First on the Moon by Jeff Sutton (1913 - 1979)

The four men had been scrutinized, watched, investigated, and intensively trained for more than a year. They were the best men to be found for that first, all-important flight to the Moon--the pioneer manned rocket that would give either the East or the West control over the Earth.Yet when the race started, Adam Crag found that he had a saboteur among his crew ... a traitor! Such a man could give the Reds possession of Luna, and thereby dominate the world it circled.Any one of the other three could be the hidden enemy, and if he didn't discover the agent soon--even while they were roaring on rocket jets through outer space--then Adam Crag, his expedition, and his country would be destroyed!(Summary by Jeff Sutton)