Getting into space was important for both countries since it was a competition between the US and the USSR where capitalism and communism prevailed respectively. Both countries were the superpowers that wanted to outcompete each other, being acrimonious. Accordingly, the reasons for space travel were linked not only to the desire to explore the new extraterrestrial dimensions but also to the aspiration of both states to win the Cold War and establish dominance on the international arena. It was a matter of political, economic, technological, cultural, and ideological standoff between the US and the USSR.
Therefore, it was crucial for the US to win the Space Race because in the USSR, Sputnik was already constructed. It was a satellite that was created due to the desire of the USSR to demonstrate its power and control. When Sputnik was launched, it only added a fuel to the Cold War because American people thought that it could be an antecedent of rocket attacks or it could be simply a tracking tool. Thus, the US tried to decipher the signals of Sputnik. It was a crucial artifact in the Space Race because it marked the superiority of the USSR in rocket production at that moment.
When it comes to the roles of the Presidents of the two countries, it is evident that they stimulated the Space Race. It was Eisenhower who launched it after the introduction of Sputnik because he realized that it challenged the technological superiority of the US. It is hard to define who won the Space Race because the USSR definitely became the first country to launch a person into space. It happened on April 12, 1961, when Yuri Gagarin completed one orbit of the Earth. Therefore, he was the first person in history who went to the outer space. The US got into space on February 20, 1962, when John Glenn, the first American astronaut, made an orbital flight on Mercury-6. Yet, the US did what the USSR could not achieve, having landed on the Moon with the help of Apollo 11, a spaceflight that was created for American Apollo program carried out by NASA. Therefore, Americans became the first people who stepped on the Moon, and historians are convinced that it marked the end of the Space Race.