Pre-Kepler Mathematical Descriptions of the Heavens

In a book review in the December 2003 issue of Physics Today (page 61 ), Gale E. Christianson states that Johannes Kepler was “the formulator of the first mathematical laws of the heavens.” Actually, although Kepler gave an excellent description with his three laws, other mathematical theories of planetary motion had been given previously, going back to antiquity. One could make a good case that the first mathematical description of the heavens predates Claudius Ptolemy, going back to Eudoxus and his theory of uniform motions on concentric spheres (around 370 BC), or even earlier. ¹

The most successful and most mathematically sophisticated planetary-motion theory was from Ptolemy in the second century AD. He gave a surprisingly accurate method for computing the positions of the five then-known planets and our moon. His lunar theory also gave good predictions concerning parallax, the size of the Moon and its distance from Earth, and lunar eclipses. The Ptolemaic system had Earth as its center point and based all motion on circles, but by use of epicycles and eccentric circular motion, it achieved great accuracy. ² In that regard, it was not superseded until Kepler’s work in the 17th century.

Another mathematically sophisticated formulation that preceded Kepler was the Copernican theory, from the 1540s. Although Copernicus had the Sun as the center point, he still used circular motion, and made greater use of epicycles than did Ptolemy. ³