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If I have the right numbers, it seems to me that even Hubble telescope might barely be able to make out a carcass of a blue whale on the surface of the moon, which puts objects as small as the lunar rovers or the American flag left there by Apollo out of range. Hubble is often lauded as the best telescope we have built. I know a large part of that is because it is in space where it's free from all of the interference of the atmosphere, but is there any ground-based observatory with better resolution? Is there any place on Earth where I could point a scope at the Sea of Tranquility and see what we left there over 40 years ago?

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up vote 11 down vote accepted

The largest optical wavelength telescope that we have now is the Keck Telscope in Hawaii which is 10 meters in diameter. The Hubble Space Telescope is only 2.4 meters in diameter.

Resolving the larger lunar rover (which has a length of 3.1 meters) would require a telescope 75 meters in diameter.

Information extracted from The Curious Team answers: Are there telescopes that can see the flag and lunar rover on the Moon?

Update: In a comment to my answer, @Envite mentions Astronomical Interferometers which are: array of telescopes or mirror segments acting together to probe structures with higher resolution by means of interferometry. The benefit of the interferometer is that the angular resolution of the instrument is nearly that of a telescope with the same aperture as a single large instrument encompassing all of the individual photon-collecting sub-components.

It also must be noted that probably this wouldn't be the best idea for watching the moon rovers since:

The drawback is that it does not collect as many photons as a large instrument of that size. Thus it is mainly useful for fine resolution of the more luminous astronomical objects, such as close binary stars.

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A new space telescope design could eventually bring us the ability to observe some of the larger man-made objects on the Moon. – called2voyage Dec 10 '13 at 22:03
To add to @Eduardo Serra's answer, you can avoid having a 75m diameter telescope if you use interferometry between telescopes 75m apart. – Envite Dec 11 '13 at 15:05

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