10.3. Johannes Kepler and celestial mechanics

Abstract

Any contemporary manual of celestial mechanics contains such notions as “Kepler's Laws”, “Kepler's Equation”, “Keplerian motion”, “Keplerian orbits”, etc. Celestial mechanics before Kepler belongs to the province of history, but modern theoretical astronomy is based on his fundamental investigations. The main work by Kepler appeared in 1609; it was entitled The New Astronomy. Ten years later Kepler published The Harmonies of the World and The Epitome of Copernicus' Astronomy; and in 1627 his famous Rudolphine Tables. These works presented the solution of the mystery of the planetary motions within the limits of the two-body problem; Kepler's success was due to new methods in research. The motion of the planets was found by Kepler to follow three laws: (1) The orbit of each planet is an ellipse, with the Sun as its focus. (2) Each planet revolves so that the line connecting it to the Sun sweeps through equal areas in equal time-intervals. (3) The squares of the periods of any two planets are in the same proportion as the cubes of their mean distances from the Sun. Kepler realized that his laws were approximate. Thus, for example, the motion of the Moon showed a number of irregularities, many of them great enough to have been discovered by ancient astronomers. Such anomalies in the Moon's motion presented the first test of Newton's theory of motion, and his law of gravitation, from which Kepler's laws are deducible, gave a rational and unifying explanation of them.