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If you assume that the origin of the Moon is due to an object hitting the Earth. The difference between far side and the near side of the Moon can be explained, if the 'chip' knocked off the Earth to form the Moon was partially solid and partially molten. Then you could consider the far side of the Moon being the solid part and the near side being the molten part. So a sample return from the far side would show a difference in mineral mixture.

The question is: why is the far side of the Moon not covered in lava flows? Since we don't have a sample returned from the far side, this is pure speculation...

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    $\begingroup$ Welcome to space! But..what is your question? This is strictly a q&a site. If you're looking for a discussion of an idea you have, this is not a good place for that. $\endgroup$ May 12 at 16:54

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A couple of interesting hypotheses are given for the difference in Why Do We Have a Two-Faced Moon?

Both hypotheses stem from a small planet colliding with Earth - The Giant Impact Hypothesis followed by a period of heavy bombardment by big asteroids.

The first states,

... the impact which formed the Moon actually formed two moons. One was big, and forms the bulk of the Moon as we know it today. But a smaller moon also coalesced out of the ejected material, and was on a very similar orbit to the bigger moon. After some time, the two collided.

But this wasn’t a high-speed impact. Some orbits allow for a low-speed collision, which would be a lot less explosive. If that were the case, the smaller moon would splash, essentially, touching down on the Moon’s far side and flowing like liquid over it. This would create a lopsided Moon, with a thicker crust on one side than the other, as we see things now.

The second hypothesis states,

After the Moon-forming impact, the Earth and Moon were very close together, and both were very, very hot from the impact.

After it first coalesced, the Moon may have only been 20,000 kilometers away, and would’ve loomed huge in our sky.

And it would’ve been hot. The surface would have been molten from the energy of impact, and that means the Earth would’ve been around 2,500° C (4,500° F). It would’ve stayed hot for some time, too.

During that time, the Earth and Moon would’ve been heavily affected by their tides on each other. Tides are complicated (read all about them here), but one effect they have is to slow the Moon’s rotation until it spun once for every time it orbited the Earth, just as it does now. That means very quickly after it formed—incredibly, in just a few months—one side of the Moon would always face the Earth, and one side would face away.

The side facing the Earth would have that huge, glowing hot blast furnace radiating away down on it.

... refractory chemicals (ones that retain their strength when heated) would have gotten mixed in all over the Moon’s surface, but would have preferentially condensed on the far side of the Moon, where it was colder due to the lack of heating from the Earth. These would have formed feldspars (in this case, minerals that contain aluminum and calcium) that would have caused the newly formed crust to be thicker on the far side.

Additionally,

The far side of the moon cooled down, while the near side remained hot.

The temperature difference played an important role in the formation of the moon's crust.

The crust has high concentrations of aluminum and calcium, which are hard to vaporize. Calcium and aluminum would have been the first elements to "snow out" as the vaporized rock cooled, and they would have remained in the atmosphere on the moon's far side. Eventually, those elements combined with silicates in the moon's mantle to form plagioclase feldspars. The far side's crust had more of these minerals, and thus became thicker.

The seas themselves were formed after huge meteors crashed into the moon's Earth-facing side, rupturing the crust and letting the basaltic lava beneath burst forth. The crust on the far side was too thick for the meteors to penetrate, in most cases, leaving the rugged surface we see today.

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    $\begingroup$ This is only one theory. Another competing one is that the Earth-Theia collision created two moons, and they slowly came together and the smaller one splatted onto the big one, leaving a much thicker crust on the far side. That's in contrast to the theory that the near side crust is thinner because it was blasted away by close proximity to a very hot Earth. Either way we shouldn't expect much difference in composition, because all the material came from the same collision. $\endgroup$
    – Dan Hanson
    Jun 1 at 20:32
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I suspect that the exact answer is not entirely clear. The evidence is a bit thin and the event happened so long ago. That said what evidence there is suggests that a Mars sized object hit another larger object (Theia) orbiting close to where Earth currently does. The energy of the collision would have been great enough to entirely disrupt the smaller body and most of the larger body. The larger body formed Earth and the debris ejected formed the Moon. Both bodies were expected to have lava ocean surfaces initially.

I think the key differences between the composition of the Earth and the Moon are far less volatile materials on the Moon and the iron core is far smaller.

The crust is also believed to be thicker on the far side. Consequently it was easier to resurface the near side with magma following large impacts than the far side which is far more rugged.

https://en.wikipedia.org/wiki/Giant-impact_hypothesis

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    $\begingroup$ Yes the crust on the near-side and the far side have the same composition having formed from a magma ocean. It's just thinner on the near side and easier to resurface with new magma following a large impact as can be seen by all the mare's on the near side and there absence on the far side $\endgroup$
    – Slarty
    May 13 at 19:54
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    $\begingroup$ You are correct there has been no sample return from the far side so it is a hypothesis that the two sides have the same composition but it is supported by calculations that suggest the entirely of the Moon would have been covered in a lava ocean following the Theia collision. What evidence is there that the far side was always solid? $\endgroup$
    – Slarty
    May 15 at 11:23
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    $\begingroup$ You are right to say that the Theia collision would have been much larger than the rock that killed the dinosaurs (by a large number of orders of magnitude). So much energy would have been released that it is likely that both the original Earth and Thiea were completely liquified by the collision. as can be seen in this NASA simulation: nasa.gov/feature/ames/lunar-origins-simulations $\endgroup$
    – Slarty
    May 17 at 20:58
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    $\begingroup$ @SRClark I really can't imagine any way for an impact to add enough energy to loft a significant amount of mass into orbit without completely liquifying it in the process. $\endgroup$ May 19 at 5:41
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    $\begingroup$ @SR Clark the first frame displayed is from the middle of the video. If you actually look at the video you can see that both objects start as uniform spheres. But the energy of two colliding planets is so utterly huge that both are liquified by the impact $\endgroup$
    – Slarty
    May 19 at 7:56

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