Kepler, Johannes (1571-1630), a German astronomer. Kepler's three laws of the motions of planets are basic to the understanding of the solar system. The laws also apply to the motions of artificial satellites. The first two laws appeared in print in 1609, the third in 1619. In spite of their importance Kepler's laws had little immediate effect on his colleagues. Later, Kepler's laws enabled Sir Isaac Newton to formulate his law of gravitation.

Kepler studied theology at the University of Tbingen, but in 1594 he accepted a professorship in natural science at the University of Graz, Austria. Because Protestants were being persecuted at Graz, he went to Prague in 1600. There he became assistant to the Danish astronomer Tycho Brahe, who under the patronage of Holy Roman Emperor Rudolph II held the post of imperial mathematician. When Tycho died suddenly in 1601, Kepler succeeded him as imperial mathematician and inherited his papers. Tycho's observations helped Kepler develop his laws. In 1612 Kepler moved to Linz, Austria, where he finished work on an astronomical table Tycho had begun.

Kepler was often short of money, and was forced to spend much time in composing horoscopes for Rudolph II and later patrons.

### Kepler's Laws

Kepler's three laws of planetary motion are as follows:

1. Planets move in elliptical orbits that have the sun as one of their foci.

2. A straight line running from a planet to the sun will pass over equal areas of the ellipse in equal periods of time. This means that the velocity of a planet is greatest at the point nearest the sun and is least at the point farthest from the sun.

3. This law expresses the relationship between the distances that the various planets are from the sun and the length of time it takes the planets to complete an orbit around the sun. A simplified statement of the law is: The cube of a planet's mean (average) distance from the sun divided by the square of the time that it takes to complete an orbit is the same for all planets.

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