Babar's Moon Trip was a pop-up book I had never come across before. It seems influenced a little by the space race and the American efforts to get to the Moon.
They face problems like: not achieving escape velocity for the Moon, failure of stage separation, failure to adjust quickly to reduced gravity on the Moon, and a very short exploration time to obtain samples before their launch window :)
It is not really a "pure" pop-up book but rather has some pop-ups and various flaps and tabs you can pull (for action.)
de Brunhoff, Laurent. Babar's Moon Trip. New York: Random House. (18 p.) 1968.