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Theory of trepidation

This diagram, from a text known as the Theorica planetarum, is a recurrent element of university manuscripts dealing with mathematical astronomy. It represents the theory of what ancient and medieval astronomers working in a Ptolemaic frame called the eight sphere, carrying the zodiac and the fixed stars. The proper motion of this sphere, also known as the precession of the equinoxes, is very slow and only perceptible over a time span of about a century. It is nonetheless very important because the sphere of the fixed stars carries most of the reference points against which the motion of all the other celestial objects are measured. Different hypotheses concerning the motion of this sphere were circulating. Ptolemy, and after him many astronomers, thought of a continuous motion at a constant pace. Others, following a text attributed to the Arabic astronomer Thabit ibn Quara, thought that this motion had a varying speed throughout the centuries and a maximum value. This motion was called trepidation. Parisian Alfonsine astronomers, and after them all Latin astronomers in Alfonsine astronomy followed a combination of the two hypotheses.

The diagram presented here follows the hypothesis of trepidation. A striking element of these diagrams is that contrary to planetary diagrams it contains no straight line. This is because the different circles represented here are to be imagined on a sphere. The motion of trepidation is based on two epicycles, which instead of being on a plane like planetary epicycles, are on the surface of a sphere.