Apollo conspiracy theory
There has been speculation that the Apollo moon landing missions never actually took place, that it was a hoax filmed in a Hollywood studio. Supporting this interpretation is the fact that the American flag placed on the Moon should not wave, though it appears it does. Also, no stars appear in the lunar sky in photographs supposedly taken on the Moon, as they would be expected to do. Moreover, the shadows in the photographs run in different directions, rather than parallel, as if the sun were not the source of light. [1]
NASA denies this, claiming that it can be conclusively demonstrated scientifically that the astronauts really went to the moon, for example, by analyzing the ages and composition of the rocks brought back by the astronauts. [2]