The geocentric, or Ptolemaic, model of the Solar System has a nice concept - the Earth is in the center. This, unfortunately, runs into trouble quickly as it tries to deal with the actual motions of the planets in the sky. The retrograde motion of planets required the geocentric model to become loaded with epicycles, off-center deferents, and orbits going around nothing. Why would anything orbit around nothing??
The much simpler heliocentric model of Copernicus eliminates the tangle of epicycles while explaining the retrograde motion in a natural way. Look at Figure 1.11. Earth and Mars are shown in a series of positions separated by approximately equal time intervals. The numbers associate Mars and Earth at a given time. The line of sight from Earth to Mars (what we see) is shown.
Earth takes about 365.25 days to orbit the Sun while Mars takes 687 (Earth) days to do the same. This means that Earth is moving faster than Mars and will pass it occasionally (about every 26 months). Retrograde motion occurs while Earth passes between Mars and the Sun moving faster than Mars. Mars actually doesn't change its motion at all - retrograde motion is an illusion caused by Earth's motion.
Also note a description of Occam's Razor. It means that, if you must choose between several explanations for something, choose the simplest one. It is a heuristic and is not guaranteed. Heuristics can fail. Lots of things about the Universe are not simple. But - old Occam will improve your chances of making the right choice.
Notice that the use of Occam's Razor would make the choice between the geocentric model and the Copernican model quite easy.