After returning to Marlinspike following a trip, Tintin and Haddock are surprised to find that Calculus had mysteriously left some time earlier. They immediately receive a telegram from the Professor explaining that he's in Syldavia and asking them to join him there. They do so and are led to a heavily guarded scientific research compound, where they are greeted by Calculus' assistant engineer Frank Wolff and the Professor himself. The latter claims they are in Syldavia's Atomic Research Center, which recruited Calculus for their Astronautical section. Calculus is currently completing plans for a nuclear power rocket that will be able to land on the Moon...and he called Tintin and Haddock so that they will be part of the landing party. Despite both having some misgivings about the plan (especially Haddock) they accept.
Of course, preparing for this unprecedented and utterly crazy venture is not simple or easy. To make matters worse, the preparation is plagued with incidents, ranging from the humorous (the Thompsons, who inexplicably were assigned as security engage in their traditional bungling) to significant (Calculus losing his memory, which puts the whole project in jeopardy though he ends up being cured by Haddock via ensued hilarity) to the serious (Miller, a mysterious spymaster working under an unnamed foreign power is interested in the project and almost succeeds in stealing the prototype rocket, only to be prevented by a Self-Destruct Mechanism installed at Tintin's suggestion). Despite all this, the rocket is completed and is successfully launched, with Tintin, Haddock, Calculus, Wolff and Snowy en route to the Moon...yet Miller seems to have an additional ace up his sleeve, involving Tintin's old enemy Colonel Jorgen...
The story is continued in Explorers on the Moon.
- Beware The Nice Ones: Calculus is generally very pleasant and friendly. But when Haddock insults his work, he goes berserk. Providing some of the most memorable moments of the album.
- Drives Like Crazy: Calculus hijacks a military vehicle to go demonstrate the results of his labor to Haddock. He driving skills fit the trope. Though he was enraged with Haddock at this point and not in his right state of mind. He even mentions that he doesn't have a driving license.
- Eek! A Mouse!: Thomson and Thompson are startled by lab mice.
- Hazmat Suit: Tintin, Captain Haddock and Wolff put on protective suits so they can view the atomic pile. Professor Calculus also ordered a dog-sized suit made for Snowy to wear so he can go with them, but Snowy keeps tripping on the sleeves because the suit is too big for him. They also forget to take the suit off Snowy afterwards.
- Inertial Dampening: Averted. The crew of the Moon-Rocket faints from the pressures caused by take-off and landing.
- Insulted Awake: Captain Haddock cures Professor Calculus' accidental amnesia by complaining about "acting the goat", a remark that had earlier served as a Berserk Button for Calculus.
- Kidnapped by an Ally: Toyed with. Tintin and Haddock are following an invitation that ends with them ending up in an armored car, getting taken through checkpoints to what looks like a military base in what they expect is a sinister kidnapping. Actually, Professor Calculus just wants them to join him working on the moon project. Calculus is their friend, but the supervisors who send the invitation aren't, so it might not count.
- Life Imitates Art: Both "Destination Moon" and "Explorers On The Moon" (1950-1953, in publication) depict a moon landing expedition. This was about fifteen years before the Americans actually landed on the moon. Tintin's moon exploration was also scientifically very accurate without any typical science fiction clichés of aliens and such.
- Mundane Dogmatic: Hergé attempted to ensure that the two space-travel books were scientifically accurate. They reflect space flight ideas and scientific theories of The Fifties. But the rocket engine designed by Calculus works like a slowly exploding nuclear fission bomb. The engine is able to withstand the extreme heat and radiation, since it is made of "calculon", a silicon-based, extremely heat-resistant material also invented by the professor.
- Minion Maracas: An enraged Professor Calculus lifts a security guard easily twice his size and suspends him off a coat rack.
- Mohs Scale of Science Fiction Hardness: Hard science fiction. The print medium enables Hergé to better display the colossal engineering needed to develop interplanetary spaceflight. Though science has marched on considerably since it was written, at the time it was practically a student's primer on both nuclear energy and spaceflight.
- My God, You Are Serious: When Calculus says he is finishing plans for a rocket that will land on the moon, Captain Haddock has a big hearty laugh about it, and facetiously suggests, "You are taking passengers, I hope?" Calculus replies, "Why else do you think I asked you to join me?", utterly stunning Tintin and the Captain.
- No Plans, No Prototype, No Backup: This turns out to be the case for the moon rocket and the entire Sylvadian moon landing mission. Which is why when Professor Calculus got amnesia, the entire project was put into jeopardy. He was the only one with memory of the designs.
- Retro Rocket: Tintin's rocket from "Destination Moon" and "Explorers on the Moon" as seen here. This is an interesting case as it's combined with a frighteningly prescient depiction of the Cold War space program. Blueprints and launchpad shown here.
- Ruritania: Syldavia. Previously featured in King Ottokar's Sceptre (1939), Syldavia is an atypically detailed version of this trope. It has its own flag, royal dynasty, historical events and even a language created by Hergé. The made-up language, despite being written in Cyrillic script, was remarkably not Slavic but a dialect of Flemish/Dutch with some curious phonetics. In this album Syldavia becomes the setting for a fictionalized space program.
- Schematized Prop: The album uses a full page to show the blueprint for the Moon-Rocket.
- Spoiler Title: The album ends on a Cliff Hanger as the astronauts have passed out and Earth has lost communication with them. As mission control gets increasingly nervous, the Narrator asks the reader rhetorically (paraphrased): "Will Tintin and his friends survive this dangerous mission to make it to the moon? Find out in Explorers on the Moon!" The title of the next album points out that they do make it to the Moon.
- Unobtainium: Professor Calculus has invented a new substance - calculon - which can "resist even the highest temperatures", with which to make the nuclear fission motor for the rocket.