He discovered Jupiter's four largest moons: Io, Europa, Ganymede and Callisto. He also found the Milky Way to be a multitude of stars instead of merely a cloud as Earth scientists had previously believed. He confirmed Copernican theories that Earth was not the center of the universe, although religious authorities made him renounce his support for those claims on the premise of a death sentence for disobedience.
He was one of six Human astronomers honored with a monument located in front of the Griffith Observatory, the others being Hipparchus, Nicolaus Copernicus, Johannes Kepler, Isaac Newton and William Herschel. (VOY: "Future's End")
In 2369, Keiko O'Brien taught her class about Galileo rather than the Prophets after Winn Adami became opposed to her teachings. When Jake Sisko commented to Benjamin Sisko that he thought it was stupid for Galileo's books to have be burned during the Spanish Inquisition for teaching that the Earth moved around the sun, his father told him it was easy to look back with hindsight to judge what was right and wrong. (DS9: "In the Hands of the Prophets")