Can someone help me estimate the diameter of a telescope that will permit a US flag on the moon planted by...?

Question

Can someone help me estimate the diameter of a telescope that will permit a US flag on the moon planted by one of the Apollo missions to be resolved from the earth? So could you possibly see the flag from earth?

Answer 1

Assume a flag is 1 meter across, and the moon is 3.6x10^8 m distance at perigee. Your telescope needs a resolving power of 1/3.6x10^8 radians.

The resolving power of a typical telescope is ~1.22lambda/D radians where lambda is the wavelength of light being observed and D is the diameter of the telescope.

Solve for D; D= 3.6x10^8*1.22*lambda

Assume a visible light telescope sensitive at 600nm = 6x10^-7 m
and your telescope must be 263m in diameter. You will want to orbit that puppy or phase errors from turbulence will kill you, with current adaptive optics technology.

Answer 2

No telescope would be large enough on Earth to see the flag. The problem isn't the size, it's the moving air. It's the same air that causes stars to twinkle. At some point, the moon will look blurry and the flag would fade out. That's why we have the Hubble telescope. It's so can get past the air for a better resolution.

Answer 3

Hubble's only a 100" mirror, relatively very limited angular resolution compared to some Earth-based scopes like the Keck 30-meter twins, which, when in interferometric mode, yield a single 85-meter scope with angular resolution measured in the milliarc-seconds, just about the minimum you would need. There is at least one other array that I know of, the Mt Wilson "Chara" which is an array of 6 1-meter mirrors spread out over a several hundred yard diameter. I'm not sure if all 6 mirrors are online yet, tho last I heard resolution was to 1/2 of a milliarc-second with only 4, and that was in infared. I think resolution might be a little better in the visible range due to shorter wavelength.

Unfortunately, I doubt if it's suitable for what you have in mind - even tho the angular resolution is more than enough, I'm reasonably sure contrast resolution would really suck due to such small apertures. The thing was really built to measure the wobble of stars caused by non-visible orbiting planets or masses, and other such high-contrast applications. I'm not up on recent astro hardware as I used to be, maybe something more suitable exists that I don't know about.

But the bottom line is, intelligent people already KNOW that there's flags, buggies, lunar modules, and other crap up there because millions of people watched them being left there. Trying to see them through a scope is not science. 100-million dollar scopes have much better things to do than let every idiot who thinks that the period before his birth was the stone age waste serious research time oogling thru the eyepiece*.

Besides, once they got a look, all such morons would just claim unmanned missions put them there to fool the kids. O yes, we even sent a bipedal robot with boots so he could leave thousands of prints. Fug. Stupid people suck, huh?

*Actually, not too many big scopes are suitable for eyepieces, or even include a place where a person could climb to to look thru one at the focal point. In fact, CHARA images aren't even images - they're probably fringes and wavefronts, and DSP, Fourier analysis, etc. is used to generate useful images from the data, much like a medical MRI.

[Additional re Gregoriy's comments below]

High altitudes and the recent addition of adaptive optics (which re-aims the scope dozens of times per second) allow many Earth-based scopes to correct for air turbulence and thus to perform well in excess of Hubble

Answer 4

Thanks for asking this. It spurred me to do some research that I always wanted to do. I found a really great website that has all the trignometry required to do the calculations. It is linked below.

The bottom line is that the Hubble Space Telescope has a resolution of 0.05 arcseconds. The largest objects we left on the moon are the bases of the lunar landers. To see them, you'd need a telescope with a resolution of 0.0024 arcseconds. That's more than 50 times better than the HST. Forget seeing one of the six flags. You'd need a space telescope more than a 1000 times better than the HST.

Answer 5

It is not possible to see it from Earth. If you were looking from a telescope in a spacecraft in orbit of the moon, perhaps, but it is still hard.

Answer 6

It would just look like a pin point since you would be looking at it from straight above, wouldn't it?