The Ptolemaic system belived that the earth was the center of everything and all the planet and sun traveled around it and the copernican system belived that the sun was the center of everything and the planets and traveled around the sun.
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The main difference between the Ptolemaic system and the Copernican system is their approach to explaining the motion of the planets. The Ptolemaic system placed Earth at the center of the universe with planets moving in complex epicycles, while the Copernican system proposed that the Sun was at the center, with planets including Earth orbiting around it.
the Copernican model proposed a heliocentric view of the solar system, which was contrary to the widely accepted geocentric view of the Ptolemaic model. The Copernican model required substantial evidence and time to gain acceptance and for people to shift their fundamental beliefs about the universe. Additionally, there were religious and philosophical implications associated with the shift from the Ptolemaic to the Copernican model, which added complexity to the transition.
The geocentric system of Ptolemy said that all the planets stay in their prescribed spheres. By that was meant that each planet has its own shell (a hollow sphere) that it stays inside. The sphere of Mercury is closest to the Earth, then Venus and then the Sun. Galileo discovered the phases of Venus with his telescope. Now it's quite OK for Venus to have a crescent phase in the Ptolemaic system, because it can travel between the Earth and the Sun. But Galileo also saw that Venus had a gibbous phase at certain times, which the Ptolemaic system fails to account for. Galileo said this was a serious fault with the Ptolemaic system (correct) but he then claimed incorrectly that this must prove that the Copernican system - with the Sun at the centre - is correct. Galileo was wrong about that because Tycho Brahe came up with an alternative model that had Mercury and Venus orbiting the Sun, but then the Sun and the other planets still orbited round the Earth. This was a geocentric system that correctly described all the phases of Venus. But after the work of Kepler and Newton it was eventually agreed generally that the Sun has to be at the centre.
Tycho Brahe believed in his model because it accounted for the absence of observable stellar parallax, which conflicts with the Copernican model. He also thought that his model better explained the retrograde motion of planets without relying on heliocentrism. Finally, Brahe argued that his model maintained a balance between the mathematical accuracy of the Copernican system and the observational data of the Ptolemaic system.
Galileo's discoveries with the telescope sowed doubts about the ancient Ptolemaic model which had the Earth at the centre. First, Jupiter's moons orbited round Jupiter and not the Earth, the first objects that had been discovered that were not orbiting the Earth. Secondly the discovery of the phases of Venus raised doubt about the Ptolemaic model, particularly the gibbous phase when, we now know, Venus is round behind the Sun as seen from Earth. In the Ptolemaic model Venus never goes behindthe Sun (as seen from Earth) and the gibbous phase cannot happen.By implying in the title of his book 'Dialogue of the two world systems' that there were only two models in contention, those of Ptolemy and Copernicus, Galielo insinuated that if the Ptolemaic model was incorrect the Copernican system must be correct. This was logically flawed because at the time there were two other systems in the public domain that both explained Venus's phases. These were the models of Tycho, which was geocentric, and finally Kepler's which was heliocentric.Of these four, Kepler's was eventually accepted by everyone after Newton's theoretical discoveries showed that Kepler's elliptical orbits for the planets agreed with the new theory of dynamics.
In the Ptolemaic system, the motions of Mercury, Venus, Mars, Jupiter, and Saturn were described with epicycles. These epicycles were small circles that the planets were thought to move in while also orbiting the Earth on larger deferent circles.