In 1960, the exploration of space was still in its infancy. Several years earlier the Soviet Union had launched the first satellite into space. The USA was very eager to catch up, which is why the Soviets were putting themselves under extreme pressure to keep their head start.
The Russo-Japanese war (1904-1905) is a major 20th century war, which is often overlooked because of the much larger conflicts (i.e. World War 1, World War 2) that happened later. The basic reason for the war between Russia and Japan was a mutual interest in controlling Korea and Manchuria.