Jag tror att boken är "The Star Seekers" av Milton Lesser från 1953. Det är en del av Winston Science Fiction Set Series of books.
Ett kort utdrag är nedan:
All Mikal knew when he embarked on the "Journey of the Four Circles" was that every eighteen-year-old from Astrosphere, the outermost circle, must visit each of the other circles if he hoped to become an Enginer. But before he completed his trip, he unearthed startling truths that threw the four circles into a state of chaos. Gradually Mikal discovered that unless the people of the four circles took immediate action the ship was doomed to crash. Mikal's desperate efforts to unite the four circles in order to save their world is a story of rising tension and clashing interests.