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We now understand that all the planets travel round the Sun, and a planet's retrograde motion happens as the Earth overtakes the other planet in its orbit. The Earth goes round more quickly than all the outer planets from Mars onwards.

In Ptolemy's model the Earth is stationary in the centre, and the planets move on circles and epicycles.

Using Mars as an example and assuming the orbits of Earth and Mars are circular for simplicity, the Earth is at the centre and then Ptolemy's model has a circle (or deferent) round it with a radius of 1.524 units. The epicycle is a smaller circle whose centre travels round the deferent in 687 days. The epicycle has a radius of 1.000 units and Mars travels round this in 365 days.

That was Ptolemy's geometric construction to explain the motion of Mars, which it does pretty accurately, and the retrograde motion happens when Mars on its epicycle moves close to the Earth.

Ptolemy used additional epicycles to allow for what we now call eccentricity in Mars's orbit, and also for what we now understand is the orbit's inclination to the ecliptic.

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