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13 12 Kepler noticed three things about planetary orbits. Firstly that they are ellipses so that a b constant opposite below, with the Sun at one focus. Secondly, that the area of space swept out by a planet in a given time is constant. Thirdly, that the period T of a planet relates to R, its semimajor axis or average orbit, so that T2R3 is a constant throughout the entire solar system. Looking for a geometric or musical solution to the orbits, Kepler observed that six heliocentric planets meant five intervals. The famous geometric solution he tried was to fit the five Platonic Solids between their spheres opposite, and detailed below. In recent years, far from diminishing Keplers vision, Einsteins laws actually showed that the tiny spacetime effects caused by Mercurys faster and therefore heavier and timeslowed motion when nearer to the Sun create a precessional rotation of the ellipses over thousands of years, thus reinforcing Keplers shells. ellipses and nested solids
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