Ptolemy's system: more accuracy, more compromise

Claudius Ptolemy (c. 100 – c. 170 CE) fashioned the theory of epicycles into the chief synthesis of astronomical knowledge passed down from antiquity to the middle ages. In doing so, however, he was forced to compromise more of the simple assumptions underlying the Greek tradition in order to align the model with observational data. Another video from the Museo Galileo explains some of the compromises he introduced. The following text provides an additional commentary on another excellent video from the Museo Galileo (in External links, to the right).

First (video 0.12-0.43), the successive periods of retrograde motion of any given planet are not identical. They are not precisely the same ‘amplitude’ (length) or figure (shape) and are not spaced at regular intervals. In order to model these irregularities more accurately, Ptolemy moved the centre of the deferent (along which the planets’ epicycles moved) some distance away from the earth to a point later called the ‘equant’. With this arrangement, although the epicycles continued to move along the deferent in uniform circular motion, the appeared to the observer on Earth as it they were moving at variable speeds. In this way, Ptolemy rescued one cardinal principle of Aristotelian cosmology (uniform circular motion) at the cost of an even more important principle of Aristotelian physics (the idea that the terrestrial world of the four elements was at the centre of the cosmos). 

However (video 0.43-1.29), even this fudge was inadequate. In order to match astronomical observations more closely, a second even less elegant fudge was required. The centre of the deferent was moved to a point closer to the Earth; but the uniform motion of the epicycle was still measured relative to the equant. The elegant philosophical conception at the centre of the Aristotelian cosmos was disintegrating in a dialogue with observational data. While the Aristotelian cosmos had had a single centre (the terrestrial globe and its four elements at the centre of all the celestial spheres composed of a fifth essence), every planet in the Ptolemaic cosmos added two more centres: its equant and the centre of its deferent. 

In addition to these inconsistencies, Ptolemy’s system had several arbitrary features (1.59-2:42). Lacking the means either of establishing the order of the planets or of measuring their distances from the Earth, Ptolemy arranged the planets in a merely plausible order (based on the periods of their orbits) and arbitrarily assumed that there were no gaps between their epicycles. Although far from perfect, the resulting system was extraordinarily accurate for its day in modelling the apparent motions of the planet. Even Copernicus found this system of calculation tolerably accurate a thousand years after Ptolemy’ (2:42-2:53). Copernicus’ achievement was not to produce a more accurate method, but to begin removing some of the arbitrary features of the Ptolemaic system. 

Commentary. Howard Hotson (January 2024)