Can there be any minerals or precious metals on the moon.

If the moon is a piece of earth that broke up could their be gold and diamonds on the moon?

Yes, but the lack of techtonic activity would mean it is unlikely that any deposits will be found. Without something stirring up the crust constantly it is difficult for stuff to be concentrated in any given location. Any elements are likely to be evenly distributed and not worth the cost of extraction, much like the old statistics about the amount of gold dissolved in the oceans.

Gold and other metals, yes, but not in easily mined form - sedimentary, metamorphic and hydrothermal processes go a long way towards making deposits of sufficient concentration to be mined here on earth. The moon doesn’t have those. Diamonds - not sure. Some of the phase transitions and conditions that make diamonds are theorised to be closely linked to plate tectonics, and the moon doesn’t have that, either. Certainly there’d be carbon there, and diamonds way down deep, but anywhere you can mine them? I doubt it.

Plus the moon has a lower density than the earth, which means it has a lower concentration of heavy elements and a higher concentration of lighter elements.

I’m sure there are plenty of minerals up there, but it’s not like we should expect gold nuggets lying on the ground. And it takes a couple billion dollars to send people to the moon, so how many diamonds do you have to bring back every trip to make it profitable?

Fact is, one of the “forces” behind the push to visit other worlds, including asteroids, is the interest in exploiting them for their natural resources for the benefit of mankind. Cynics might suggest that there is a simpler, more personal drive behind this type of exploration, similar to the push to discover oil, for example, or diamonds. (Don’t want to leak into politics here).

The light elements, like Helium-3, might be much more valuable.

Wouldn’t lower gravity and lack of environmental restraints (i.e., tailings can go anywhere) tend to offset the cost of extraction?

Wouldn’t it have to in order to offset the bajillions spent on getting to and fro, maintaining working environments, werewolf insurance, etc.?

You still have to deal with Earth’s gravity for getting equipment up to the moon and then some sort of a system to bring the material back to Earth in reasonably sized re-entry cargo vehicles. If you wait long enough for the technology to build a space elevator to become feasible and maybe the costs of moon/asteroid mining become more manageable.

The moon is not just a chuck of earth, it’s a chunk of the earth’s crust. This is important because the earth’s core has different composition than the crust. So while the earth has molten iron at the center and a large magnetic field, the moon has neither.

The moon will be more useful for its water at the poles (if there really are good supplies there) and components for propelents for future voyages than for any “precious” minerals.

Googling mining the moon brings up a number of useful resources.

Popular Mechanics

Space.com

Gold and diamonds? No. No matter how many bad sci-fi movies you’ve seen, there is no romance in space. It combines the worst features of the Gobi Desert, the Antarctic, and the top of Mt. Everest.

There’s been plenty of time since the moon formed for impacts by metal rich asteroids of the type which formed the Sudbury basin in Ontario.
Maps of Lunar mascons may even show us exactly where to look.

Keep in mind that you’ll be working in a vacuum, so there’s no water available. All machinery lubrication would need to be sealed to avoid boiling off, and any excess heat can only be disposed of by radiation or conduction, rather than convection. ie: typical air cooled radiators wouldn’t work at all, and any moving parts would risk overheating quickly and seizing. This would pose serious constraints on your ability to move vast quantities of matter using conventional mining equipment designs.

There is certainly gold, although probably in the same trace amounts found in the Earth’s crust. Diamonds are a bit more questionable, but still possible. If it is mineral wealth you are after, however, it is far more accessible in the asteroids in near orbit of the Earth and the asteroid belt. Based on the minerals content of meteors, many asteroids have high concentrations of not only iron, nickel, copper, and other valuable commodity metals, but also more rare earth elements, and would be much easier to mine than the Moon; basically, blow them apart (or melt them, using concentrated sunlight) and extract the valuables, then plate the remaining sillicate slag around your spacecraft as armor against solar radiation.

Of course, this makes it all sound very simple. In reality, this is several decades worth of development in spaceflight and vacuum industry technology. And the end result, instead of ending up with a lot of monetarially valuable mineral commodities, is to glut the market so that the value of all minerals drop dramatically. (This is assuming that your space mining interest isn’t controlled by some cartel which doles out materials at just enough of a rate to make buckets of money without undercutting the market.) While mining in space might offer some benefit to Earth (we’re down to about 60 years of known copper reserves, assuming current usage and recycling rates) the real benefit is to inhabitants of space themselves who, once they have developed the necessary industrial infrastructure, won’t have to import goods and materials from Earth or some other planetary body at great effort and expense.

So I wouldn’t go investing in any Moon-mining speculations. The Moon is visible and relatively easy to get to, but if you want to build serious permanent space industries you’re going to be sifting your elements from floaty stuff, not out of gravity wells.

Stranger

As I understand it, they use graphite-based lubricant on machinery that has to work in a vacuum. But it’s not a perfect replacement for petroleum-based lube. For instance, it doesn’t stick to the parts it’s lubing as well, so vibration can cause it to fall off. [This is what is thought to have caused the malfunction in the deployment of the high gain antenna on the Gallileo mission to Jupiter.]

Once again, the problem comes in that the actual meteorite itself isn’t the source of the minerals - post-impact magmatism is what forms the ore-body itself, same as the Bushveld I.C.. A large part of the ore body genesis in both complexes is gravitationally-driven fractionation. Different gravitational pull = different processes. We can’t say that the same or similar processes would happen in Moon impacts.

The Sudbury Igneous complex is not like Bushveld:

Timing of sulphide saturation and ore formation in the Sudbury Igneous Complex

Ha! Primitive man-animal! That’s just what your future Psychlo overlords want you to think!

They are both mineralized layered igneous complexes associated with bolide impacts. That the Bushveld has a larger mafic component is to be expected given the larger size (hence, depth) of its impacting body. But the important point? They are both gravitationally-fractionated ore bodies. From your own quote, my bolding:

My point is that we don’t know how this particular form of ore seperation would work on a different world.

I’d think that the important point would be that in the case of Sudbury, the actual meteorite itself is the source of the ore.
It’s not come up for the mantle as it did at Bushveld.
Whether gravitationally driven fractionation of sulfides occurs on the moon or not, and I would think not given the absence of water, the ore body is there, supplied by the meteor.