As far as I understand, the Ptolemaic model explains day and night by postulating that the whole celestial system revolves around the Earth once every day. Since we observe the sun to move from East to West over a day, the whole system would have to move in an East to West direction once a day. But over the year, the planets move (usually) towards the East and the constellations towards the West. So in this model, the planets on their different move opposite to the daily motion of the whole system? Whereas the sphere of stars moves in the same direction as the daily motion of the whole system? I ask since I just found this odd for some reason.
You are in a train that is moving down a railway line at high speed (100km/h).
Next to the railway line is a trail. And on the trail are some people and some bikes. Some people are walking in the same direction as the train, some people are walking in the opposite direction. There are also trees (which are stationary.)
What do you see?
Everything appears to be moving backwards at about 100km/h !
But if you look more carefully, you will notice that some walkers are moving backwards at 95 km/h and some are moving backwards at 105 km/h, but the trees are all moving at exactly 100km/h
It is just the same in the sky. Everything moves at about one revolution per day East to West. But some things move a little bit faster and some move a little bit slower (and the planets sometimes move faster and sometimes slower)
The Sun takes 24 hours (1440 minutes) to go around once, the stars take 23 hours 56 minutes to go around once (or more precisely 3.94 minutes per day less than 24 hours) So the sun and the stars move relative to each other. How long does it for the sun and stars to sync up again? 1440÷3.94 = 365 days. That is the year.
As I remember, the Ptolemaic model involved a series of concentric transparent spherical shells around the Earth.
The stars were attached to the outermost shell or sphere which revolved about once a day, but not exactly once a day since there was also a yearly cycle to which stars were visible at night.
The innermost sphere was the sphere of the Moon, which sometimes passed in front of the Sun and thus was closer, and the next innermost sphere was the sphere of the Sun.
The Sphere of hte Moon revolved about once a day, but not exactly, since there was a difference which added up to a full circle every 28.5 days. So, if i remember correctly, the sphere of the Moon would revolve about 360 degrees minus 12.63 degrees every day, or about 347.37 degrees per day.
The sphere of the Sun made a full and complete revolution of 360 degrees in exactly one day.
And the spheres of Mercury, Venus, Mars, Jupiter, and Saturn also revolved about 360 degrees per day, but not exactly, the differences accounting for their various synodic periods.
Since the geocentric model was totally different from the actual heliocentric model, and the giant transparent spherical shells didn't really exist, there were a lot of problems fitting the directions to various planets at various times predicted by the system with the actual observations of the directions to those planets at those times. Even though the ancient Greeks had to rely on naked eye observations, they were able to notice deviations of the planets from their predicted paths across the background of the stars. Which meant that the theories had to be improved to make the predictions better.
So Ptolemy had to do a lot of thinking and explaining to account for those deviations and to make correct future predictions of the movements.
So Ptolemy took the basic geocentric model I described above and elaborated it with various modifications which are called eccentrics, epicycles, deferents, and equants. And if that sounds complicated, that is correct.
There is a famous story that King Alfonso X The Wise (1221-1284), King of Castile, etc., and rival King of the Romans, once said of the Ptolemaic model of the universe that if the creator had asked Alfonso's advice during the creation the universe would be simpler.
And the Ptolemaic model was able to predict the apparent motions and apparent positions of the planets well enough to satisfy almost all European and Muslim astronomers for over a thousand years.