Doomwatch - Season 1 Episode 6 Re-Entry Forbidden

The first nuclear-powered rocket, Sunfire One, is sent into space with the first British astronaut, Dick Larch, on board. After the rocket enters Earth orbit, Larch enters an incorrect course alteration, and fails to see the error indicator, which results in Sunfire One splashing down in the sea. Quist is asked by Doctor Goldsworthy to determine whether Larch is suitable for any further missions, as another such mistake could result in the spacecraft becoming a nuclear bomb.