Please help improve this section by adding citations to reliable sources. Isaac Newton showed in 1687 that relationships like Kepler's would apply in the Solar System as a consequence of his own laws of motion and law of universal gravitation. The third law expresses that the farther a planet is from the Sun, the slower its orbital speed, and vice versa. The second law helps to establish that when a planet is closer to the Sun, it travels faster. From this, Kepler inferred that other bodies in the Solar System, including those farther away from the Sun, also have elliptical orbits. The elliptical orbits of planets were indicated by calculations of the orbit of Mars. The square of a planet's orbital period is proportional to the cube of the length of the semi-major axis of its orbit.A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.The orbit of a planet is an ellipse with the Sun at one of the two foci.The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular orbits and epicycles with elliptical trajectories, and explaining how planetary velocities vary. In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 16, describe the orbits of planets around the Sun.
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