Kepler's Laws of Planetary Motion

In astronomy, Kepler's laws of planetary motion are three mathematical laws that describe the motion of planets in the Solar System. German mathematician and astronomer Johannes Kepler (1571–1630) discovered them.Kepler studied the observations of the legendarily precise Danish astronomer Tycho Brahe. Around 1605, Kepler found that Brahe's observations of the planets' positions followed three relatively simple mathematical laws.Kepler's laws challenged Aristotelean and Ptolemaic astronomy and physics. His assertion that the Earth moved, his use of ellipses rather than epicycles, and his proof that the planets' speeds varied, changed astronomy and physics. Nevertheless, the physical explanation of the planets' behavior came almost a century later, when Isaac Newton was able to deduce Kepler's laws from Newton's own laws of motion and his law of universal gravitation, using his invention of calculus. Other models of gravitation would give empirically false results. Kepler's three laws are:The orbit of every planet is an ellipse with the sun at one of the foci. An ellipse is characterized by its two focal points; see illustration. Thus, Kepler rejected the ancient Aristotelean and Ptolemaic and Copernican belief in circular motion. A line joining a planet and the sun sweeps out equal areas during equal intervals of time as the planet travels along its orbit. This means that the planet travels faster while close to the sun and slows down when it is farther from the sun. With his law, Kepler destroyed the Aristotelean astronomical theory that planets have uniform velocity. The squares of the orbital periods of planets are directly proportional to the cubes of the semi-major axes (the "half-length" of the ellipse) of their orbits. This means not only that larger orbits have longer periods, but also that the speed of a planet in a larger orbit is lower than in a smaller orbit.
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The three laws which explain the motion of objects in elliptical orbits, developed by Johannes Kepler and announced by him in 1609 and in 1618. The rules apply to any body in circular or elliptical orbit around the Sun. Equally, the rules also apply to satellites, both natural and artificial, in orbit around a planet. The first rule states that planets move in elliptical orbits with the Sun placed at one focus. Rule two states that equal areas are swept out in equal times, so the planets must be travelling faster when they are closer to the Sun. Rule three states that the square of the planet's orbital period is proportional to the cube of its mean orbital radius from the Sun. More and more .