Can you see the American Flag on the moon from a telescope

I have heard this before, if it is true then doesn't that pretty much debunk any moon landing conspiracy?

The flag is way too small to be seen from a telescope on Earth (or even around Earth).

The "smallest resolvable angle" in a telescope is calculated using Dawes' limit.

The crude (= easy to use) approximation goes like this:

A = 116/D

where A is the angle in seconds (there are 3600 seconds in one degree)
D is the diameter of the telescope (primary lens or mirror) in millimeters.

Let's be generous and pretend that the flag is 1 metre wide (40 inches).
The distance to the Moon is more than 300,000 km (but let's use that number to keep things easy)

the angle in radians is

1 m / 300,000,000 m = 0.0000000033333... radians
(there should be 8 zeros after the decimal point, before the first "3")


There are 206264.8 seconds in one radian

206,265 * (1 m / 300,000,000) = 0.000068755"

Using Dawes' limit

0.000068755" = 116 / D
solving for D

D = 116 / 0.000068755
D = 168,715 mm
There are 1,000 mm in one metre
D = 168.7 m (a little over 550 feet in diameter)

The largest telescope on Earth is the South African large Telescope, at 11 metres (36 feet).
Hubble is "only" 2.4 metres (around 8 feet).

To make matters worst, our atmosphere on Earth is nasty on telescope resolution. The S.A.L.T. has adaptive optics that try and correct that. Despite the system, S.A.L.T. is barely better than Hubble... on good days.

And the killer: Even if we DID have a 550-foot telescope, a one-metre flag would appear as a single dot (because that would be the limit of resolution). If you wanted to confirm that it was a flag (and not a one-metre rock that happens to lie there) you'd need the flag to cover at least 16 pixels (4x4), so that you would really need a 2,000-foot telescope (675 metres).