Tintin's friend Professor Calculus has been secretly commissioned by the Syldavian government to build a rocket ship that will fly from the Earth to the Moon. Tintin and Captain Haddock agree to join the expedition, even though Captain Haddock shows considerable reluctance. Upon arriving in Syldavia, they are taken to the Sprodj Atomic Research Centre, called simply "the Centre", headed by the scientist Mr. Baxter. They are escorted by the "ZEPO" (Zekrett Politzs), a special security force charged with protecting the Centre from outside threats. While working for Syldavia, Calculus is assisted by engineer Frank Wolff, who works in the Centre, and accompanies Tintin and Haddock around the facility. Prof. Calculus reveals that the Syldavian government invited nuclear physicists from other countries to work at the Centre, which was created four years earlier when large uranium deposits were discovered in the area. The Centre is entirely dedicated to peaceful uses of nuclear energy. Calculus heads the Centre's astronautics department, since this is his primary area of expertise.

While in the Centre, they soon come to realize the purpose of the ZEPO: They are to block a foreign power that is also interested in the project. On one particular night, spies are parachuted into areas surrounding the facility and the Centre is placed on high alert. The security staff later arrest and interrogate two men dressed in Greek dance costumes, but discover they are the detectives Thomson and Thompson, whom Tintin instantly recognizes and clears. The pair remain in the Centre.

An unmanned subscale prototype of the rocket . the "X-FLR6", resembling a V-2 rocket . is launched on a circumlunar mission to photograph the far side of the Moon, as well as test Professor Calculus's revolutionary nuclear rocket engine. The rocket successfully orbits the moon, but is then intercepted by the foreign power, giving the research team no other option than to destroy their rocket...