I am trying to compute the amount of energy received by the Earth from the sun, by integrating over the Earth's surface. I keep reading that the formula should be:(adsbygoogle = window.adsbygoogle || []).push({});

E = e-max * cos @ * area

e-max is the solar insolation,

@ is the angle between the sun and the perpendicular to the land, @=0 at noon (at equator)

It's the cosine that I am having trouble with. What is wrong about the following argument against a factor of cosine for the received energy?

Cosine changes fastest at cos @ = 0, and slowest at cos @ = 1. That means that at sunrise(SR) and sunset(SS), the amount of sun that the land gets is changing most rapidly, and at noon(N) least rapidly. When I picture a mental image of the Earth rotating about its axis, it seems to me that the change in amount of sun at SR, SS, and N should be the same, should all be at a minimum, and at +/- 45 deg should be at a maximum.

That would correspond to cos^2, not cos.

It also seems that the factor at +/- 45 should be half of the maximum, by symmetry. A factor of cosine means half of e-max occurs at @=60, which seems anti-intuitive.

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# What's wrong with argument against cos?

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