Equant

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The basic elements of Ptolemaic astronomy, showing a planet on an epicycle with a deferent and an equant point.

For the telecommunications company named Equant, see Equant (France Télécom).

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.

The equant point is placed so that it is on a line with the Earth and the center of the deferent, indicated in the diagram by an X. 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. 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, and Nicolaus Copernicus.