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In the Hipparchian and Ptolemaic systems 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. 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 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 second century BC, then formalized and extensively used by Ptolemy of Thebaid in his 2nd-century AD astronomical treatise the ''Almagest''. Epicyclical motion is used in the Antikythera Mechanism, 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. ==Introduction== In both Hipparchian and Ptolemaic systems, the planets are assumed to move in a small circle called an ''epicycle'', which in turn moves along a larger circle called a ''deferent''. Both circles rotate clockwise and are roughly parallel to the plane of the Sun's orbit (ecliptic). Despite the fact that the system is considered geocentric, each planet's motion was not centered on the Earth but at a point slightly away from Earth called the ''eccentric''. The orbits of planets in this system are similar to epitrochoids. In the Hipparchian system the epicycle rotated and revolved along the deferent with uniform motion. However, Ptolemy found that he could not reconcile that with the Babylonian observational data available to him; in particular, the shape and size of the apparent retrogrades differed. The angular rate at which the epicycle traveled was not constant unless he measured it from another point which he called the ''equant''. It was the angular rate at which the deferent moved around the point midway between the equant and the Earth (the eccentric) that was constant; the epicycle center swept out equal angles over equal times only when viewed from the equant. It was the use of equants to decouple uniform motion from the center of the circular deferents that distinguished the Ptolemaic system. 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. He generally ordered the planets outward from the Earth based on their orbit periods. Later he calculated their distances in the ''Planetary Hypotheses'' and summarized them in the first column of this table: :Had he known accurate deferrent sizes or even sizes with relatively close ratios to modern values to use in his model, the epicycle sizes would have all approached the size of the sun's orbit about the Earth. Although all the planets are considered separately, in one peculiar way they were all linked: the lines drawn from the body through the epicentric center of all the planets were all parallel, along with the line drawn from the sun to the Earth along which Mercury and Venus were situated. That means that all the bodies revolve in their epicycles in lock step with Ptolemy's sun (that is, they all have exactly a one year period). Babylonian observations showed that for superior planets the planet would typically move through in the night sky slower than the stars. Each night the planet appeared to lag a little behind the stars, in what is called prograde motion. Near opposition, the planet would appear to reverse and move through the night sky faster than the stars for a time in retrograde motion before reversing again and resuming prograde. Epicyclic theory, in part, sought to explain this behavior. The inferior planets were always observed to be near the sun, appearing only shortly before sunrise or shortly after sunset. Their apparent retrograde motion occurs during the transition between evening star into morning star, as they pass between Earth and the sun. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「deferent and epicycle」の詳細全文を読む スポンサード リンク
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