It says that when calculating gravitational pull on an object by the Moon(or any other spherical body), it doesn't matter whether the mass is contained in a single point in its centre(the so-called "point mass"), spread uniformly throughout its volume, or contained in a shell of arbitrary thickness. The effect is the same in all those cases.
Should you decide that the Moon is hollow inside, you just need to take its mass(~10^23 kg), and divide it by the volume of the shell(volume of the sphere with R=actual radius of the Moon [~2'000'000m] minus volume of the hollow space inside[let's say it's r = 1'000'000m]) [pi is approximated to 3 in the following calculations]:
density=10^23 / (4/3*3*(8*10^18) - 4/3*3*(1*10^18)) = 10^23 / (8 - 1)*4*10^18 = 10^5 / 21 =~ 5000kg/m^3
...or roughly the Earth's for a 1000km thick crust hollow Moon.
Let's make that equation more general by expressing the radius of the hollow sphere inside the Moon as a fraction of the radius R (r=R*a; where a is in the range of (1, 0)):
density=10^5 / 32*(1-a^3) = 3000 / 1-a^3 [kg/m^3]
substitute e.g. a=9/10 for a 200km thick crust and you get:
density= 3000 / 1-(729/1000) = 3000 / (~3/10) = 10000 kg/m^3
...or roughly the density of silver.
Thanks, that was all very interesting and Informative.
The problems start when you try to explain the physics of such hollow Moon's existence. How come the shell doesn't collapse under its own gravitational pull? How could such a Moon ever come into being? Certainly not by accretion of material.
The physics would be improbable. Leaving only artificial methods, which, according to history are most unlikely and as well. It would be a fun thing to build a computer model, or see if it could be engineered on paper though. Or simulated. Also drilling or digging into the moon would illuminate this process. So to "know for sure" is a good reason enough for me to advocate real effort here on our part =) Time for a moonbase!
Additionally, MASCONs do not support your hypothesis in any way that I could imagine. Your assertion that "MASCONs therefore Hollow Moon" is completely arbitrary and unsupported.
Correct, my assertion is wrong by itself because many things could cause MASCONs. They still may be an indication of potential hollowness, or be one side effect of such. Its a bit like saying an orange tastes sweet, therefore it has sugar. While this is proven to be correct, one might call it fructose, also, it might be a genetically engineered orange that has splenda instead... They are not evident at altitude, but greatly effect low orbiting satellites, which leads me to believe whatever is causing the increased gravity is not very far beneath the surface as apposed to what might be at the center. If mars is an indication you probably can have MASCONs without a hollow center. I can believe Mars is solid through and through much easier then the moon. Yet there are debates still over the hollowness or not of even earth... A very thick crust can be deceptive. Or a liquid core for our planet seems more feasible. I just logically think the moons MASCONs illustrate the greater possibility for it to have such an anomalous structure. Like I said before much more engineering, modeling, simulation, or investigation would be nice in knowing with a certainty. So my assertion could be restated as MASCONs increase the possibility that the moon is hollow. It would be less evidence if the moon was known to have a uniform structure.
The current view is, that they're remnants of dense impactors(Moon is quite a bit less dense than your common asteroid) that have not been fully "assimilated" due to lack of active tectonics, which fits nicely with their presence on Mars as well as lack of such on Earth and Venus.
That's pretty much my assumption, if it is proven conclusively to be solid and formed from a cooled molten core
I haven't decided. Need more data. Eventually if we get the chance we may collectively know for sure by the end of the century.
What else? If you don't like wikipedia, grab a uni-level book or browse online resources.
Cornell University's Curious About Astronomy is a very well written site to start with.
Hyperphysics is maintained by Georgia State University and has a good section on astronomy/cosmology/astrophysics among others.
Physics forums are rife with people asking questions and providing answers to those, so you should be able to find lots of non-technical explanations there.
Good advice. I felt like dropping it here because Bay12'ers are serious nerds, and I figured I would get some interesting responses.
It actually does make some sense.
The prevailing theory for the moon is that something big hit the earth a long time ago. This shot a large chunk of mass up into orbit around the earth which eventually coalesced into the moon. Now, this proto-moon, would have originally been molten material, the smaller chunks cooling a lot faster than the larger chunks. The larger stuff formed together in a big blob, but since the earth was there, with it's not insignificant gravity well. The mass of the moon is slightly lop sided towards the earth. This is also why the moon is "tidally locked" with the earth. That is, the same side of the moon always faces the earth. Now, while the moon was most of it's current size, but was still cooling internally, some large things hit it, puncturing the cooler surface crust, and allowing the still hot center to flow up, forming the darker seas. This would make the darker areas significantly more massive than the lighter areas which are mostly less dense rocks which tended to float to the surface as the moon was originally cooling.
The earth doesn't have anything all that pronounced, mostly because our core is still molten and it's not being affected significantly by a larger gravity well. However, there are differences in the gravity across various places on the earth. If you look at the earth, it's not a perfect sphere. This is because it's constantly spinning. The equator spins faster than the poles, so the whole planet is slightly smushed, as if someone took it between two hands at each pole and pressed it a little flat. Now, if you measure the gravity at the equator vs the gravity at the poles, you'll notice a slight difference. Wikipedia suggests that gravity exerts a force of roughly 9.78 m/s^2 while at the poles it's roughly 9.83 m/s^2 This may or may not be what you're looking for though, since this change can generally be attributed to spin and distance from the core rather than any "lumpiness" of the gravitational field.
I don't pretend to know everything, but it seems as if there are plausible explanations out there, even if we can't prove any of them. It's not as if we're still on the moon to do experiments.
Also, if you really want to know more about the cosmos. Why not check out a college or university level astronomy class. The number of professional astronomers in the world is shockingly low and if you manage to find a class taught by one, it's almost guaranteed to be interesting and informative. Plus, if you're not talking graduate level classes, it's much more likely to be comprehensible information than the scientific papers that are published. I will say that the astronomy class I took was really the most fun class I took in college, taught me the most, and spurred me on to do more of my own study than anything else. And it had next to nothing to do with my major. I know some people were bored and only took it for the elective credit, but the enthusiasm and knowledge my teacher displayed kept me interested the entire semester.
I thought about that as well. Its a safe assumption to make. The fact that the moon is tidally locked to us may be good evidence for it having been formed in our gravity well.
I agree with both of you that college can be a good start to learning this stuff. Professors usually have connections to sources of information on special topics pertaining to their fields that most don't readily have. To be honest though, I tried college, burned out, and figured I was not really made for it. I was an IT major, and ended up only finishing my welding classes. Though I had a productive 7 years in IT anyway without a degree. If I had plenty of free time and money to spend I would go to school for some fun classes for sure. That is time I have to make, and for now I have the free time to debate on a few web forums
Also I really wish I could reverse engineer and understand those equations for finding the density of silver for a 1000km thick crust. I had a basic understanding of algebra over 10 years ago, now I struggle to do foil without a textbook next to me. I think its important to point out that it could be a bubble of crystallized quartz or quartz bearing rocks, though that is less dense then silver (just an example here), something like a mixture of elements in a compound or mineral would more likely occur naturally. Some kind of silicate glass might even be better. Or something like Osmium. I am no materials scientist though and I am not even going to postulate on what would be the best material, natural or artificial to support a hollow moon =) I cant even give a really good guess at what might make a naturally occurring hollow sphere in the vacuum of space at those scales haha. But its fun to think about. Maybe one day.... Then they're will be something better to test against.
Just for fun with some imagination I can picture a huge comet hitting the earth with enough force to pull away some of the molten crust. Then having the the molten material spinning rapidly with a cloud of extremely hot water vapor which it then might cool around, compress and keep hot enough to provide pressure. There might not be enough material to collapse it as it cools. There's always the possibility of shattering and fracturing during the cooling process, allowing some material to escape and leave, or collapsing the thing entirely. Depending on what materials it should be made out of we could figure out if its the right size or not to be solid. I think we've made some good guesses based on gravity in general, but its always hard to know for sure. I'm pretty sure the studies I have seen on what the moon is made of simply assume it is solid, leaving them as untested theories or hypothesis on their own. We know whats on the surface, at least according to NASA, I think they have found ice, or some helium isotopes there through satellites, but I'm not 100% sure (or hydrogen, been watching to much Star Trek). I would in this regard need to break out the books and learn all I could about the competing theories on lunar geology to make another guess. Again, being there, and having samples is the best way of knowing for certain =)
My lack of knowledge probably illustrates my skepticism for what we do know, because allot of it I don't fully understand, most of it I heard from Nova and stumbling upon the random articles around the web, reading pop-sci or National Geographic.
Ham radio operators have been bouncing radio waves off the moon for a long time, there is some data on that. I wonder what kind of materials might resonate at what frequencies? Sonar/radar would be a good way of guessing at whats inside. Particularly when coupled with other theories and gravity/density/mass stuff. I have heard less reliable sources (have not personally checked citations and such) claim that the Moon has a very odd resonance (which does not fit the standard idea of lunar "geology". But haven't had the time to research it further.
It just dawned on me, that you could think of a process like forming a giant
geode or
nodule. For how a hollow moon might form. Though geodes don't form from accretion.
Thanks for your input =)