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Scientists were surprised and delighted that Surveyor 1 - America's first attempt at a "soft" landing - succeeded.
They had expected it to take at least four tries.
The Soviet Union was the first to achieve the feat four months ago. It is believed to have sent four failed missions before landing the Luna 9 probe successfully.
The Surveyor 1 craft landed at 0617 GMT in the Ocean of Storms, about 590 miles (950 km) from where Luna 9 came down.
Just over half an hour later, it began transmitting a series of astonishing photographs of the Moon's surface.
The American President, Lyndon B Johnson, used the occasion to emphasise the openness of America's space programme.
In a comment directed at the Soviet Union, which earlier this year delayed the release of photographs from Luna 9, he said Surveyor's "remarkable photographs" would be made available as soon as possible.
In fact, national television networks in America broadcast the first pictures taken by the 10ft (3m) high triangular-shaped spacecraft as they came in.
Scientists at the Jet Propulsion Laboratory in Pasadena, California began counting down the spacecraft's descent from an altitude of about 60 miles (95 km) from the Moon's surface, when Surveyor was travelling at about 6,100 mph (9,800 km/h).
The altitude marking radar started the powerful main braking rocket. This burned out in about 40 seconds, about 25 miles (40 km) above the Moon's surface. The rocket's speed had been reduced to 250 mph (400 km/h).
By the time Surveyor was 13 feet (four metres) from its target it had been slowed to about eight mph (13 km/h).
"It settled on the surface in a fairly soft fashion, just a few degrees off the horizontal," said one of the scientists.
The first pictures showed a number of objects which appeared to be rocks about an inch (2.5cm) across, and pebbles strewn about the lunar surface.
Dr Leonard Jaffe, chief Surveyor project scientist, discounted previous theories about deep layers of soft dust, pointing at photographs taken after touchdown of the Surveyor's pad on one of the spacecraft's tripod legs.
Scientists believe that the success of the Surveyor 1 mission has put the lunar landing program about a year ahead of schedule.
Surveyor 1 spent the lunar night on the Moon and was successfully reactivated the next lunar day, on 6 July. Contact was lost on 7 January 1967.
The United States sent another six Surveyor probes to the Moon over the following 18 months. Only two were failures.
Later Surveyor missions were able to take samples of the rocky surface of the Moon, discovering them to consist largely of basalt.
The Apollo 12 mission was planned to land close to where Surveyor 3 had touched down to demonstrate the accuracy of its navigation.
Astronaut Pete Conrad was able to retrieve the camera and scoop from the Surveyor's landing site and return them to Earth.
The information gathered from the Surveyor missions was essential for the success of the American Apollo manned expeditions which began the following year.
Budget constraints brought the first phase of American lunar exploration to an end in 1972.
Then, in January 2004, US President George Bush announced American astronauts would return to the Moon by 2020 as the launching point for missions further into space.
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