![]() Of course, a circle is also an ellipse-an ellipse with eccentricity 0 and in which the foci coincide in the center-and indeed the orbits of most planets are far more nearly circular than the diagram would suggest. Kepler’s laws imply that the speed of revolution of a planet around the sun is not uniform, but changes throughout the planet’s “year.” It is fastest when the planet is nearest the sun (called the perihelion) and slowest when the planet is farthest away ( aphelion). These laws are illustrated in the following diagram: The square of the period of revolution of a planet about the sun is proportional to the cube of the semimajor axis of the planet’s elliptical orbit.The line segment joining a planet to the sun sweeps out equal areas in equal time intervals.The orbit of each planet is an ellipse with the sun at one focus.After studying this data for 20 years Kepler came to understand that his earlier assumptions about planetary motion had been naïve, and that if an earth-centered (Ptolemaic) understanding of the universe were abandoned for a sun-centered (Copernican) model then the motion of the planets was clearly elliptical.įrom this basis, Kepler generated his three famous “laws” of planetary motion: ![]() When Tycho Brahe died, in 1601, Kepler inherited this enormous mountain of raw data. However, he was also a friend and assistant to the great Danish astronomer Tycho Brahe, who was making precise and detailed observations of the planets and stars. The German mathematician and astronomer Johannes Kepler (1571–1630) was an avowed Platonist, and set out early in his professional career to demonstrate that the motion of the planets was circular, in accordance with the established Aristotelian doctrine, and that they could be described in terms of the Platonic solids. Kepler’s Platonic Solids Model of the Cosmos ![]() ![]() Zeno’s Paradox of the Tortoise and Achilles. ![]()
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