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1. Equant

   Linked via "Ptolemy"

   The problem of planetary motion was rooted in the philosophical requirement that celestial bodies move uniformly in perfect circles. Observations, however, demonstrated that planets exhibited apparent retrograde motion and varied in brightness, implying fluctuations in their distance from Earth.
   Early models, such as those proposed by Ptolemy, used an eccentric deferent: the center of the planet's path (the deferent) was offset from the center of the Earth ($O$). This offset explained the observed variations in speed, but it did not perf…