= Epicycle
An <epicycle> is a <circle> whose centre moves along another path, traditionally a larger <circle> called the deferent. Combining these motions can reproduce loops and changes of apparent <speed> in a <planet>'s position on the <celestial sphere>. In <Ptolemy>'s <geocentric model>, such constructions supplied quantitative planetary predictions.<Almagest by Ptolemy>[Planetary books IX–XIII: geometric models of planetary motion]{ref}
A simple planar example is
$$
\mathbf r(t)=R(\cos\Omega t,\sin\Omega t)+r(\cos\omega t,\sin\omega t).
$$
The second term is the <epicycle> relative to its moving centre. Suitable radii and angular rates can produce locally backward <motion>, illustrating <apparent retrograde motion>. The construction is a geometric representation; fitting an observed track does not by itself establish what <force> governs the actual <orbit>.
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