It is always very difficult to debunk conspiracy theories because the claims made by the conspiracists need no justification at all and are often based on an actual ignorance of the science.
Debunking their claims requires an understanding of basic...
Firstly, no telescope on Earth is that powerful. Our most powerful telescope could only resolve something 42 metres across – about 140 feet. That is why you can't see the landing sites from Earth.
When the Lunar Reconnaissance Orbiter was launched in 2008 it resolved the question. It has taken many images of each of the lunar landing sites at different times of the month so that the objects on the surface are clearly real and have different lengths of shadows at different times. Conspiracists rarely mention them except to claim they were all photoshopped by NASA.
In fact, this is where their stupidity can be most clearly demonstrated.
When a photographic image from film is faked, the manipulation can be almost invisible. However, digital photography is different. It is made up of digits. Any attempt to fake a digital photograph can be easily spotted by digital photography experts. None of the Lunar Reconnaissance Orbiter's digital images show any sign of any manipulation whatsoever! That is because they are real pictures of real landing sites!
Here are just one of each landing site. Go to NASA.gov for the rest.
Apollo XI
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Apollo XII
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Apollo XIV
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Apollo XV
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Apollo XVI
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Apollo XVII
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NASA thought the Lunar Orbiter Satellite would resolve all of this faked-landings nonsense. Unfortunately, not. It doesn't fit in with conspiracists' view of authority being out to trick the world in all things.
Above are each of the landing sites. Apollo 11 first, followed by 12, 14, 15, 16 & 17. There are repeated versions of these on the Internet, many showing different times in the lunar day with shadows from various directions – that would be some elaborate faking to get the tampering of shadows etc. right in every image, but photo experts say they are pristine, unaltered digital images.
If you check the second image above, Apollo 12, you will see surveyor crater and also the actual Surveyor 3 Lander. The picture below shows an astronaut standing beside it with the LEM in the distance. The images match up well. Part of Surveyor 3 was returned to Earth for study to see how alloys reacted after many years on the surface.
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