Galileo is short of money. A prospective student tells Galileo about a novel invention, the telescope ("a queer tube thing"), being sold in Amsterdam. Galileo replicates it, but then sells it to the Venetian Republic as his own creation.
Galileo uses the telescope to substantiate Copernicus' heliocentric model of our solar system, which goes against both popular belief and church doctrine, and which he publishes in vernacular Italian, rather than traditional scientific Latin, so that it is accessible by the common people. His daughter's marriage to a well-off young man (with whom she is genuinely in love) fails because of Galileo's reluctance to distance himself from his unorthodox teachings.
Galileo is brought to the Vatican for interrogation. Upon being threatened with torture, he recants his teachings. His students are shocked by his surrender in the face of pressure from the church authorities.
Galileo, old and broken, living under house arrest, is visited by one of his former pupils, Andrea. Galileo gives him a book (Two New Sciences) containing all his scientific discoveries, asking him to smuggle it out of Italy for dissemination abroad. Andrea now believes Galileo's actions were heroic and that he just recanted to fool the ecclesiastical authorities. However, Galileo insists his actions had nothing to do with heroism but were merely the result of self-interest.