There are several important reasons why Galileo found Copernicus' heliocentrism more compelling than Ptolemy's geocentrism. First off, you have to understand t

There are several important reasons why Galileo found Copernicus' heliocentrism more compelling than Ptolemy's geocentrism. First off, you have to understand the intellectual background. Aristotelian physics dominated Europe at the time. Aristotle held the Earth to be separate from the heavens, with the heavens being the realm of perfect forms. All imperfect objects seek to move to the center of the Universe, which is the center of the Earth, while perfect objects move in circles in the heavens. This was the intellectual foundation of geocentrism. Galileo was the first human in history to point a telescope at the sky, and what he saw fundamentally undermined Aristotelian physics. The Moon is not a perfect form: it has mountains, just like the Earth. Not everything revolves around the Earth: Jupiter has its own moons that orbit it. The Sun is also not perfect: it has spots. Galileo also did mechanical experiments that demonstrated the principle of inertia (Newton's first law), which further undermined Aristotelian physics. With Aristotelian physics out the window, the strong intellectual bias towards geocentrism was also gone. Until Galileo's telescopic observations, he himself had been a geocentrist, like most people. If you then look at geocentrism and heliocentrism with fresh eyes, there are a lot of appealing aspects of heliocentrism. * Geocentrism needs epicycles to explain even the most basic elements of planetary motion (retrograde motion). Heliocentrism already explains retrograde motion without any epicycles. Not only that, but heliocentrism correctly predicts exactly where (in relation to the Sun) retrograde motion occurs. In the geocentric model, retrograde motion could occur anywhere, but in the heliocentric model, it has to occur when planets are opposite the Sun, and lo and behold, that's exactly where it occurs. * The Jovian system and the Earth-Moon system also suggest that small objects orbit larger objects, according to some as-of-yet (at Galileo's time) undiscovered principle. Why would the Sun (which was then known to be much larger than the Earth) orbit the Earth? * The phases of Venus decisively rule out Ptolemy's model. In order to save geocentrism, you have to invent some weird geo-heliocentric hybrid model (Tycho's model). To many people, a pure heliocentric model was much more appealing, and the hybrid model appeared to be an awkward attempt to save some of geocentrism.