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.
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The Geocentric or Ptolemaic Model put the earth at the center of the Universe. The Heliocentric Model postulated by Copernicus and, before him, Aristarchus, places the Sun at the center of the Solar System. Galileo's observations proved the validity of the Heliocentric Model.
Venus goes through phases similar to those of Earth's moon.#1Direction
Galileo Galilee
Other people recorded their observations of the stars and planets with astrolabes. Ptolemy came up with a (very complicated) mathematical system that would predict the location of planets over time. His basic, geocentric idea was modified over the centuries, but only became more complicated as observations became more exact. Copernicus took these observations that others had written down, and proposed a heliocentric system that he (correctly) noted was far simpler in making accurate predictions.
Heliocentric = The Sun is at the center of our solar system. Geocentric = The Earth is at the center of our solar system. Insisting the Sun is at the center, which it is, once very much angered the church.