Ptolemaic system

Claudius Ptolemy perfected the theory of epicycles developed by Apollonius and Hipparchus.

To explain the fact that the planets' retrograde movements are not consistently of the same amplitude, and do not occur at equal intervals, Ptolemy placed the deferent in an eccentric position with respect to the Earth. In this way, the epicycle, while moving at uniform velocity across the deferent, appeared to the observer on Earth as if it were moving at variable speed: more slowly near the apogee, faster near the perigee.

Ptolemy found, however, that the only way to achieve full congruence with observations was to place the center of the deferent at the midpoint of the segment joining the center of the Earth to the point relative to which the center of the epicycle travels in uniform motion. Such a point, later called equant, thus no longer coincided with the center of the deferent. In practice, this expedient violated the dogma of uniform celestial motion: equal angles traveled in equal times with respect to the equant do not intercept equal arcs on the deferent.

By tilting the deferent relative to the ecliptic by a particular angle for each planet, Ptolemy explained latitudinal motions as well. In its travel along the deferent, the epicycle always remained parallel to the plane of the ecliptic. In this way, seen from the Earth, the planet described the complicated slipknot- and S-shaped paths observed during retrograde motion.

With the instruments at his disposal, Ptolemy could establish neither the true distances of the planets from the Earth, nor the planetary sequence. Moreover, the positions of the planets in the epicyclical theory do not depend on the dimensions of the epicycle and the deferent, but only on the relationship between their radii. Ptolemy accordingly designed his system on the assumption that there were no voids between the planets. He therefore specified the dimensions of the epicycles and deferents so that the perigee of each planet would lie immediately above the apogee of the underlying planet. The resulting system remained popular until the sixteenth century.

Last update 09/feb/2008