After Apollo 11 first landed on the Moon in 1969, there have been conspiracy theories that this never really happened and that it was all a hoax. In 2010 NASA released photos from its Lunar Reconnaissance Orbiter (LRO) mission of some landing sites which showed both a lunar lander and footprints (as dark trails).
The question is, how big (aperture) of a telescope would you theoretically need on earth to see the lunar module or even better, the dark trail of footprints? What about from orbit, without the atmosphere, would a smaller diameter scope work, how big would it need to be?
Best Answer
Google led me to this page which goes through the math to answer your question about the theoretical size of a telescope needed to resolve the lunar modules. It should come as no surprise that no, it can't be done with a small telescope: according to the math found at that link, you would need a telescope 100m in diameter to just about be able to see the LM on the moon (from earth). The largest telescope on earth is 10m in diameter.
He also posits that building such a telescope would be more expensive than going there and taking a picture yourself.
Another thing to consider is the atmospheric effects. If you've ever seen an amateur video of Jupiter made from pictures taken through the atmosphere, you've seen it bubble and deform as though you were observing it from underwater. The atmosphere is in fact a fluid and this would make observing details as small as footprints on the moon next to impossible.
Using an orbiting telescope would avoid this, but the situation's not much better: it would have to be of similar size to the ground telescope (a ~300km difference in altitude wouldn't do much for the resolution), and you would actually have to get the thing into orbit.
I think the LRO pictures are the best we're going to get for a while. (BTW, moon hoax believers love to say that the LRO pictures are also fake, since they, too, came from NASA (they didn't really). JAXA's KAGUYA spacecraft, while not photographing the footprints etc., did map the topography of the apollo landing sites and it matches perfectly with the pictures. If the landings were filmed in the desert, how did they get the scenery to match up exactly with what's on the moon at the "fake" landing sites, according to JAPAN'S space agency?)