Claudius Ptolemaeus (c. 90—c. 168 CE)

The main problem with Hipparchus’ deferent-and-epicycle model was in its description of the retrograde loops of Mars, Jupiter and Saturn. In this regard, the model had been an acknowledged failure until it was finally fixed by Claudius Ptolemaeus, who is now commonly known as Ptolemy.

Ptolemy’s great treatise on astronomy eventually came to be called the Almagest, from the Arabic word meaning “greatest”. Due to the success of Ptolemy’s model in predicting the positions of astronomical objects, the works of his predecessors, including Hipparchus, were lost over the centuries as they failed to be transcribed.

Ptolemy’s first innovation over Hipparchus was to add an eccentric to the deferent-and-epicycle orbits of the planets. Recall that the original purpose of the eccentric was to shift the circular paths of the Sun and Moon, so that they would appear to move at different speeds when they were at different points, even though they moved uniformly along a circle. In Hipparchus’ system, the Earth was eccentric to the actual paths of the Sun and Moon. In Ptolemy’s system, the Earth was eccentric to the deferents of the planets, which the planets looped around on their epicycles, not following circular paths.

While Ptolemy’s eccentric was different from Hipparchus’ (or, Apollonius’), its effect was similar. While Hipparchus needed the eccentric to produce a variable rate in the Sun’s and Moon’s motions, Ptolemy used it to change the lengths of the loops of retrogression that occurred in different places along the ecliptic.

Ptolemy’s second innovation over Hipparchus was his invention of the equant. With his eccentrics, he managed to get the loops of retrogression to bunch up in the right places, but he couldn’t quite get their lengths right. He solved this problem by introducing another point, on the opposite side of the centre of the circle from the eccentric, called the equant. Ptolemy made the equant the point about which the epicycle would be perceived to move uniformly. That’s right: there was no more uniform circular motion in Ptolemy’s model; there was motion about a circle that would be perceived as being uniform about some other point. He tweaked the theory just enough, and made it fit with hundreds of years worth of data! Watch the following video to see a demonstration of how Ptolemy combined deferents, epicycles, eccentrics and equants to produce a model that could finally accurately describe and predict the motion of the planets.

Ptolemy solved a centuries-old puzzle, showing that the general geocentric framework which scientific evidence had been pointing towards for centuries could produce an accurate description of all celestial motions. It was a mess of deferents and epicycles; but even Copernicus, with his 16th century heliocentric model and more than a thousand years’ worth of further observation, could not manage better. Ptolemy’s was one of the greatest achievements in the history of science, and his work was deserving of the name Almagest. It was ready to be scrutinised through centuries of observation and contemplation of its hypotheses, and ultimately it did not stand the test of time; however, it still remains the longest standing accepted model in the history of physics.