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.^[ref]

A simple planar example isThe 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.