This page contains information regarding Star Trek: Picard, and thus may contain spoilers.
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 to be tried and convicted and his books burned by the 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")