Editing Deferent and epicycle (section)

{{short description|Planetary motions in archaic models of the Solar System}}
{{Redirect|Deferent|the acknowledgement of the legitimacy of the power of superior or superiors|Deference}}
{{Redirect|Epicycle|the similar mathematical curve|Epicycloid}}
{{Use American English|date=January 2019}}{{Use dmy dates|date=November 2017}}
[[File:Epicycle and deferent.svg|thumb|280x280px|The epicycles of the planets in orbit around Earth (Earth at the center). The path-line is the combined motion of the planet's orbit (deferent) around Earth and within the orbit itself (epicycle).]]

In the [[Hipparchus|Hipparchian]], [[Ptolemaic system#Ptolemaic model|Ptolemaic]], and [[Copernican heliocentrism|Copernican system]]s of [[astronomy]], the '''epicycle''' ({{etymology|grc|''{{wikt-lang|grc|ἐπίκυκλος}}'' ({{grc-transl|ἐπίκυκλος}})|upon the circle}}, meaning "circle moving on another circle")<ref>{{OEtymD|epicycle}}</ref> was a geometric model used to explain the variations in speed and direction of the apparent motion of the [[Moon]], [[Sun]], and [[planet]]s. In particular it explained the [[apparent retrograde motion]] of the five planets known at the time. Secondarily, it also explained changes in the apparent distances of the planets from the Earth.

It was first proposed by [[Apollonius of Perga]] at the end of the 3rd century BC. It was developed by Apollonius of Perga and [[Hipparchus]] of Rhodes, who used it extensively, during the 2nd century BC, then formalized and extensively used by [[Ptolemy]] in his 2nd century AD astronomical treatise the ''[[Almagest]]''.

Epicyclical motion is used in the [[Antikythera mechanism]], <sup>[citation requested]</sup> an ancient Greek astronomical device, for compensating for the elliptical orbit of the Moon, moving faster at perigee and slower at apogee than circular orbits would, using four gears, two of them engaged in an eccentric way that quite closely approximates [[Kepler's second law]].

Epicycles worked very well and were highly accurate, because, as [[Fourier analysis]] later showed, any smooth curve can be approximated to arbitrary accuracy with a sufficient number of epicycles. However, they fell out of favor with the discovery that planetary motions were largely elliptical from a [[heliocentrism|heliocentric frame of reference]], which led to the discovery that [[Newton's law of universal gravitation|gravity obeying a simple inverse square law]] could better explain all planetary motions.