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Museo Galileo, Virtual Museum, Keplers Laws

Kepler, who embraced Copernicanism in his youth, strove to identify the harmonicrule thatin his viewwas used by God in creating the Cosmos. In his MysteriumCosmographicum, he formulated the hypothesislater discardedthat thedimensions of the spheres of the six planets then known were linked to the five

regular solids. The radius of each planetary sphere was determined by its exact fitbetween two successive solids.Kepler later became the assistant of Tycho Brahe, from whom he inherited a corpusof highly accurate celestial observations. Using Tycho's data, Kepler tried to solvethe arduous problem of determining the orbit of Mars. After many attempts, herealized the need to abandon the postulate of the circularity of planetary orbits: infact, each planet's orbit was an ellipse with the Sun located in one of the foci.Kepler thus established what is now known as his First Law.Kepler had previously found that the planets travel on their orbits in non-uniformmotion. In consequence, the segment joining the planet to the Sun covers equalareas in equal time intervals. This principle, now known as Kepler's Second Law,

implies that the planets move faster when they are closer to the Sun and moreslowly when they are farther away. In so doing, Kepler breached another ancientdogma: the uniform motion of the planets.In his Third Law, Kepler states that, for any given pair of planets, the squares oftheir revolution periods were in the same proportion to each other as the cubes ofthe major semi-axes of their orbits. Kepler thus clarified the exact rule governingthe gradual decrease in the orbital velocity of the planets, proceeding from theinnermost ones to the outermost ones.Kepler wanted to root his three laws in a physical explanation. He voiced thehypothesis that the Sun was a magnet capable of exerting on the planets a motive

power whose intensity varied with distance. Kepler saw the planets, too, asmagnets permanently oriented in the same direction. Consequently, in one part ofthe orbit, being attracted by the Sun, the planets tended to accelerate and drawcloser to the Sun; in the other part of the orbit, they were repelled by the Sun,moved away from it, and thus lost velocity.