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?
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.