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Apollonius of Perga (3rd century BC) realized that this cyclical variation could be represented visually by small circular orbits, or epicycles, revolving on larger circular orbits, or deferents. Hipparchus (2nd century BC) calculated the required orbits. Deferents and epicycles in the ancient models did not represent orbits in the modern sense ...
For the ratios of the radii of the outer planets' deferents to radius of the Earth, the Commentariolus gives 1 13 ⁄ 25 for Mars, 5 13 ⁄ 60 for Jupiter, and 9 7 ⁄ 30 for Saturn. For the ratios of the radii of their deferents to the radii of the larger of their epicycles, it gives 6 138 ⁄ 167 for Mars, 12 553 ⁄ 606 for Jupiter, and 11 ...
Noted critics of the equant include the Persian astronomer Nasir al-Din Tusi who developed the Tusi couple as an alternative explanation, [10] and Nicolaus Copernicus, whose alternative was a new pair of small epicycles for each deferent. Dislike of the equant was a major motivation for Copernicus to construct his heliocentric system.
The epicycles of the planets in orbit around Earth (Earth at the centre). The path-line is the combined motion of the planet's orbit (deferent) around Earth and within the orbit itself (epicycle). Around 210 BCE, Apollonius of Perga shows the equivalence of two descriptions of the apparent retrograde planet motions (assuming the geocentric ...
Copernicus's observation that his system could explain the planetary motions with no more than 34 circles has been taken to imply that a large number of additional epicycles had been subsequently introduced into the Ptolemaic system in an attempt to make it conform with observation. [6]
Size of deferents, epicycles Only ratio between radius of deferent and associated epicycle determined; absolute distances not determined in theory Interior planets: Average greatest elongations of 23° (Mercury) and 46° (Venus) Size of epicycles set by these angles, proportional to distances Interior planets Limited to movement near the Sun
For this reason, he was unable to account for the observed apparent motion of the planets without retaining a complex system of epicycles similar to those of the Ptolemaic system. Despite Copernicus' adherence to this aspect of ancient astronomy, his radical shift from a geocentric to a heliocentric cosmology was a serious blow to Aristotle 's ...
However, while Apollonius is often credited with developing this theory, some think that the evidence for this is tenuous. Some evidence may tie in an earlier author, Archimedes, with knowledge of epicycles and eccentrics, and the Antikythera mechanism also appears to presuppose eccentrics and epicycles in the way it produces calculations. [30]