Deferent and epicycle  

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Train wreck at Montparnasse (October 22, 1895) by Studio Lévy and Sons.
Train wreck at Montparnasse (October 22, 1895) by Studio Lévy and Sons.

In the Ptolemaic system of astronomy, the epicycle (literally: on the circle in Greek) was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets. It was first proposed by Apollonius of Perga at the end of the 3rd century BC and formalized by Ptolemy of the Thebaid in his 2nd-century AD astronomical treatise the Almagest. In particular it explained the retrograde motion of the five planets known at the time. Secondarily, it also explained changes in the apparent distances of the planets from Earth.

It is called Ptolemaic after the Greek astronomer Ptolemy, although it had been developed by previous Greek astronomers such as Apollonius of Perga and Hipparchus of Rhodes, who used it extensively, during the second century BC, almost three centuries before Ptolemy. Epicyclical motion is used in the Antikythera Mechanism, an ancient Greek astronomical device for computing the phase and position of the Moon using four gears, two of them engaged in an eccentric way that closely approximates Kepler's second law, i.e. the Moon moves faster at perigee and slower at apogee.

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