Galileo, an eminent professor and scientist in the 17th century Venetian Republic, is short of money. A prospective student tells him about a novel invention, the telescope ("a queer tube thing"), that is being sold in Amsterdam. Galileo replicates it, and offers it to the Republic as his own creation. He gains an increase in his salary, but within a short time his ruse is discovered.
Galileo then uses the telescope for careful observations of the Moon and the planets, and he discovers the moons orbiting Jupiter. His observations strongly support Nicolaus Copernicus' heliocentric model of our Solar System, which is counter both to popular belief and to the doctrine of the powerful Roman Catholic Church. He furthermore publishes in vernacular Italian, rather than traditional scientific Latin, thus making his work and conclusions more accessible to the common people.
His daughter's engagement to a well-off young man (with whom she is genuinely in love) is broken because of Galileo's reluctance to distance himself from his unorthodox teachings. Galileo is brought to the Vatican in Rome for interrogation by the Inquisition. 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, now living under house arrest with a priest monitoring his activities, 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.