A model is never technically disproven or proven. The ptolemaic model is no longer accepted because it does not adequately explain observations. The heliocentric model was accepted gradually because it was a better explanation for observed phenomena. However, people continued to believe the ptolemaic model long after it was irrational to do so.
The phases of Venus are well supported by the heliocentric system, but they are also supported very well by the previous geocentric system. All you need for Venus to have phases is that Venus should pass between Earth and Sun. That happens in both the heliocentric system and the geocentric system.
Mercury and Venus do, becoming crescents as they pass near us, between us and the Sun. The other planets do not show significant phases. The phases of Venus were important in the development of the theory of the Solar System, because after they were discovered by Galileo, people realised that the gibbous phase could not be explained by the ancient Ptolemaic system.
It happened with the accumulation of discoveries that showed that the heliocentric model was superior, and the final discovery by Newton of the law of gravity and the laws of motion, which he used to show that the planets must move in elliptical orbits under the Sun's gravity, confirmed what Kepler had discovered from Tycho's observations, that the planets move in elliptical orbits. The most convincing single discovery was the phases of Venus. In the Ptolemaic geocentric system Venus stays between us and the Sun, and it can only have a crescent phase. But Galileo's discovery of Venus's gibbous phase was a clear sign of a fault with the Ptolemaic system. However Tycho's geocentric system allowed Venus to show the full range of phases, so Galileo's discovery was not conclusive.
Galileo did not directly provide evidence for the heliocentric principle but he did discover important evidence that raised doubts about the Ptolemaic system with the Earth at the centre. First, he discovered the moons of Jupiter, and these were the first objects discovered that definitely orbited round something that was not the Earth. That was one thing. Secondly, he discovered that Venus has a gibbous phase when seen from Earth in certain positions in its orbit. This is not explained by the Ptolemaic system because Venus cannot go round behind the Sun in the Ptolemaic system. Again this did not prove the heliocentric principle because Tycho Brahe came up with an intermediate system that had Mercury and Venus orbiting round the Sun, and then the Sun and the other planets orbit round the Earth. So this was still a geocentric system that explained all Venus's phases. Therefore Galileo did not have enough evidence to prove the heliocentric principle, and after his trial he recanted. But 60-70 years later enough new evidence had been gathered to convince most people that the Sun is at the centre, as we believe now.
Galileo was able to observe Venus going through a full set of phases, something prohibited by the Ptolemaic system (which would never allow Venus to be fully lit from the perspective of the Earth or more than semi-circular). This observation essentially ruled out the Ptolemaic system, and was compatible only with the Copernican system and the Tychonic system and other geoheliocentric models such as the Capellan and Riccioli's extended Capellan model.
The Ptolemaic system predicts that Venus goes through phases similar to the Moon, from crescent to full. This model was proposed by the ancient Greek astronomer Ptolemy and was used to explain the varying appearances of Venus in the sky as seen from Earth.
We sometimes see gibbous (nearly but not quite full) Venus. In the Ptolemaic system, we should never see more than a crescent in Venus. Because we do in fact see more, the Ptolemaic model must be wrong. The full range of phases that we see for Venus is consistent only with the idea that Venus orbits the Sun. Galileo was the first to observe the phases of Venus - and hence to find this evidence in support of the Sun-centered system - because he was the first to observe Venus through a telescope. Without a telescope, we cannot tell that Venus goes through phases.
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.
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.
A model is never technically disproven or proven. The ptolemaic model is no longer accepted because it does not adequately explain observations. The heliocentric model was accepted gradually because it was a better explanation for observed phenomena. However, people continued to believe the ptolemaic model long after it was irrational to do so.
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.
Galileo saw the four largest moons of Jupiter in orbit around the planet, proving that the Ptolemaic system was not simpler - the solar system was not geocentric (the planets and the sun did not orbit around the earth). As far as the observations of Venus go, Galileo saw that Venus displayed phases very much like our moon. Now, according to the Ptolemaic system, Venus could only display a crescent phase because its epicycle put it always in between Earth and the sun. The Copernican system put everything rotating around the sun, and in this way it explained the phases of Venus. Think of it this way, if Venus is always in between the sun and the earth, how can we ever see it completely lit up, like a full moon? The sun is always on the other side of it, so Venus must at some point go on the other side of the sun.
The phases of Venus are well supported by the heliocentric system, but they are also supported very well by the previous geocentric system. All you need for Venus to have phases is that Venus should pass between Earth and Sun. That happens in both the heliocentric system and the geocentric system.
The phases of Venus are well supported by the heliocentric system, but they are also supported very well by the previous geocentric system. All you need for Venus to have phases is that Venus should pass between Earth and Sun. That happens in both the heliocentric system and the geocentric system.
Mercury and Venus do, becoming crescents as they pass near us, between us and the Sun. The other planets do not show significant phases. The phases of Venus were important in the development of the theory of the Solar System, because after they were discovered by Galileo, people realised that the gibbous phase could not be explained by the ancient Ptolemaic system.
Galileo discovered two important things: the moons of Jupiter and the phases of venus. Both discoveries raised doubts about the old Ptolemaic system which was geocentric, and the phases of Venus showed that it was definitely wrong. But neither discovery proved that Copernicus's theory - supported by Galileo - was right. This is because Tycho's geocentric system explained the phases of Venus satisfactorily.