[KineticLensman]

> Also, IIRC, the predictions made by heliocentric model were less accurate than geocentric ones

> work of Kepler

Yes. One problem of the early Copernican heliocentric model was that it stated that the orbits of planets around the sun were perfect circles. It wasn't until Kepler showed that a) the orbits were actually elliptical and b) the planets speeded up when they approached the sun and slowed down as they moved away that the actual movements of the planets could be more accurately predicted. Until this time, the older earth-centric models with all of the epicycles were 'better', even though totally unrelated to reality.

[avereveard]

one important point is that ground observations include mars moving backward fairly often. it took a while to formulate a movement form that satisfied that constraint better than epicycles

[KineticLensman]

Yes. This is one example of the fact that the Earth 'laps' the outer planets because it has a faster orbit. So the outer planets sometimes appear to go backward with respect to a fixed point such as a star as the Earth undertakes them. They also can move up and down with respect to that fixed point because their orbits are tilted somewhat compared with the Earth's orbital plane around the sun. The overall effect is that the outer planets sometimes trace out a little spiral, and the further they are from the sun, the more these spirals dominate their overall motion (because we are lapping them more often).

Obviously it's different for Mercury and Venus, whose orbits are inside ours. They instead switch between being visible in the morning or the evening.

All very complicated for those ancient astronomers!