They don't get to the moon, but get return to earth safely. The guy who had to stay behind didn't have the measles as suspected. However, had he gone with them on the mission it is unlikely they would have survived, as he worked in the simulators to figure out a way to save them.
Factual error: Moments before and during the lift-off of the Saturn V, Ken Mattingly is shown to be watching from a somewhat private grassy field. Wherever he is supposed to be, he is far too close to the launch pad. No unauthorized persons were allowed to be that close, and certainly not in an undisclosed and unsupervised area, not the least of which was for security reasons. The fact that Mattingly is an astronaut would not give him carte blanch to do this, and his training and discipline would prevent his ever attempting doing so in the first place. In reality, Mattingly was in Houston at Mission Control at the time. Otherwise it is a nice shot.
Trivia: The Apollo 13 mission set a record for the greatest distance from Earth ever achieved by mankind. This occurred because unlike the other Apollos, Apollo 13 did not make a burn behind the moon to drop into lunar orbit. The free-return trajectory the mission followed took the spacecraft farther behind the moon than any other mission.
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