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It is said that a 25m telescope would render the lunar lander as 1 pixel. However the lunar surface has an albedo of about .1 while the lander is highly reflective. So it would be about 10x brighter than the surrounding terrain.

So shouldn't a 10m telescope be able to render the lander as a single pixel 2-3x brighter than the surrounding terrain?

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    $\begingroup$ “It is said that a 25m telescope would render the lunar lander as 1 pixel” -- said by who? A telescope where -- on Earth's surface, in low Earth orbit, or low lunar orbit? Which lunar lander are you referring to, one of the Apollo LMs? $\endgroup$ – Russell Borogove Jun 13 '18 at 2:40
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    $\begingroup$ @RussellBorogove I'm curious also who said it, but at 350,000 km (i.e. roughly Moon from Earth) that's about right within a factor of 2-ish. These days adaptive optics on Earth telescopes is pretty good for narrow fields and near IR (almost visible) so an orbiting telescope and a fancy terrestrial might be roughly comparable. cf. Will the E-ELT use Adaptive Optics at visible wavelengths? and also Why (actually) aren't ground-based observatories using adaptive optics for visible wavelengths? $\endgroup$ – uhoh Jun 13 '18 at 4:33
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    $\begingroup$ Related: space.stackexchange.com/questions/12347/… $\endgroup$ – Hobbes Jun 13 '18 at 7:34
  • $\begingroup$ To see as bright dot - actually lunar lander can be much LESS than 1 pixel. It needs favorable lighting angle conditions. Good reflecting surfaces at the lander would be very helpful, but I'm afraid the Apollo landers were damaged by launches of ascent stages. We can see damage on video youtube.com/watch?v=9HQfauGJaTs $\endgroup$ – Heopps Jun 13 '18 at 8:09
  • $\begingroup$ The biggest telescopes are not used to look at the Moon. Also he Moon would be too bright for their instruments. I thought about NASA Lunar Impact Program: nasa.gov/centers/marshall/news/lunar/overview.html. The program uses 0.5-meter telescopes to monitor lunar transient events. But the study focused at dark side of the Moon, so I think the bright side wil be overexposed, so reflection from the lander would not be ditingiused. $\endgroup$ – Heopps Jun 13 '18 at 8:17
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I checked the LRO images and you're right: the albedo of the lander is higher than its surroundings. Here is a Lunar Reconnaissance Orbiter image of the Apollo 17 landing site:

Apollo 17 LM is brighter than its surroundings

I found several places where the telescope size is calculated to resolve the LM. Phil Plait (in his Bad Astronomy blog) arrives at a telescope size of 100 m to do this.

Just seeing a bright dot requires less resolution than this. Reusing the calculations from here and doubling the telescope diameter to 10 m, I get a resolution of 23.2 m. So in your telescope you see the average color/brightness of a square of 23x23m.

I did a quick and unscientific test, grabbing a roughly 23x23 m square from the above photo and scaling it to 1x1 pixel, then checking the grayscale value of that pixel. The square with the lander in it was darker than an adjacent square, so a 10 m telescope wouldn't see a bright spot where the lander is. It looks like the lander's shadow pulls the average brightness down to a level that's not reliably distinguishable from the surroundings.

Here is the above image downsampled to 16x12 pixels to get a pixel size of 25x25 m, then upscaled to 400x300px to get an image that is easier to view than a 16x12 px image. As you can see, you can't distinguish between the variations in albedo due to shadowing and variations caused by the LM.

enter image description here

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  • $\begingroup$ The shadow at dawn or dusk would also be much bigger than the object itself, so might be easier to resolve. $\endgroup$ – Steve Linton Jun 13 '18 at 11:27
  • $\begingroup$ You can build a football stadium on the Moon and current telescopes won't be able to find it. A long shadow (still only a few meters wide) isn't going to help. $\endgroup$ – Hobbes Jun 13 '18 at 11:40
  • $\begingroup$ A 10m telescope with adaptive optics at 1um wavelength has a resolution in principle of 100 n rad ($\lambda/d$) which is about 40m on the Moon. A football stadium should be easy enough to spot. the shadow would just be a couple of dark pixels at best, I admit. $\endgroup$ – Steve Linton Jun 13 '18 at 12:29
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    $\begingroup$ Note that the shadow lowers the averaged albedo. $\endgroup$ – amI Jun 13 '18 at 22:11
  • $\begingroup$ @amI that's a really good point! Collecting extensive data over time (years) one would get dozens of cycles of Sunlight with incident angle scanning from -90 to 0 to +90 degrees (synched with a small variation of viewing angle due to nutation). This modulates the shadow as well as illuminates different parts of the object, and all would be "encoded" in the light curve. While not an observation, it does add a bit of extra data beyond a single photo with a single hot pixel. $\endgroup$ – uhoh Jun 14 '18 at 3:36

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