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. If you observe an outer planet (Mars, Jupiter or Saturn) over a period of time and plot its position on a star map, you will see a very interesting motion. The backward (east to west) part of the motion is called retrograde (backwards) motion. This retrograde motion of planets required the geocentric model to become loaded with epicycles, off-center equants, and orbits going around nothing. Here's another illustration. One might question why anything would orbit around nothing. The whole model represents the planets visible to the ancient observers.One might object to the Ptolemaic model based on its treatment of the inner planets They remain on a line drawn between the Earth and the Sun, which is different from the mechanism of the outer planets.
The much simpler heliocentric model of Copernicus eliminates the tangle of epicycles while explaining the retrograde motion in a natural way. The simplicity is obvious; the epicycles and off-centering are gone. Look at Figure 1.5. 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. Here's a NASA animation that shows how it works.
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.