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 behind
the 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.
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The discovery did not support Copernicus's theory directly but it raised doubts about the ancient theory of Ptolemy that said that all objects in the sky are in orbit round the Earth. Galileo was an aggressive supporter of Copernicus's theory but eventually it was Kepler's theory that became accepted and is still used today. Both Copernicus and Kepler placed the Sun at the centre but Kepler's elliptical orbits are supported by the later theory of dynamics.
Venus goes through phases similar to those of Earth's moon.#1Direction
Galileo's observations with his telescope supported the concept of heliocentricism. He noted that the satellites of Jupiter and Venus, based on their range of phases, did not match geocentricism supported by Ptolemy. He noted that based on these findings, that the Heliocentric theory was correct.
He thought of and supported the heliocentric model, which states the "heavens" revolve around the Sun.
Kepler completely replaced Copernicus's theory of the orbits of the planets, which was based on circles an epicycles, with a new theory using elliptical orbits. However Kepler retained Copernicus's idea of placing the Sun at the centre.