How do you calculate the radius of the penumbra during a solar eclipse?

by Ken Lund
Question by : How do you calculate the radius of the penumbra during a solar eclipse?
What is the formula to calculate the radius of the penumbra? I'm looking for the pure formula not necessarily in regards to the Earth and the moon.

If it helps, the formula for the length of the umbra can be found here: http://en.wikipedia.org/wiki/Eclipse


Best answer:
Answer by coldfieldgirlYou must know the umbra can fall on Earth's surface, but also it can just not fall on it (it is an annular eclipse then!).

So for your calculation of the penumbra on Earth's surface, the whole distance between Earth and Moon must be taken.

If you suppose:

s = radius Sun
m = radius Moon
N = distance Moon to Sun
D = distance Moon to Earth

then you can do the following:

angle A of one penumbra line = ArcTan ( ( s + m ) / N )

and the radius of the penumbra becomes m + D * Tan ( A )

What do you think? Answer below!







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