Just to add to what Vincent Maldia says (Vincent Maldia's answer): this is about ideas that you might be able to use to get beyond the limitations of Earth based telescopes - but whether it is worth anyone's time to actually do this given what a major challenge it is and you can see them anyway with lunar orbiters, I don't know.
So, first, there's the the blurring effect of the atmosphere which makes the image dance around all the time means that the Keck telescope for instance has an effective resolution of 0.1 arc seconds instead of the 0.02 arc seconds it would have if it was in space. A human on the Moon would be 0.001 arc seconds.
Adaptive optics can help unblur the image by keeping track of how the image moves and distorts, and countering the effect of that.
Just a thought, don't know if it is practical - I wonder, what if you used the laser reflectors that have been left on the Moon (conveniently, just next to the landers) as a guide - shine a laser light from Earth to Moon to those reflectors, and then use the light that comes back to stabilize the adaptive optics? Would you be able to spot the laser light in the resulting image? By looking for its exact frequency programmatically? And then use that to stabilize the dancing images effects of atmospheric refraction?
If you could do that, maybe you could get down to near the limit, but it's clear that even Keck with adaptive optics has no chance to observe the landers (never mind anything smaller).
You can get beyond that with optical interferometry. That increases the resolution by combining the effect of several smaller telescopes further apart - but makes the things you see much fainter because they don't catch much light. But brightness is not an issue for the Moon.
This instrument is used mainly for measuring widths of stars - but it's measured stars of width as small as 1.7 milliarc seconds: Navy Precision Optical Interferometer
So in principle, with optical interferometry - and if you also could stabilize the image with adaptive optics as well perhaps, by detecting the reflection of laser light in all the telescopes to align the images - if that actually worked - you'd be able to see them. I'm sure there would be many technical challenges.
There's also Phil Platt's idea that if you were to photograph at just the right time of day, then they would cast much longer shadows across the landscape, and those could be photographed from Earth.
But - try explaining that in your allocation request that you want to take up precious telescope time on one of the biggest most capable telescopes to photograph the shadow of the lunar lander :). Especially since they can be and have been observed by satellites in orbit around the Moon.
For Phil Platt's article where he talks about the idea of photographing the shadows of the lunar landers from Earth: Moon hoax: why not use telescopes to look at the landers? - Bad Astronomy
So, first, there's the the blurring effect of the atmosphere which makes the image dance around all the time means that the Keck telescope for instance has an effective resolution of 0.1 arc seconds instead of the 0.02 arc seconds it would have if it was in space. A human on the Moon would be 0.001 arc seconds.
Adaptive optics can help unblur the image by keeping track of how the image moves and distorts, and countering the effect of that.
Just a thought, don't know if it is practical - I wonder, what if you used the laser reflectors that have been left on the Moon (conveniently, just next to the landers) as a guide - shine a laser light from Earth to Moon to those reflectors, and then use the light that comes back to stabilize the adaptive optics? Would you be able to spot the laser light in the resulting image? By looking for its exact frequency programmatically? And then use that to stabilize the dancing images effects of atmospheric refraction?
If you could do that, maybe you could get down to near the limit, but it's clear that even Keck with adaptive optics has no chance to observe the landers (never mind anything smaller).
You can get beyond that with optical interferometry. That increases the resolution by combining the effect of several smaller telescopes further apart - but makes the things you see much fainter because they don't catch much light. But brightness is not an issue for the Moon.
This instrument is used mainly for measuring widths of stars - but it's measured stars of width as small as 1.7 milliarc seconds: Navy Precision Optical Interferometer
So in principle, with optical interferometry - and if you also could stabilize the image with adaptive optics as well perhaps, by detecting the reflection of laser light in all the telescopes to align the images - if that actually worked - you'd be able to see them. I'm sure there would be many technical challenges.
There's also Phil Platt's idea that if you were to photograph at just the right time of day, then they would cast much longer shadows across the landscape, and those could be photographed from Earth.
But - try explaining that in your allocation request that you want to take up precious telescope time on one of the biggest most capable telescopes to photograph the shadow of the lunar lander :). Especially since they can be and have been observed by satellites in orbit around the Moon.
Let the Cognitive Dissonance Begin
For Phil Platt's article where he talks about the idea of photographing the shadows of the lunar landers from Earth: Moon hoax: why not use telescopes to look at the landers? - Bad Astronomy
About the Author
Robert Walker
Writer of articles on Mars and Space issues - Software Developer of Tune Smithy, Bounce Metronome etc.Studied at Wolfson College, Oxford
Lives in Isle of Mull
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