The Americans won the race to the Moon when Neil Armstrong set foot on the lunar surface in 1969.
That single act trumped the Soviet achievement of sending the first man into space eight years earlier. But what might have happened if the Soviet Union had got to the Moon first?
The first manned lunar landing was a triumph for Nasa, and when the Americans won the Space Race, they also sounded its death knell.
The Apollo lunar programme continued until 1972 and 12 astronauts touched down on the Moon's surface. But US TV networks quickly bored of the Moon landings. When politicians lost interest, the Apollo programme was scrapped.
Of course, we have not been back since. Instead, human exploration of space has been confined to low-Earth orbit.
Piers Bizony, who has co-written a biography of Gagarin called Starman, says: "The Russians were in the business of conquering space... The Americans felt they were in a race and the nature of a race is that once you think you've won it you tend to stop running."
Had the Soviets got to the Moon first it is unlikely that they would have abandoned it as swiftly as the Americans.
Not being a democracy may have enabled the USSR to spend money and marshal the talents of their population in a way that America could not.
Space historian Dr Christopher Riley believes that not only would the Soviet Union have continued with Moon missions, but they might also have built lunar bases.
And he believes that the Americans would have been compelled to do the same and even try to continue to outdo their communist rivals.
"The history that followed in the decades afterwards would have been completely different," he says.
Summer of '69
In the summer of 1969, when the Apollo 11 crew were on their way to the Moon, US vice-president, Spiro Agnew declared that America would be on Mars by 1980. At the time, this was seen as a relatively feasible goal given how fast things had progressed in the 1960s.
"They certainly had it in their minds and on their drawing boards and there were designs of methods to get to Mars that might have been put into action in response to a Soviet landing on the Moon," says Dr Riley.
So how close were we to following this alternative reality?
Quite close, according to Piers Bizony: "Those who imagine Apollo had the Moon race to itself are wrong," he says.
The US seemed to have taken the lead in 1968 when it successfully boosted three astronauts into lunar orbit with its Apollo 8 mission.
But the Americans rushed ahead with that mission because they were afraid that the Soviet Union was about to beat them yet again and pull off another space coup.
The USSR was using a rocket called the Proton which is still in use today. The Soviets were sending payloads into space with a view to putting a cosmonaut into a so-called circumlunar flight which would take him around the Moon and straight home again without going into orbit.
They had flown an unmanned mission a few months before Apollo 8 that had taken just such a trajectory around Earth's natural satellite.
The Soviets had also built their own Moon rocket (known as the N-1) and their own lunar lander.
So how did the Americans win?
The first seeds were sown in 1957 by President Eisenhower following the launch of the first satellite by the USSR.
The launch of Sputnik 1 generated fear across the US - and a quiet realisation that the country had fallen technologically behind the Soviet Union.
President Dwight Eisenhower's response was to increase the budget for education to raise the academic standard in universities across America.
Dr Riley comments: "To increase the brainpower they'd need to pull off these technological feats to take on the Russians and win."
Eisenhower also commissioned the Saturn V rockets, principally to launch multi-tonne satellites for spying. But when President Kennedy inherited the White House and had to respond to Gagarin's flight, the Saturn V was already in development.
It was the Saturn V rocket that enabled the US to send astronauts to the Moon.
The early Soviet Space triumphs were managed and steered by Sergei Korolev, the man who built the R7 rocket that put Sputnik and Yuri Gagarin into orbit.
But after Korolev's death in 1966, the Soviet space effort lost focus.
Because he was not there to assert his authority, there was not one Soviet attempt to reach the Moon, but several rival schemes to reach the Moon.
According to Piers Bizony, the rival schemes sucked resources from each other: "There was a great deal of confusion in the Soviet space effort in the late 1960s and as a result they didn't have the technology to send a man to the Moon," he says.
Nor did they have the computing power. By today's standards the Apollo 11 onboard computer was pretty crude, but it was ahead of its time and was crucial for America's successful Moon landings.
Who might have been first to walk on the Moon in this alternative reality is anyone's guess. Yuri Gagarin died in 1968 in a plane crash and so would not have been available for any Soviet Moon shot. In any case he was too much of a national treasure to have been sent on such a risky mission.
However, if Korolev had lived a little longer and if Soviet spies had stolen US computer technology, then the Moon might well have been colonised and have been a base for international manned missions to Mars and - perhaps - beyond.
But 50 years on from Gagarin's historic flight, the Russians will once again be the planet's pre-eminent space-faring nation. This year, the US will retire its space shuttle fleet, its only craft capable of sending astronauts into space.
According to Mr Bizony: "America has no clear idea of what will replace the shuttle and no clear idea of whether as a nation they are truly committed to the human spaceflight adventure.
"Meanwhile Russia will be flying American astronauts and those from other countries on board their Soyuz capsule. And that Soyuz lifts on a rocket very similar in its essential construction to the one that launched Yuri Gagarin."