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Why they would fake it
The Soviet Union had been making all the early advances and the greatest progress in the great Moon race.
The Soviet Union launched the first man and the first women in space in 1961 & 1963 and were also the first to orbit the Earth.

With the above happening the US Government had to make some kind of success with President Kennedy promising that the US would put a man on the moon by the end of the 1960's.

Many people believe that NASA had released that it was not possible to go to the moon with the technology available
(Computer chips being as powerful then as a modern washing machines chip) so they resorted to faking the landing to ensure a
victory of the Soviet Union and keep the dollars coming in for real space projects.