Why were countries competing to get to outer space?

The competition began in earnest on August 2, 1955, when the Soviet Union responded to the US announcement four days earlier of intent to launch artificial satellites for the International Geophysical Year, by declaring they would also launch a satellite "in the near future". The Soviet Union achieved the first successful launch with the October 4, 1957, orbiting of Sputnik 1, and sent the first human to space with the orbital flight of Yuri Gagarin on April 12, 1961. The USSR also sent the first woman, Valentina Tereshkova, to space on June 16, 1963, with numerous other firsts taking place over the next few years with regards to flight duration, spacewalks and related activities. According to Russian sources, these achievements led to the conclusion that the USSR had an advantage in space technology in the early 1960s.

According to US sources, the "race" peaked with the July 20, 1969, US landing of the first humans on the Moon with Apollo 11. Most US sources will point to the Apollo 11 lunar landing as a singular achievement far outweighing any combination of Soviet achievements. The USSR attempted several crewed lunar missions, but eventually canceled them and concentrated on Earth orbital space stations, while the US landed several more times on the Moon.

A period of détente followed with the April 1972 agreement on a co-operative Apollo–Soyuz, resulting in the July 1975 rendezvous in Earth orbit of a US astronaut crew with a Soviet cosmonaut crew and co-developing the enabling docking standard APAS-75. Though cooperation had been pursued since the very beginning of the Space Age, Apollo–Soyuz eased the competition to enable later cooperation. The end of the Space Race and competition is not clear cut, since the Apollo 11 Moon landing and the ASTP have been identified as such,[8] but with the December 1991 dissolution of the Soviet Union it was ultimately replaced through increased spaceflight cooperation with the APAS enabled Shuttle–Mir and International Space Station programs between the US and the newly founded Russian Federation.

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source - Wikipedia

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