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Ptolemy was a Greek-speaking scientist in the Roman colony of Alexandria Egypt. The model of Ptolemy states that all heavenly bodies travel in perfectly circular paths at constant speeds around a point that is near the Earth but not exactly at the Earth. Since Ptolemy did not believe in oval paths and did not know that the planets traveled around the sun instead of around the Earth, he used the concept of the epicycle to make a circular adjustment to the circular paths.

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geocentric model of Ptolemy

(Large dotted-line circle is the path of a planet around the Earth. The “x” is the center of that circle. The Earth is located near but not exactly at the “x”.  Small dotted line circle is the epicycle, that can make the apparent path of a planet around the Earth appear to slow down or even reverse direction.

Different heavenly bodies have different “x” points as the center of their circular path around the Earth.

Some Greeks noticed apparent changes in the speed of heavenly bodies across the sky, but since they believed the sun and planets moved at constant speeds in circular paths, they interpreted this as changes in the distance to the Earth caused by the Earth not being exactly at the center of the circle.

Ptolemy used a model with different centers, and with epicycles.
The Muslim astronomers did not invent any new models of the solar system (except the weird Tusi couple explained later), but merely argued about whether to accept Aristotle, or part or all of Ptolemy.
A few Muslim astronomers, (such as Avempace and Nur ad-Din al-Bitruji in the 12th century) did not like the epicycle concept and attempted to devise models in which each planet moves in a perfectly circular path around a point that is neither the Earth nor the sun.
Nur ad-Din al-Bitruji (Alpetragius) (1150? – 1204) invented a model of the solar system that had no ovals and no epicycles. It was based on the incorrect 4th century BC model of Aristotle, but modified so that each planet had a different point for the center of its constant speed circular orbit around the Earth.
In around the year 200 BC, a Greek-speaking scholar named Apollonius of Perga and other Greek-speaking scholars modified the model by adding epicycles to make it better agree with observations of astronomers.
The epicycle model was copied and formalized by a Greek-speaking astronomer named Ptolemy who lived in Alexandria Egypt at a time when it was a Roman colony.
An epicycle is a small circle (called the equant) moving on a much larger circle (called the deferent). The center of the equant circle is on the much larger deferent circle. The path of the planet is a point on the equant circle.
The model with epicycles better agreed with observations of variations in speed and direction of the apparent motion of the moon, sun, and planets, and explained the apparent retrograde motion of the planets.
The motion appears to the observer to be linear motion because the Earth, sun, planets and both circles are in the same plane.
A diagram is at
An exaggerated animation of an epicycle path is at
This concept of the motion of a point on the equant allowed Ptolemy to claim his model obeyed Aristotle’s rules of uniform circular motion by stating that the path of heavenly bodies was at a constant speed in a perfect circle around a point that traveled at a constant speed in a perfectly circular path around the Earth.
Muslim astronomers argued among themselves which Greek model was best. Ptolemy’s model best agreed with observations, but was furthest from the doctrine of a perfect universe in which paths of heavenly bodies were at a constant speed in perfectly circular paths.
Image by Fastfission, via Wikimedia Commons.
image credit

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