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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.

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.


Example problem
Assume that the Sun behaves like a perfect black body of temperature T and radius r.
Therefore energy emitted by the Sun = σT44πr2.
Area of sphere with a radius (R) equal to that of the Earth’s orbit = 4πR2.
Therefore taking the solar constant to be 1400 J m-2s-1

σT44πr2 = 4πR2x1400    T = 5740 K



 
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© Keith Gibbs 2013