The crystalline sphere universe of Aristotle makes a simple prediction all the wheels move in the same direction.
This means that any planet should always move in the same direction, with respect to the background stars (which are the coordinate system here).
Yet, the retrograde motion of Mars was well known at the time.
Mars generally moves west to east (right to left) on the background of stars. But every 780 days it goes through period of 83 days during which it moves east to west against the stars, the retrograde motion. The retrograde period is centered around the time when Mars is in opposition - Mars is directly opposite the Sun. Thus, this phenomena could be established as repeatable and realiable after only a decade's worth of observations.
Plato gave his students a major problem to work on. Their task was to find a geometric explanation for the apparent motion of the planets, especially the strange retrograde motion. One key observation: as a planet undergoes retrograde motion (drifts westward with respect to the stars), it becomes brighter. Plato and his students were, of course, also guided by the Pythagorean Paradigm. This meant that regardless of the scheme they came up with, the Earth should be at the unmoving center of the planet motions. One student named Aristarchus violated that rule and developed a model with the Sun at the center. His model was not accepted because of the obvious observations against a moving Earth.
In order to preserve the geocentric cosmology of the time and to account for retrograde motion, Ptolemy had to make a model of epicycles. This makes the orbits of planets very complicated and violates the scientific search for simplicity.
A visualation of epicycles:
Class Discussion: This model makes a prediction. What is that prediction?
Full Animated Epicycle
The Ptolemaic Moment will stand for about 1500 years with this model for planetary orbits remains unchallenged, partly because Ptolemy's model did improve the precision to which planetary positions could be predicted. Remember, however, the precision at measuring planetary positions was quite poor and therefore there was a large random error involved when comparing predictions with observations.
The Ptolomaic model represents an excellent example of "cultural" bias in science. Most citizens of the cultural wanted to accept the idea of the Earth being the center of the Universe (i.e. the earth was special) and therefore observations were molded in such a way so as to preserve that cultural norm. (Things may not be very different today).
Recall, there was a competing model of the time, that of Aristarchus of Samos (280 BC):
Aristarchus' advanced ideas on the movement of the Earth are known from Archimedes and Plutarch; his only extant work is a short treatise, "On the Sizes and Distances of the Sun and Moon." The values he obtained, by using geometry, are inaccurate, because of faulty observations. Aristarchus found a more precise value for the length of the solar year.)
Aristarchus was extremely clever and also figured out a way to determine the ratio of distances between the earth and the moon and the earth and the sun. While wrong, at least he reasoned that the sun was much farther from the earth than the moon.
Just Try and Follow this!
Summary of Greek Science