = sT44pr2.
Area of sphere with a radius (R) equal to that of the Earth’s orbit = 4pR2.
Therefore taking the solar constant to be 1400 J m-2s-1
sT44pr2 = 4pR2x1400

T = 5740 K

This radiation also exerts a very small pressure on the Earth of about 0.45x10-5 Pa; compare this with the atmospheric pressure at sea level of 105 Pa.
© Keith Gibbs 2011