The story continues from Destination Moon. Professor Calculus is taking Tintin, Tintin's dog Snowy, Captain Haddock and Calculus' assistant Frank Wolff to the Moon in his rocket. However, the detectives Thomson and Thompson come up from the hold, having mistaken the time of the launch (1:34 a.m. on Tuesday, 3 June 1952). Calculus is concerned at the effect this will have on their air supplies. Haddock is furious, and severely lambasts the detectives for being too stupid to understand the difference between 1:34 a.m. and 1:34 p.m.

The journey to the Moon is not uneventful. Haddock has smuggled some whisky aboard in hollowed-out books, becomes drunk, and engages in an unscheduled spacewalk that results in him briefly becoming a satellite of the asteroid Adonis. Tintin also dons a space suit to fetch him, and, in a very rare display of temper, chews out the Captain, declaring that the latter's recklessness has "nearly cost us our lives." When the rocket engine must temporarily be shut down in order to execute the turnaround maneuver that will enable it to land on the moon right side up, the momentary lack of artificial gravity also poses problems for Haddock, who has neglected to put on his magnetic-soled boots in time...