An obsolete Russian communications satellite is about to fall out of orbit, and NASA agrees to deal with it. The onboard systems are so archaic that nobody at NASA understands them, so they ask retired United States Air Force pilot and electrical engineer Dr. Frank Corvin, who designed the original guidance systems from which the satellite has been copied, to help them, despite the longstanding animosity between the engineer and project director Bob Gerson due to a past grievance. A flashback reveals that 40 years ago, Corvin's prospects as an astronaut were dashed with the formation of NASA, a civilian agency, for Corvin and his three-man team were replaced by a chimp.
Corvin insists that there is not enough time to train anybody; he proposes going himself, and he will not go without his old team, team Daedalus: structural engineer Jerry O'Neill who is a skirt-chasing roller coaster designer with Coke-bottle glasses, maniacal pilot-turned crop duster William 'Hawk' Hawkins, and former navigator 'Tank' Sullivan who is now a Baptist minister. With no choice, the director agrees. Gerson intends to string Corvin along until younger astronauts are up to speed on the system. But the press soon learns of the situation, and the four men become celebrities - even appearing on the Tonight Show with Jay Leno. They become so popular that Gerson is forced to actually send them on the mission by the Vice President of the United States. During medical tests, Hawk is found to have terminal pancreatic cancer, and has only about eight months left to live. Due to the urgent nature of the mission and since he won't be impaired, he is considered as flightworthy and put on the mission.