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 [[{{Ruritania}} 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 [[TechnologyMarchesOn 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 [[HilarityEnsues 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 SelfDestructMechanism 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 [[Recap/TintinKingOttokarsSceptre Colonel Jorgen]]...

The story is continued in ''[[Recap/TintinExplorersOnTheMoon Explorers On The Moon]]''.
* BerserkButton: Do not tell Professor Calculus he is acting the goat.
* [[BewareTheNiceOnes/ComicBooks 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.
* ContinuityNod: The Thom(p)sons are still suffering from eating Formula Fourteen pills in ''[[Recap/TintinLandOfBlackGold Land of Black Gold]]'', meaning they occasionally burp coloured bubbles and have their hair grow crazily.
* DrivesLikeCrazy: Calculus hijacks a military vehicle to go demonstrate the results of his labor to Haddock. His 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.
* EasyAmnesia: Happens to Calculus at one point, and almost scuppers the project, until Haddock accidentally triggers his memory by pushing his BerserkButton.
* EekAMouse: Thomson and Thompson are startled by lab mice.
* ExpoSpeak: The "acting the goat" scene is actually an InfoDump that explains the features of the moon rocket, but Calculus' rage makes it entertaining.
* HazmatSuit: 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.
* InertialDampening: Averted. The crew of the Moon-Rocket faints from the pressures caused by take-off and landing.
* InsultedAwake: Captain Haddock cures Professor Calculus' accidental amnesia by complaining about "acting the goat", a remark that had earlier served as a BerserkButton for Calculus.
* KidnappedByAnAlly: 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.
* MinionMaracas: An enraged Professor Calculus lifts a security guard easily twice his size and suspends him off a coat rack.
* MohsScaleOfScienceFictionHardness: Hard science fiction. The print medium enables Hergé to better display the colossal engineering needed to develop interplanetary spaceflight. Though [[ScienceMarchesOn 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.
* MundaneDogmatic: Hergé attempted to ensure that the two space-travel books were scientifically accurate. They reflect space flight ideas and scientific theories of TheFifties. 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.
* MyGodYouAreSerious: 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, [[TemptingFate "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.
* NoPlansNoPrototypeNoBackup: 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 [[EasyAmnesia amnesia]], the entire project was put into jeopardy. He was the only one with memory of the designs.
* OOCIsSeriousBusiness: This is the first time we see Calculus getting angry and it ain't pretty.
* RetroRocket: The Moon-rocket, as seen [[ here]]. This is an interesting case as it's combined with a [[ShownTheirWork frighteningly prescient]] depiction of the UsefulNotes/ColdWar space program. Blueprints and launchpad shown [[ here]]. The rocket's external appearance is based on the German V2.
* {{Ruritania}}: Syldavia. Previously featured in ''[[Recap/TintinKingOttokarsSceptre 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.
* SchematizedProp: The album uses a full page to show the blueprint for the Moon-Rocket.
* SpoilerTitle: The album ends on a CliffHanger 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 ''[[{{Recap/TintinExplorersOnTheMoon}} Explorers On The Moon]]''!" The title of the next album points out that they do make it to the Moon.
* SwissCheeseSecurity: Averted; Tintin and Haddock have to go through countless security checkpoints to get to the compound, which is even guarded by anti-aircraft guns. Nevertheless the project has somehow been infiltrated...
* {{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.