[mosqzzig] Geocentric view of the solar system

Under a coordinate transformation keeping earth at the origin (but rotating once every sidereal day), what do the motion of the planets look like?

To first approximation, assuming circular heliocentric orbits, it probably is epicycles on cycles, with each main cycle (deferent) the planet's heliocentric orbit, and each epicycle exactly the same, namely the earth's heliocentric orbit, and all exactly in phase.

It might seem curious that Mercury and Venus have epicycles larger than their cycles; alternatively, flip them, yielding only Venus, Mercury, and the sun having exactly the same cycle but differing epicycles.

To second approximation, the cycles and epicycles could be elliptical, which I think can yield exactly Keplerian motion.  (Wikipedia, in "Deferent And Epicycle", says an infinite series of circular epicycles on epicycles can also approximate any motion by the Fourier series.)

This explains why the Ptolomaic geocentric model was accepted for so long: there's nothing mathematically wrong with it!  It's just unwieldy (but not impossible) for producing accurate predictions of planetary motion. Physically, of course, it's harder come up with an elegant explanation of why the planets move this way.