When did the space race begin according to the nonfiction book, The Heavens and the Earth?

The space race began when the Russians launched Sputnik and put a satellite into space ahead of the Americans. Eisenhower downplayed the situation, but the Russians got as much mileage out of it as possible. They had the prestige of being first and were using it to their advantage, saying that the U.S. lagged behind Russia in science and technology. This was also being used to prove the superiority of the Soviet system over capitalism which the Russians tried to use to their advantage in the Third World and in Europe. Most of the world believed in the Soviet superiority. It wasn't until years later that the magnitude of Khrushchev's bluff became known.

But this set the stage for the American entry into the space program with all of its emphasis on R & D and all of its spending. It also set the stage for all of the events involving treaties and agreements at the United Nations and why most of them were window dressing: the United Sates didn't want to give away any of its secrets and the Russians didn't want anyone to know how far behind they actually were. McDougall does a good job of presenting the history of the space age in its proper political framework and shows how various international events led to various events in the space race.