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Edit:
For clarification of what I mean with "static in space above the Lunar south pole " please see this answer from @Tom Spilker or his answer to the question Orbits that allows observation of a polar region as an example.

When near the south pole of our Moon a permanent human community is established to search for and produce water in the permanently shadowed regions there, it would be nice to have some light from above !

Would it be possible to instal a framework of mirrors in space above such a human settlement so there would not have to be worked in constant darkness ?

Within the framework the mirrors could turn independent from each other and could function as solar sails as well to withstand the gravity of the Moon.

Of course, software would be needed to anticipate the constantly changing position of the framework by changing the angle of the different mirrors independently.

Cornelis
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    Theoretically, you could have a moon rotation synchronous satellite that reflects sunlight onto the moon's surface. Of course, mirrors can't reflect more light that they receive, so the total mirror surface area would have to be at least 10% as large as the village, probably more. –  Nov 26 '19 at 15:43
  • I mean we haven't even managed to stabilize a satellite around the moon for an extended period of time due to the mass concentrations from large impacts billions of years ago that caused large regions of highly dense material. I can't imagine doing this with current technology, let alone a moon base on the south pole. I don't know why you'd need this system either, because the poles of the moon are in perpetual light at certain high points (as well as perpetual darkness at others)... The axis spin is 88.5 degrees from the plane of the elliptic. – Magic Octopus Urn Nov 26 '19 at 15:47
  • Are you saying that the mirrors are in orbit or on the ground? I may have misread a little. On the ground I doubt they'd get significant enough sunlight to reflect anything more than they'd be able to get by picking a spot illuminated constantly. – Magic Octopus Urn Nov 26 '19 at 15:53
  • @MagicOctopusUrn I wouldn't write "in orbit" because of possible confusion, i would rather say "static in space above the pole" . – Cornelis Nov 26 '19 at 16:09
  • @MagicOctopusUrn The mass concentration would stay the same for the framework if it can stay above the pole. Because the water could stay only in the permanently shadowed regions, there in the darkness it would have to be excavated. – Cornelis Nov 26 '19 at 16:21
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    So... you're proposing an object that floats above the surface, in a completely impossible orbit; or am I missing something here? If it's not in orbit, and it's "static" then it needs propulsion to counteract the moons gravity. You cannot have an orbit that "stays above the pole" 100% of the time. The whole statement "static in space" doesn't really make sense. – Magic Octopus Urn Nov 26 '19 at 16:32
  • @MagicOctopusUrn The mirrors can function as solar sails which could counteract the moons gravity. https://en.wikipedia.org/wiki/Statite – Cornelis Nov 26 '19 at 16:47
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    Can you actually position a statite over the moon, though? – Starfish Prime Nov 26 '19 at 16:48
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    @starfishPrime Not over a pole while reflecting light to a specific position and maintaining attitude to counter-act gravity... Maybe the question should've been, "is a statite over the moon possible? What about over the poles?". I feel like that would've been more answerable than this is in its current state. This adds a bunch of extra layers of complexity to an already complex problem. – Magic Octopus Urn Nov 26 '19 at 16:48
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    Software wouldn't help the problem. You cannot get the delta-v you need, in the direction you need to counter-act gravity *AND* reflect the light back to a specific location on the surface in quantities that are needed for illumination at the poles. Especially seeing as this sail would need to be absolutely massive. – Magic Octopus Urn Nov 26 '19 at 17:05
  • You're right, the mirrors would have to be ultralight, and a high percentage of them would have to serve as solar sails. – Cornelis Nov 26 '19 at 18:02

3 Answers3

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The answer is no, you cannot have a static satellite. It would require high delta-V continually thrusting the mirror upwards. Solar sails do not have high delta-V. But that is okay - if all you want is polar moonbase illumination, that problem is already solved:

  • Solution 1 -

Have a network of satellites with mirrors, and use them in turn as they pass near the poles - software could do this fairly easily.

  • Solution 2 -

Build mirrors on polar mountains - there are some that are continually in sunlight. This solves the entire problem at much lower cost, no fiddly orbits to worry about, and you could climb up and fix issues if there are problems.

  • Solution 3 -

Floodlights powered by solar panels, as suggested by Magic Octopus Urn

Rory Alsop
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There isn't a problem with sunlight supply at the south pole. It's actually the opposite situation. One of the biggest attractions to the lunar south pole (after water) is the fact that there are areas there that are in almost constant sunlight. From the rim of Shackleton crater, the sun skims the horizon to a complete 360˚ as the lunar day progresses. It's quite feasible to have constant solar power for a polar settlement by placing cell arrays in the right places and linking them into a network.

If a base is deep into a crater (say to run an ice harvest operation) they could save on cable by beaming microwave power from the rim.

Johnny Robinson
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    the close proximity between always in shadow regions + thermal mass of the moon as a cold source, and always in sunlight hot source could be the spot for continuous stirling operation – user721108 Oct 15 '23 at 16:32
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Answer: No, it ain’t gonna work.

Pole-sitter orbits for the inner planets (using a combination of light sail pressure and low-thrust propulsion) have been modeled.

enter image description here

https://www.researchgate.net/publication/260082614_Trajectory_and_Spacecraft_Design_for_a_Pole-Sitter_Mission/figures?lo=1

However, they produce high orbits which are many planetary radii in altitude.

Molniya orbits would also answer your need to have perpetual clear sightlines to both the sun and lunar pole, but once again the high orbit is many lunar diameters in altitude.

The high altitude of these orbits presents the problem of a very large projection area on the Lunar surface and therefor a very dim light. This is because any mirror which is significantly smaller than the sun will function as a pinhole lens, projecting an image of the sun the same angular diameter as the Sun itself. If your proposed mirror is at an altitude of 10,000km, the projected image on the surface of the moon will be 90 km in diameter. Even if you had an optically perfect mirror 0.9km in diameter, the light intensity on the lunar surface would be 1/10,000 of daylight.

It’s tempting (with handwaving) to propose a slightly concave mirror to concentrate the reflected sunlight in a smaller region. However, the 2nd law of thermodynamics forbids optics which form an image with a smaller angular diameter than the object being imaged (unless there is a large loss of intensity). If it were possible to create a smaller image, it could have a higher black body temperature than the source and thereby “transfer heat from a cooler to a hotter”

It's easier to give the workers headlamps.

Woody
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  • I'm not quite following the 2nd law prohibition. I'm thinking of those parabolic fire starters for camping. Placed close to an object it creates a concentrated area of high radiation. If the parabolic fire starter was placed several feet away I would think it would create a larger area of radiation equal to being in direct sunlight. I'm just saying that's intuitively how it seems like it would work, maybe the physics says differently. Also they wouldn't need the same candlepower as the Sun which is overkill as it requires our eyes to dim it down. Probably need just sports stadium candlepower. – Steve Pemberton Oct 16 '23 at 09:26
  • @StevePemberton ... An analogy is the difference between heat and temperature. Solar collector furnaces can produce almost limitless heat. Want more heat? Add more mirrors. But the furnace can never exceed the temperature of the radiating body (the surface of the Sun). That would be violation of the 2nd Law. If it were possible to produce an image of the Sun with a smaller angular diameter than the Sun, the temperature of a solar furnace could exceed the surface temperature of the Sun, so the 2nd Law would be broken. – Woody Oct 16 '23 at 14:08
  • @StevePemberton ... A small image can be produced with non-imaging optics (as opposed to traditional geometric optics) but this attenuates the light beam, so the 2nd Law is upheld. (This is one reason lasers are so useful: they produce light beams much more highly collimated than can be produced by collimating an incandescent source.) – Woody Oct 16 '23 at 14:08
  • Very convincing answer for me, especially the projecting image of the Sun on the Moon of 90 km diameter. – Cornelis Oct 17 '23 at 08:13