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# 3.5 Johannes Kepler

Deeply religious and a believer in astrology, Johannes Kepler was sure that planetary motions would turn out to be governed by hidden regularities. Kepler was greatly influenced by Pythagoras, who had discovered that two musical notes an octave apart are produced by vibrating strings with lengths in a ratio of 2 to 1. Kepler hoped that the ratios of the planet’s distances would be simple mathematical ratios like those vibrations that produced harmonious sounds in music. They are not.

Kepler discovered that planets do not orbit in circles, but in ellipses around the Sun. Click here for original source URL.

However, Kepler continued his studies using Tycho Brahe’s twenty-year accumulation of measured planetary positions. He first studied the orbit of Mars, whose movements in the sky had plagued astronomical theorists since Ptolemy. He found something astonishing. After all the centuries of debate about circular orbits and circular epicycles, the orbit that best fitted the observed positions of Mars was not a circle at all, but an ellipse! Ellipses are figures that can range from circular to highly elongated loops. Eventually, Kepler found that all planets move around the sun in elliptical paths. Any ellipse has two special points, called foci. As an ellipse becomes more like a circle the two foci move closer together. In a circle they merge to a single point at the center. Kepler made the surprising discovery that in each planet’s elliptical orbit, the Sun lies not at the center of the ellipse, but at one focus of the ellipse. Although all planets’ orbits are elliptical, most are so slightly elongated that they look almost circular.

A 1610 portrait of Johannes Kepler by an unknown artist. Click here for original source URL

Kepler achieved his breakthrough by giving up one of the most cherished Greek ideas — the perfect symmetry of a circular orbit. He did not do this lightly. It took him eight years of analysis and hundreds of pages of calculations to be sure of his conclusion. However his insight allowed him to dramatically simplify the description of planetary orbits. Within the Ptolemaic model, the accurate data of Tycho could only be matched using circular orbits by adding many epicycles. Ironically, the Copernican model also needed epicycles to fit the data equally well. The problem is that the motion of the planets is not uniform, but a circular orbit produces uniform motion regardless of whether the Earth or the Sun is at the center. Kepler avoided the contortion of epicycles by having a single ellipse to describe the orbit of each planet. His results did not fit the geocentric theory of Ptolemy, but they fit beautifully the heliocentric hypothesis of Copernicus.