This is an old-school book about people going to another planet, just out of reach from being able to contact Earth. The ship's fuel source starts slowly dying leaving them to drift, hopefully eventually reaching their destination. The people on the ship are unaware of this.
Only a few people, the captain or someone, have been using the DNA of the people on board, so that when they die they will be reborn via another family, so the population doesn't die and the ship keeps functioning. It goes in more depth about the DNA side of it.
Anyway someone who is to take the Captain's job, who hasn't been told everything, starts to think things are weird and trying to figure out what's going on.
I believe there was a second book but not very well known.