It is a well-known fact that when meteorite hits surface of the Moon, a part of debris can end up on Earth because the escape velocity for Moon is low - 2.38km/s. A similar effect can be achieved by landing spacecrafts on the surface of the Moon because the speed of rocket exhaust gases in a vacuum are in the range 3.0 - 4.5km/s. Besides launching debris in space, there is a possibility to make them orbit the Moon because orbit velocities for Moon are from 0.92 - 1.082 km/s.

What is the danger of creating an impenetrable cloud of micrometeorites around the Moon if the landings on its surface become frequent?

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    $\begingroup$ Those are the velocities of the Moon relative to the Earth. Velocity of Low Lunar orbit relative to the surface will be more lie 1.5 kms. More relevantly, though, low lunar orbits are very unstable, and anything kicked up from the surface will be in an orbit that hits the surface again one orbit later. $\endgroup$ – Steve Linton Nov 24 '20 at 13:04
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    $\begingroup$ somewhat related items about the possibilities of "orbital dust" around bodies with no atmosphere: When Chang'e-3 landed on the moon, did LADEE notice? and Could “Asteroid Redirect” make the moon more dangerous for astronauts for a long time? and Could ejecta from asteroid Bennu enter into temporary orbit around it? If so, how? $\endgroup$ – uhoh Nov 24 '20 at 13:26
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    $\begingroup$ my very (very) back-of-the-envelope calculation suggests that the exhaust from an Apollo-type mission is at most ~1% of the energy from small meteorites (100g or less) hitting the Moon over an average year, so it feels like any risk from this effect may be a long way off. $\endgroup$ – Andrew Nov 25 '20 at 12:09
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    $\begingroup$ I have a vague recollection of lunar orbits not being stable (or there being very few stable orbits) due to mass concentrations in the moon. $\endgroup$ – user6916458 Nov 25 '20 at 13:09

In general terms any particles placed on an orbit by a single impluse will pass through the point that impulse was applied again one orbit later. So for dust kicked up from the moon surface it will arrive back at the surface somewhere (rotation and sub orbital trajectories mean most will not actually hit the landing site).

This obviously does not apply for particles launched at beyond escape velocity, so it is possible a faint torus/ring of dust might form around earth, but since the particles would still intersect lunar orbit the moon would tend to further disrupt the orbits with more time, with dust either impacting the moon, impacting earth, being gravity assisted into solar orbit or ending up in vicinity of the lagrange points.

Rather than risk to space vehicles the problem is more likely to be to surface infrastructure, since the vast majority of the displaced material will impact 'somewhere' on the moon again, hits to base areas become probable. When Apollo 12 landed near Surveyor one of the surprises was the paint damage to surveyor despite not being in direct line of sight to the LM touch down point.

Protection of the base being landed at may be as simple as putting the base on a reverse slope, but if multiple bases exist it may become more important to engineer landing areas to avoid FOD to someone else's base half way round the moon if particles concentrate into a unfortunate range of launch angles and velocities.

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    $\begingroup$ That's it! The real risk so far as there is one is stuff impacting other structure on the Moon. It might be worth adding that there is some small 'single-pass' risk of damage to objects in orbit as outgoing or returning debris passes through their orbits. $\endgroup$ – tfb Nov 24 '20 at 13:39
  • $\begingroup$ Would solar radiation and solar winds give an extra impulse and make smaller particles orbit longer around the moon? And could an impact of larger particle after first orbit set a cascade of and orbit of smaller particles? $\endgroup$ – WOW 6EQUJ5 Nov 24 '20 at 15:15
  • $\begingroup$ @WOW6EQUJ5 those would perturb the orbits, but that's more likely to shorten the orbital lifetime than to prolong it. And collisions will be extremely inelastic and dissipate most of their energy as heat and suborbital debris from both the impactor and ground. It's in principle possible for some material to be thrown back into orbit, but very little compared to the impactor. This is more of an issue for things like natural meteorites that come in on interplanetary trajectories and impact at much, much higher than lunar orbital velocity. $\endgroup$ – Christopher James Huff Nov 24 '20 at 16:42
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    $\begingroup$ @WOW6EQUJ5 Summary: making an orbit is much harder than it looks, which is why we need rockets to execute precisely timed and sized burns to achieve it. The fact that so many man-made satellites orbit our planet incorrectly biases your intuition about how unnatural this process really is. If we had super-volcanoes which could launch rocks up past 100 km, how many orbital rocks would they create? Pretty close to 0, for most all of the same reasons. $\endgroup$ – Lawnmower Man Nov 24 '20 at 21:41
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    $\begingroup$ If and when landings on the Moon become common they will cluster around bases/work areas. One could prepare the landing sites by cementing/fusing/removing dust and debris there, i.e. start building a spaceport. $\endgroup$ – Peter - Reinstate Monica Nov 25 '20 at 12:31

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