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There is the strong theory that the Earth and the Moon were part of the same core at one point. This would lead one to believe that there are precious minerals under the surface of the Moon.

Metals are normally heavier than dust and we don't want to send the moon out of orbit, so when we mine the moon we intend to put back as much mass as we take.

Will this prevent the Moon from going out of orbit?
What other astronomical challenges would we face?

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Little to no effect incurred by mining

The mass of the moon is about 7.3×1019 metric tons. That means if we removed a billion tons of mass from it every year for a billion years, we'd have removed about one-seventieth of it. We can make no significant different to the mass of the moon with any plausible mining operation. And its orbit doesn't depend very much on its mass anyway. There is absolutely no need to ship rocks from Earth or elsewhere to replace mass we remove from it, and that would also make mining the moon far more expensive.

More useful leaving it in space

The only plausible good reason for mining the moon would be to get materials for large-scale construction in space, because lifting them off the moon is far easier than from Earth.

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    $\begingroup$ To put this in perspective we apparently (wikipedia) mine about 8 billion tonnes of coal and 3 billion tonnes of iron ore per year (my guess of the two biggest easy-to-find mined materials). Of course there's no coal on the moon, but to remove 1/70 of the moon's mass in a billion years would take something like 1/10 of our mining capabilities on earth, which is easy $\endgroup$ – Chris H Sep 2 '16 at 13:23
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    $\begingroup$ I think we'd be unlikely to carry on mining the moon alone for a billion years. $\endgroup$ – John Dallman Sep 2 '16 at 13:29
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    $\begingroup$ "doesn't depend very much on its mass anyway." - I think actually if the moon was replaced by a pebble, it would stay in the same orbit. Orbit is totally independent of mass. $\endgroup$ – Jonathan Hartley Sep 2 '16 at 15:51
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    $\begingroup$ I don't want to claim there would be no effects at all. The tides would be reduced if the Moon lost a lot of mass, and that would affect the slow changes in the Moon's orbit. $\endgroup$ – John Dallman Sep 2 '16 at 16:25
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    $\begingroup$ @JonathanHartley You are right, and I think the misconception that a lighter moon would change orbit (probably "fly away"??) is at the heart of the OP's question. John's "tide" objection is probably almost wrong; the moon's orbit slightly increases over astronomical time scales because it sucks away earth's rotational energy via tidal forces. But I don't think the (already minimal) effect would be much smaller or larger with a smaller moon. $\endgroup$ – Peter - Reinstate Monica Sep 2 '16 at 18:12
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Valuable minerals are rare compared to regular rock on earth.

If it is the same on the moon, the amount of mass taken away by mining will be insignificant beside moon's total mass.

Moreover, when you consider the mass added by mining (miners will need infrastructure to work properly and generate waste during their stay), the mass ratio after mining/before is even lower.

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    $\begingroup$ In fact, if it is refined up there as well (which makes sense because it's much cheaper to bring back 1 kg of iron rather than 10 kg of ore) the mining operation is probably leaving more mass up there than it is bringing back $\endgroup$ – Annonymus Sep 2 '16 at 11:02
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    $\begingroup$ I'm not aure if @Annonymus's totals would work, but there's a need for oxygen on the moon, and most refining operations would produce oxygen (they'd have to unless you shipped loads of coal up there to produce CO2 instead from all the oxides) $\endgroup$ – Chris H Sep 2 '16 at 13:25
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    $\begingroup$ Yeah, but it means you've only taken away 1 kg of mass rather than 10 kg. The mass of just the refined ressource is smaller than the mass of all the stuff that is brought up to the moon for various uses (Oxygen, water, pieces of our method of transport, food etc.). $\endgroup$ – Annonymus Sep 2 '16 at 14:08
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    $\begingroup$ @Annonymus So that's what you mean. I'm not quite sure I agree. Oxygen and Water can be recycled, food can be grown with the proper facilities, and the facility could be mostly or completely automated to remove the need for food and water all together. Structures on the moon (Not air-tight buildings, built-things-that-stand) can be built lighter, cheaper, and easier, because the moon only has 1/6th earth gravity. Same goes for vehicles - an earth bound F150 can hold a little under 2 metric tons in the bed, on the moon the exact same truck could hold 12. $\endgroup$ – UIDAlexD Sep 2 '16 at 14:18
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    $\begingroup$ If the total mass of your mining equipment is more than the total mass of material you extract, then depending what you're mining you may be doing it very, very wrong ;-) $\endgroup$ – Steve Jessop Sep 2 '16 at 14:44
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There is the strong theory that the Earth and the Moon were part of the same core at one point. This would lead one to believe that there are precious minerals under the surface of the Moon.

Actually, the theory isn't quite like that. The leading theory for the formation of the Moon is of two proto-planets colliding to form the Earth and Moon system. The collision left the main planet (Earth) in-tact, but a large volume of debris in orbit. After the collision, the heavy material that was ejected sank back down to the primary body (Earth), while the lighter debris material stayed in orbit and went on to coalesce and form the Moon.

The result is that the Moon has a much lower density than Earth, and a much lower concentration of heavy elements. In addition, the lack of vulcanism on the Moon means that those heavy elements that did end up forming it are mainly deep in the core, making them inaccessible to mining.

Metals are normally heavier than dust and we don't want to send the moon out of orbit, so when we mine the moon we intend to put back as much mass as we take.

Seriously, the Moon isn't going to worry about a bit of mining -- it may be smaller than the Earth, but it's still a very very large body.

The Moon's mass is 73 quintillion metric tonnes (ref). You could take a 100 billion tonnes off it, and you'd barely cause a rounding error in that figure.

More significantly, if you're thinking of replacing the material that you extract... what exactly are you going to replace it with? Virtually any Earth rock you could think of (even the 'worthless' ones) would have more mineral value than the Moon rocks you're mining.

Will this prevent the Moon from going out of orbit?
What other astronomical challenges would we face?

No it won't.

Your biggest astronomical challenge will be if you think you're going to be able to transport all that mined material off the surface of the moon.

You would certainly be looking at an astronomical amount of rocket fuel!

You would be much better off leaving the mined material on the Moon and building things with it in-situ.

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    $\begingroup$ The heavy material fell out of orbit and the lighter stuff stayed up?! Um, well, I'm no expert but can we have a bit of clarification of mechanism there? — I've assumed (or maybe heard) that the Moon is less dense because the parent body was already differentiated and the lighter matter was preferentially affected by the glancing blow. $\endgroup$ – Anton Sherwood Sep 3 '16 at 4:45
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There are sensible and knowledgeable answers here to the effect that our mining operations won't affect the mass of the moon much. I do not disagree with that, but it is irrelevant.

Even if we invented a magical process to turn moon rocks into diamond and rocket fuel, and depleted the mass of the moon to half building a Dyson sphere, it would make no difference to the orbit of the moon. The shape and speed of an orbit depends on the body's velocity alone, not its mass.

Such drastic decrease in the Moon's mass would decrease the tides in Earth's oceans, which might be ecologically catastrophic, but we'd probably do it anyway, with our track record. But this wouldn't be caused by changes to the Moon's orbit.

Remember that astronaut dropping a hammer and a feather in sync? Same deal.

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