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How did Kepler arrive at his laws? If one already knows the distances to the planets (and the eccentricity of the orbits, etc.), it is understandable that one might proceed to establish Kepler's second and third laws. However, how did Kepler do this without knowing the distances? His third law seems a true revolution since it establishes the distances between the Sun and the planets (in astronomical units at least); it just seems such a huge and daring step ahead. What he was basing this on?

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    $\begingroup$ I believe that people knew the distances, in astronomical units, of the known planets from the Sun before Kepler. This is how he built his "platonic solid" model of the solar system. You only need distances in AU, and these can be gleaned by parallax and triangulation. Some idea of absolutes was also known around this time in terms of diameters of the Earth (again I think this must have been by triangulation) - Ole Roemer calculated the speed of light to be 7600 times the Earth's speed around the Sun, whence Huygens deduced $c$ was 16.7 Earth diameters each second. $\endgroup$ – WetSavannaAnimal Feb 17 '14 at 10:32
  • $\begingroup$ @WetSavannaAnimalakaRodVance thank you, I did not know about this! I found physics.stackexchange.com/a/36011/37125 , so just the notion of heliocentrism gave the means to measure the planet distances from the sun in AU. This is so beautyful. $\endgroup$ – John Donn Feb 17 '14 at 10:51
  • $\begingroup$ Yes, I agree, Ron's answer is an extremely insightful take on it. However, it would be good to get a summary of exactly how the measurement history went from a real historian/astronomer, because the other question didn't really get such an answer. $\endgroup$ – WetSavannaAnimal Feb 17 '14 at 12:19
  • $\begingroup$ Also see this. $\endgroup$ – orome Sep 23 '15 at 20:02
  • $\begingroup$ @raxacoricofallapatorius this is interesting, thank you $\endgroup$ – John Donn Sep 24 '15 at 9:04
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about the third law:
I've read that Kepler was actually a mathematician. believing in heliocentric universe, Brahe's observations of planets some times deviated significantly from the place expected by the Copernican theory of circular orbits. strongly believing Brahe haven't made such great mistakes, Kepler thought, what if the orbits weren't circular???? he made a guess! how about elliptical orbits?? considering him being a mathematician, it wasn't such a revolutionary change, but in the understanding of the universe, of course it was! and then he devoted about 10 years of his life to examine this guess. a guess that could be completely wrong!!! actually, it was only a fortune that he thought about elliptical orbits.

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