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For the Moon, Ptolemy began with Hipparchus' epicycle-on-deferent, then added a device that historians of astronomy refer to as a "crank mechanism": [28] he succeeded in creating models for the other planets, where Hipparchus had failed, by introducing a third device called the equant. Ptolemy wrote the Syntaxis as a textbook of mathematical ...
The basic elements of Ptolemaic astronomy, showing a planet on an epicycle (smaller dashed circle), a deferent (larger dashed circle), the eccentric (×) and an equant (•). Equant (or punctum aequans) is a mathematical concept developed by Claudius Ptolemy in the 2nd century AD to account for the observed motion of the planets. The equant is ...
Ptolemy did not predict the relative sizes of the planetary deferents in the Almagest. All of his calculations were done with respect to a normalized deferent, considering a single case at a time. This is not to say that he believed the planets were all equidistant, but he had no basis on which to measure distances, except for the Moon.
Unfortunately, the system that was available in Ptolemy's time did not quite match observations, even though it was an improvement over Hipparchus' system. Most noticeably the size of a planet's retrograde loop (especially that of Mars) would be smaller, or sometimes larger, than expected, resulting in positional errors of as much as 30 degrees.
Ptolemy's Almagest was an authoritative text on astronomy for more than a thousand years, and the Tetrabiblos, its companion volume, was equally influential in astrology, the study of the effects of astronomical cycles on earthly matters.
Ptolemy emphasised that the epicycle motion does not apply to the Sun. His main contribution to the model was the equant points. He also re-arranged the heavenly spheres in a different order than Plato did (from Earth outward): Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn and fixed stars, following a long astrological tradition and the ...
An introduction to Ptolemy's Almagest, the Tashil al-Majisti, believed to be written by Thābit ibn Qurra, presented minor variations of Ptolemy's distances to the celestial spheres. [33] In his Zij , Al-Battānī presented independent calculations of the distances to the planets on the model of nesting spheres, which he thought was due to ...
Ptolemy emphasised that the epicycle motion does not apply to the Sun. His main contribution to the model was the equant points. He also re-arranged the heavenly spheres in a different order than Plato did (from Earth outward): Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn and fixed stars, following a long astrological tradition and the ...