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Kepler's Three Laws
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Tycho's model for the solar system.

Kepler's first and most revolutionary law was that the planets move in
simple elliptical paths, not in some combination of pure circles as every-
one before him had supposed.
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His second law was the Law of equal areas, thus:

A planet moves most rapidly on its elliptical orbit when it is at position A, nearest the focus of the ellilpse, S, where the sun is. The planet's orbital speed varies in such a way that in equal intervals of time it moves distances AB, BC, CD, and so on, so that regions swept out by the line connecting it and the sun (shaded and clear zones) are always the same in area.

 
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Kepler's third law states that the planet's sidereal period (the time it takes to complete a circuit through the stars) squared is proportional to the semimajor axis of its orbit cubed.

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