Laika’s arrival on board Sputnik II delighted science fans - but angered animal lovers and humiliated the Americans, who at that time were yet to send up even a satellite.
The mongrel – chosen partly because she would be more proletarian than a purebred dog – died within hours due to overheating and panic.
But the USSR claimed that Laika had died painlessly after her oxygen ran out on day six - and her agonising death was kept secret until 2002.
A British Pathé newsreel reveals the West’s astonishment at the achievement as it tried to explain how a rocket might deliver a capsule containing an animal into space.
It included an artist’s impression of how the 'flying dog kennel' might be arranged as Laika orbit around Earth sent her between 100 and 1,000 miles from the surface.
Inside Sputnik II were instruments to study space and radio equipment to beam information back to the USSR, which timed the launch to coincide with the 40th anniversary of the 1917 Bolshevik Revolution.
Apart from tests on radiation and solar rays, Soviet scientists wanted to find out how living creatures dealt with the weightlessness and other conditions in orbit.
But animal welfare organisations were horrified by what they saw as an act of cruelty.
The National Canine Defence League called on dog lovers to observe a minute's silence and the RSPCA organised a protest outside the Soviet Embassy in London.
Similarly aghast were American politicians – although not for reasons of animal welfare.
The launch of Laika, who U.S. newspapers nicknamed Muttnik, came a month after their bitter Cold War rivals sent Sputnik I, the first satellite, into orbit.
Americans feared that the rockets used might be capable of delivering nuclear weapons thousands of miles.
In response, U.S. President Dwight Eisenhower ordered more of his country’s superior economic resources to be devoted to what became known as the Space Race.
The U.S. ultimately won the contest by landing men on the moon – after both countries had developed rockets that could fire nuclear warheads at each other.
But, in the early years, it was the Soviets who scored the biggest advances and – to American consternation – raised the prestige of the communist system.
The Sputniks – meaning satellites in Russian - particularly irked the U.S because the U.S. had previously twice failed to launch a transmitter under Project Vanguard.
They suffered another setback when, on December 6, their third rocket crashed, leading to the Daily Express nicknaming the craft 'flopnik'.
The U.S. Army finally put their own satellite in space on January 31, 1958 – with the National Aeronautics and Space Adminstration (NASA) being set up soon after.
By December 1958, the Americans had sent a living creature into space and in May 1959 monkeys Able and Baker became the first animals to survive the trip.
Yet these early American achievements were eclipsed on April 12, 1961 when the Soviet Union put the first human, Yuri Gagarin, into space.
Just weeks later, Alan Shepherd became the first American to be sent into the orbit and from then on both sides competed to be the first to put a man on the moon.
The Americans got there first – and effectively won the Space Race – when Neil Armstrong, Buzz Aldrin and Michael Collins touched down on July 20, 1969.
Yet few people at the time realised just how close the USSR came.
The secretive Soviets kept under wraps the fact that, 17 days earlier, its own N1 moon rocket exploded seconds after lift-off, causing the biggest non-nuclear blast in history.
Details of the explosion, which was powerful enough to level a town the size of Luton, were only revealed after the fall of communism in the 1990s.
The lid was also lifted on how the brave Bolsheviks kept on trying – and failing – with ten launches between 1969 and 1974, when its moon programme was axed.
NASA successfully landed six manned shuttles on the moon between 1969 and 1972 when the U.S.
government ended its expensive programme.