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{{For|the telecommunications company named Equant|Equant (France Télécom)}}
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[[Image:Ptolemaic elements.svg|250px|right|thumb|The basic elements of [[Ptolemaic astronomy]], showing a planet on an [[epicycle]] with a [[deferent]] and an equant point.]]


'''Equant''' (or '''punctum aequans''') is a [[mathematical]] concept developed by [[Claudius Ptolemy]] in the 2nd century AD to account for the observed motion of heavenly bodies.
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The '''equant point''', indicated in the diagram by the large&nbsp;•&nbsp;, is placed so that it is directly opposite the Earth from the center of the [[Deferent and epicycle|deferent]], indicated by the ×. A planet or the center of an [[epicycle]] (a smaller circle carrying the planet) was conceived to move with a uniform speed with respect to the equant. In other words, to a hypothetical observer placed at the equant point, the center of the epicycle would appear to move at a steady speed. However, the planet/center of epicycle will not move uniformly on its deferent.
The angle α between the axis on which the equant and the Earth lie is a function of time&nbsp;''t'':
 
: <math> \alpha(t) = \Omega t - \arcsin\left(\frac{E}{R} \sin(\Omega t) \right) </math>
 
where Ω is the constant angular speed seen from the equant which is situated at a distance ''E'' when the radius of the deferent is&nbsp;''R''.<ref>[http://www.mathpages.com/home/kmath639/kmath639.htm  Eccentrics, deferents, epicycles and equants (Mathpages)]</ref>
 
This concept solved the problem of accounting for the anomalistic motion of the planets but was believed by some to compromise the goals of the ancient astronomer, namely uniform circular motion. Noted critics of the equant include the Persian astronomer [[Nasir al-Din Tusi]] who developed the [[Tusi-couple]] as an alternative explanation,<ref>Craig G. Fraser, '[http://books.google.com/books?id=3tJr_vl6rYsC&lpg=PA39&pg=PA39#v=onepage&q&f=false The cosmos: a historical perspective]', Greenwood Publishing Group, 2006 p.39</ref> and [[Nicolaus Copernicus]]. Dislike of the equant was a major motivation for Copernicus to construct his heliocentric system.<ref>{{cite book
  |last = Kuhn
  |first = Thomas
  |authorlink = Thomas Kuhn
  |title = The Copernican Revolution
  |publisher = Harvard University Press
  |series =
  |year = 1957 (copyright renewed 1985)
  |doi =
  |isbn = 0-674-17103-9
  |pages=70–71}}
</ref><ref>[[Arthur Koestler|Koestler A.]] (1959), ''[[The Sleepwalkers]]'', Harmondsworth: Penguin Books, p.&nbsp;322; see also p.&nbsp;206 and refs therein. [http://www.archive.org/details/ArthurKoestler-TheSleepwalkers-AHistoryOfMansChangingVisionOfThe]</ref>
 
==References==
<references/>
 
==External links==
*[http://galileo.rice.edu/sci/theories/ptolemaic_system.html Ptolemaic System] – at Rice University's Galileo Project
*[http://jove.geol.niu.edu/faculty/stoddard/JAVA/ptolemy.html Java simulation of the Ptolemaic System] – at Paul Stoddard's Animated Virtual Planetarium, Northern Illinois University
 
==See also==
*[[Equidimensional]]: This is a synonym for '''equant''' when it is used as an adjective.
 
{{Greek astronomy}}
 
[[Category:Ancient Greek astronomy]]
[[Category:Trigonometry]]
[[Category:History of astronomy]]
[[Category:Ancient astronomy]]
 
{{Mathapplied-stub}}
{{sci-hist-stub}}

Latest revision as of 08:53, 26 December 2014

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