# The Complete System

Ptolemy is said to have visualized his syatem as being composed of nested crystal spheres each rotating inside one another. The idea of crystal spheres goes back long before Ptolemy and it was taken up again by Christian theologians in the Middle Ages. Whether Ptolemy himself actually believed in them we shall never know. This model shows how the three bodies treated by this program (Moon, Venus and Mars) together with the Sun were supposed to fit together.

This program only deals with the position of the planets in longitude. In reality, their orbits are slightly incluned to the ecliptic but this is easily accomplished in the crystal sphere model by inclining the respective axes of the sheres.

What is not so clear is why every one of the planets has an epicycle or a deferent which has a period of exactly one year. Indeed it was surely this coincidence above all others which stimulated Copernicuc to put the Earth in orbit round the Sun. In Ptolemy's basic system, each of the five planets had one deferent and one epicycle making 12 circles in all (including one each for the Sun and Moon). Using eccentric deferents with equants, this system can be made to work extremely well.

Copernicus simplified the scheme by giving each planet, Moon and Sun one circle making 7 in total, but then complicated it again by removing all the equants and replacing them with one or, in some case even two epicycles. In the end, Copernicus' system was neither simpler nor more accurate than Ptolemy's.