Comments : For Ptolemy, the Earth E is the center of the world
and only is acceptable the uniform circular motion.
To explain the movements of planets (= wandering stars), he imagines
the epicycle , circle centered on the deferent, another circle centered on the Earth.
The Planet P revolves at constant speed on the epicycle
whose center describes a uniform circular motion on the deferent.
It is then enough to correctly adjust the various parameters to find
the relative motion of Planet compared to the Earth and
to explain the phenomenon of retrogradation (retrograde motion).

Note: the introduction of equant has further improved the model.