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When I was in school learning to derive that fact, it took vector calculus

and some pretty serious geometry to do it.

The answer can't be presented here, for 3 main reasons that I know of:

1). Vector calculus is somewhat beyond the scope of this website.

2). I don't remember how to do it.

3). I don't have any other simpler way to explain it.

More information: Newton's Law of Gravitation is part of it and some calculus is needed, but the most important thing is the fact that "angular momentum" must be conserved. I would say that it is the "law of conservation of angular momentum" that explains this phenomenon (which is "Kepler's second law of planetary motion").

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Q: How does Newtons law of gravitation explain why a planet would sweep out equal amounts of area in equal amounts of time?
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