This question is obvious enough, and I’ve gotten it so many times I decided to write this description of just why this won’t work.The answer is pretty surprising to most people, but the science doesn’t lie.
But I don’t think that will help us in our argument. Not to prove to Apollo deniers anything, of course.
Moon Hoax believers have made it their mission in life to deny the veritable tsunami of evidence that the landings were real. Once you stick your fingers in your ears and start saying "LALALALALA I can’t hear you" all bets are off, and no amount of evidence will help. They can sit here back on Earth and pretend it’s flat for all I care.
In other words, take the physical size (d) of an object, divide it by the distance (D), multiply that by the constant 206265, and that gives you the angular size (α) in arcseconds (make sure D and d are in the same units! In fact, if you do the math (set Hubble’s resolution to 0.1 arcseconds and the distance to 400,000 kilometers) you see that Hubble’s resolution on the Moon is about 200 meters! Hubble’s resolution is 0.1 arcseconds no matter how far away an object is.
Those wisps of gas appear to be finely resolved, but they’re billions of kilometers across. So even if we built a colossal sports arena in Tycho crater, Hubble would barely see it at all.
But from a mile away that human is far more difficult to see, and from ten miles away is just a dot (if that).
The ability for a telescope to resolve an object is, as you’d expect, directly related to the size of the mirror or lens.
However, this is a very tricky observation and has to be timed just right (and the landscape itself may hide the shadow; crater rims, mountains, and natural dips and bumps might prevent sunlight from hitting the lander until the Sun is high in the sky, and that will shorten the shadows).
Plus, try to convince a committee in charge of hotly-contested and hugely over-subscribed telescopes to give you a night to try this and see how they react. The other method is obvious enough: go back to the Moon and take a look.
That’s an incredibly small size; a human would have to be nearly 8000 kilometers (4900 miles) away to be 0.05 arcseconds in size! But this is pretty minor compared to mirror size, and we can ignore it here (plus it’s already compensated for in the constant 11.6 that we used above).