From the Super Mario Wiki
Galileo Galilei was an Italian scientist and astronomer whose innovations and methods progressed the field of observational astronomy, physics, and the scientific method. After securing a teaching job at the University of Pisa, he conducted experiments and gave lectures that went fully against the studies that had been previously done by Aristotle some 2000 years earlier. As Aristotle's theories were widely popular and supported by the Roman Catholic Church, he was largely shunned until he was put under house arrest by the church. Still, during his lifetime he created the proportional compass as well as a Telescope that was strong enough to view the moons of Jupiter. However, before he could properly use it, his Telescope is stolen by Bowser after he travels back in time (according to Mario's Time Machine).
Mario's Time Machine
In Mario's Time Machine, Galileo is in Padua in the year 1610 when his Telescope is stolen by Bowser. Mario later travels back in time to Padua with the Telescope in an attempt to return it to Galileo without knowing that it belongs to him. If Mario tries talking to him regardless, Mario visits him at the top of a building. Mario asks him what's up, and Galileo replies with the sky. He wants to examine the sky in closer detail, but he lacks the means to do so. The Telescope can only be given to him after talking to the inhabitants of Padua, including one of Galileo's students, and questioning them about Galileo's life history and scientific endeavours. After exhausting all dialogue options and absolutely confirming that the Telescope belongs to Galileo, Mario returns to him and gives back his Telescope. Galileo graciously accepts it and immediately begins to look at Jupiter. He excitedly says that there are moons around Jupiter, confirming the theories of Nicolaus Copernicus. Mario is surprised at the discovery. Galileo says that he planned on naming them after the ruling Medici family to gain favor with them, but he is now considering naming them the "Mario Moons".