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Kepler's laws of planetary motion 1.The orbit of a planet is an ellipse with the Sun at one of the two foci. 2.A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. 3.The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit. Most planetary orbits are almost circles, and careful observation and calculation is required in order to establish that they are actually ellipses. Calculations of the orbit of the planet Mars first indicated to Johannes Kepler its elliptical shape, and he inferred that other heavenly bodies, including those farther away from the Sun, also have elliptical orbits. Kepler's work (published between 1609-1619) improved the heliocentric theory of Nicolaus Copernicus, explaining how the planets' speeds varied, and using elliptical orbits rather than circular orbits with epicycles.[2] Isaac Newton showed in 1687 that relationships like Kepler's would apply in the solar system to a good approximation, as consequences of his own laws of motion and law of universal gravitation. Kepler's laws are part of the foundation of modern astronomy and physics Kepler