Earlier theories of planetary motion, such as the geocentric Ptolemaic system and the heliocentric Copernican system, had allowed only perfect circles as orbits and were therefore compelled to combine many circular motions to reproduce the variations in the planets' motions. Kepler eliminated the epicycles and deferents that had made each planet a special case. His laws apply generally to all orbiting bodies.

Kepler's first and second laws were published in 1609 in *Commentaries on the Motions of Mars.* Because Mars was the planet whose motions were in greatest disagreement with existing theories, its orbit provided the critical test for his hypotheses. To do this Kepler was able to rely on the astronomical observations of his mentor, Tycho Brahe, which were much more accurate than any earlier work. The third law appeared in 1619 in *Harmony of the Worlds.*

- Introduction
- Summary of Kepler's Laws
- Development of Kepler's Laws
- Kepler's Foretelling of the Law of Gravity

*The Columbia Electronic Encyclopedia,* 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

- Kepler's laws: Development of Kepler's Laws - Development of Kepler's Laws Earlier theories of planetary motion, such as the geocentric ...
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