But to actually SEE anything and recognize it, here is what the Hubble telescope could see.

But to actually SEE anything and recognize it, here is what the Hubble telescope could see.

But to actually SEE anything and recognize it, here is what the Hubble telescope could see.

Hubble's 94.5-inch mirror has a resolution of 0.024″ in ultraviolet light, which translates to 141 feet (43 meters) at the Moon's distance. In visible light, it's 0.05″, or closer to 300 feet. Given that the largest piece of equipment left on the Moon after each mission was the 17.9-foot-high by 14-foot-wide Lunar Module, you can see the problem.

So if you are talking a human-made feature, 300 feet would be the minimum size for a very powerful telescope.

If you want binoculars, then to see a covered dome over a hundred km. diameter crater, the minimum would be a good 40x or 50 x binocular would work. You are not going to see a typical lunar habitat, of course, or make out any detail - you will only be able to see that something is there.

Magnification 40x, 50x Binoculars with magnification 40x and 50x are very powerful and produced by such optical companies as Oberwerk, Orion.

They are very expensive BTW. With such powerful optical instruments you can see a big picture of the Moon and craters, even small ones.

But 90X is better

Magnification 90x This powerful instrument with magnification 90x by Oberwerk gives you a huge power and you can see unbelievable picture of the Moon and craters.

But I would recommend image stabilization binoculars.

Of course, something like this Orion GiantView BT-100 ED 90-degree Binocular Telescope would give you a clear view of a domed crater, for sure.

Views of lunar craters to wispy nebulae will take on an almost 3D feel in the GiantView BT-100 ED. The 100mm aperture objective lenses gather 56% more light than 80mm binoculars, so you'll be able to see more objects in the sky with greater clarity. Blockquote

But let us go the reverse - what can we see on Earth from the Moon? Seems to me that if we can see it in one direction, we could see it in the other direction. This article is about using remote sensing of the Earth from the Moon.

The largest technical constraint to observing the Earth from a lunar base is spatial resolution. At the sub-Moon point, the diffraction-limited resolution (R) can be approximated (in km) by R = λ/D where λ is the wavelength (in microns) and D is the telescope diameter (in meters). At visible wavelengths a spatial resolution of 1 km or less requires a 1 meter or larger telescope. Figure 2 shows this relation for three telescope diameters. Blockquote

The chart in this pdf demonstrates that a 0.1 m lens would have a resolution of 30 km of a wavelength of 3.0 microns and a resolution of 5 km. of a wavelength of 0.50 microns.

So obviously we could not see an individual building, or even a city block, on the Earth from the Moon. Likewise, we could not reasonably see it in the other direction, either.

But features bigger than a large city on Earth could be discerned from the Moon using a 100 cm. lens. Mind you, this is just discerning that it is there, not seeing any details about it. Like seeing a blob.

Put in perspective, it is doubtful that a nuclear explosion on Earth would be more than a speck as seen from the Moon through very powerful binoculars.

This article concludes by saying

While the arguments for Earth observations from a lunar observatory are intriguing, it is typically considered unlikely that the advantages outweigh the challenges when viewed insularly. However, as stated by [10], “a lunar astronomy program should complement the earth-orbiting satellite program.” For example, one can easily imagine simultaneous observations of the Earth from instrumentation on the Moon and from geosynchronous Earth orbit (GEO) meteorological satellites in order to provide radiometric crosscalibration between instruments.

Let's take another approach. Can we see a meteor impact on the moon from Earth with the naked eye? Apparently, we can. NASA has been looking carefully at the Moon for meteorite impacts, and has logged some that could be seen by the naked eye, if you happened to be looking at just the right time,

To get an idea of how nontrivial, NASA began counting visible strikes. So far it’s tallied more than 300. The one on March 17 was the biggest so far, ten times brighter than anything seen previously, although nowhere near the hypothetical one-kilometer catastrophe you’re talking about. This rock was more like a foot in diameter and weighed maybe 90 pounds.

Still, it was traveling close to 56,000 miles per hour and had an impact equivalent to five tons of TNT, gouging a crater perhaps 65 feet across. NASA has asked the scientists operating the Lunar Reconnaissance Orbiter, now mapping the moon’s surface, to take a picture of the March 17 crater, and they expect to get around to it later this year.

So an explosion of five tons of TNT would do it. That is some industrial accident. Or a very big mining operation.

However, if you were looking at the moon with an infrared imaging device on your binoculars, you could most certainly see evidence of heat signatures from a reasonably large enough colony, say 5 km.in diameter or so. Seen as a pin-prick of light, perhaps.

So apparently you will have to wait until the moon colony develops a substantial light pollution night time map, or a heat signature, of a major city before we will see it reliably and be able to make anything of it, using binoculars, from Earth.