In geocentric models, did the Earth rotate around its axis?
I assume that if the Earth rotated around its axis, then the Sun would not have to orbit around the Earth at a very fast rate, whereas if the Earth didn't rotate, then the Sun would have to orbit the Earth every day.
In the historic geocentric models, and in particular in the Ptolemaic model, the earth is immobile in the centre of the cosmos, and the sphere of the fixed stars rotates around it once a day, carrying the sun, moon and planets with it. There were astronomers who realised that this apparent motion could also be explained, from a purely mathematical point of view, by assuming that the earth rotates on its axis, but they rejected this option. By the way, neither Ptolemy nor any other serious astronomer believed that the earth was flat.
The idea of a rotating Earth was the biggest hurdle for the non-geocentric ideas to overcome. If the Earth were rotating, wouldn't we notice it? Riding a horse is a motion which one cannot help but notice. And a rotating Earth would be much more violent, at 465 meters per second, as was estimated already in ancient times. Ten times a hurricane. That is obviously not the case. I can stand up on the ground without falling over, but I can't stand up on a galloping horse's back, people argued quite reasonably.
It requires careful cleverness to apply our gardening-evolved intuition to the reality beyond the fence. I personally find the Oberth effect to be unintuitive, that in empty space a push gives more acceleration to a fast object than to a slow one. With friction from roads, rails and air the opposite is true in our everyday life.
The resolution (certainly with ancient predecessors if documents are preserved) is called Gallileo's ship.