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The deferent/epicycle models worked as well as they did because of the extraordinary orbital stability of the solar system. Either theory could be used today had Gottfried Wilhelm Leibniz and Isaac Newton not invented calculus. [20] According to Maimonides, the now-lost astronomical system of Ibn Bajjah in 12th century Andalusian Spain lacked ...
The basic elements of Ptolemaic astronomy, showing a planet on an epicycle (smaller dashed circle), a deferent (larger dashed circle), the eccentric (×) and an equant (•). Equant (or punctum aequans ) is a mathematical concept developed by Claudius Ptolemy in the 2nd century AD to account for the observed motion of the planets.
Ragep, F. J. "The Two Versions of the Tusi Couple," in From Deferent to Equant: A Volume of Studies in the History of Science in Ancient and Medieval Near East in Honor of E. S. Kennedy, ed. David King and George Saliba, Annals of the New York Academy of Sciences, 500. New York Academy of Sciences, 1987.
A given planet then moves around the epicycle at the same time the epicycle moves along the path marked by the deferent. These combined movements cause the given planet to move closer to and further away from the Earth at different points in its orbit, and explained the observation that planets slowed down, stopped, and moved backward in ...
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 model), one using eccentrics and another deferent and epicycles. [42]
Ptolemy's planetary model showing the deferent and epicycle as dashed lines and the Earth and equant equidistant to the center of the deferent. Claudius Ptolemy's planetary model consisted of a stationary earth surrounded by fixed circles, called deferents, which carried smaller, rotating circles called epicycles. Planets rotated on the ...
For the Moon, Ptolemy began with Hipparchus' epicycle-on-deferent, then added a device that historians of astronomy refer to as a "crank mechanism": [28] he succeeded in creating models for the other planets, where Hipparchus had failed, by introducing a third device called the equant. Ptolemy wrote the Syntaxis as a textbook of mathematical ...
Ptolemaic model of the spheres for Venus, Mars, Jupiter, and Saturn with epicycle, eccentric deferent and equant point. Georg von Peuerbach , Theoricae novae planetarum , 1474. In his Almagest , the astronomer Ptolemy (fl. c. 150 AD) developed geometrical predictive models of the motions of the stars and planets and extended them to a unified ...