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The first law states that the shape of each planets orbit is an ellipse with the sun at one focus The sun is thus off-center in the ellipse and the planets distance from the sun varies as the planet moves through one orbit The second law specifies quantitatively how the speed of a planet increases as its distance from the sun decreases If an imaginary line is drawn from the sun to the planet the line will sweep out areas in space that are shaped like pie slices The second law states that the area swept out in equal periods of time is the same at all points in the orbit When the planet is far from the sun and moving slowly the pie slice will be long and narrow when the planet is near the sun and moving fast the pie slice will be short and fat The third law establishes a relation between the average distance of the planet from the sun the semimajor axis of the ellipse and the time to complete one revolution around the sun the period the ratio of the cube of the semimajor axis to the square of the period is the same for all the planets including the earth 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 Keplers 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
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