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 th Sun, which is rule different from that 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.
Notice that the use of Occam's Razor would make the choice between the geocentric model and the Copernican model quite easy.
Modern astronomy begins with the telescope. Before that, no one had any way of knowing what planets looked like. Venus could have been a circular disk, a square, or a brilliantly shining hamburger - no one could tell.
What Galileo did was get hold of a Dutch invention, the telescope, and look up with it. He saw things never before seen. This is how discoveries get made and old models get overthrown.
As far as we know, Galileo didn't invent the telescope himself. He somehow (means unknown) got his hands on a Dutch invention and later improved it. It's what Galileo did with the telescope that was significant - aim it upward into the sky and observe the objects found there.
Galileo observed a number of important things. He noticed four small points of light apparently going around Jupiter (he was right). Those four large moons of Jupiter are called the Galilean satellites. You can see these satellites with binoculars (Galileo didn't have them). These little objects were very clearly going around Jupiter and not getting left behind as Jupiter moved. This showed that there was at least one other center of revolution in the Solar System.
He also observed that Venus obviously displayed phases just like the Moon. This was ample evidence that the Ptolemaic (geocentric) model was wrong. Here's how that works. Look at figure 1.8. We are looking at a real test of the Ptolemaic model. Using the Ptolemaic model (part b of the figure), predict what Venus should look like if one had a telescope to see it with. Venus should progress from a thin crescent to a fatter crescent, then back to a thin crescent again. Remember that the Ptolemaic model has Venus orbiting a "nothing" that always stays directly between Earth and the Sun. "Here's an animation of Venus going through its phases. Here's a really good animation from Astronomy Picture of the Day.
Galileo looked through his telescope and saw a nearly full Venus. The Ptolemaic model CANNOT account for this; it is not possible in that model. This is one real proof that the Ptolemaic model is wrong - it cannot account for the full phase of Venus. Look at part a of figure 1.8.
