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The sun radiates in all directions, towards the earth, away from the earth, at right angles to the earth and so on. It radiates roughly equally in all these directions.

Suppose you could draw a sphere with the sun as its centre and radius = average distance between the earth and the sun (1 astronomical unit). Then the amount of incident energy is proportional to the area of cross section of the earth relative to the surface area of the sphere.

Now, mean earth-sun distance = 1 AU = 149,597,871 km

So surface area of sphere = 4*pi*r2 = 2.813*1017 km2

Radius of earth = 6371 km

Cross-sectional area of earth = 1.275*108 km2

So the earth occupies 1.275*108 /2.813*1017 of the surface area of the sphere and therefore receives 1.275*108 /2.813*1017 of the sun's energy output.

= 4.5*10-10 or approximately one half of one billionths.

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