Which phrase or set of words shows the professional rivalry of USA and Soviet Union?

Directions: Read the passage and answer the question that follows.

The space age began in 1957 when the Soviet Union launched Sputnik 1, the world's first man-made satellite. Also in 1957, Sputnik 2 was launched carrying a dog named Laika. Laika was the first animal to orbit the Earth. In 1961, Yuri Gagarin became the first human to pilot a spacecraft when he was launched aboard Vostok 1 by the Soviet Union. Later that year, Alan Shepard became the first American to pilot a spacecraft. He was followed by John Glenn, who orbited the Earth three times in 1962.
In 1963, the United States and the Soviet Union started a race to see who could put a man on the moon first. In 1969, the United States won when Neil Armstrong and Buzz Aldrin landed the Lunar Module Eagle on the moon's surface.

The United States and the Soviet Union have also put space stations into orbit around the Earth. These space structures serve as both a home and a laboratory for space travellers. The United States created and launched the first reusable manned spacecraft, the Space Shuttle, in 1981. Since then, five different Shuttles have made over one hundred flights into space.