Measured density of Moon: 3.344 g/cm^3
Assuming the moon was a hollow sphere with 50 miles of surface (a nearly impossible megastructure), compared to a solid moon which is 1079 miles in radius. Assuming uniform distribution of materials, the moon would need to be 7.53 times denser to retain the same physical properties. This puts the material that it would be made out of at 25 g/cm^3.
Which is about 3g/cm^3 higher than iridium, which would make it the heaviest nondegenerate stable matter we that know of. The structural strength of this unobtanium would need to be incredible as well. Very large objects with significant gravity have a tendency to collapse on themselves. We know the surface gravity of the moon to be 1.624 m/s^2, which means that a 1 kilogram weight on its surface will exert 1.624 N. Let's take the outermost layer of this sphere, the first mile of our 200 mile thick surface. Turns out to mass more than the Earth's oceans put together. (Admittedly, the actual weight is a bit lower). Consider that the Earth's oceans are 3 or 4 miles deep on average, and that they cover most of the planet. Now consider that this is just 1 mile of material in our shell. The mechanical requirements here are beyond my ability to calculate, but I can assure you that it's quite implausible that the material unobtanium even exists, and that it can also withstand its own weight. Steel can't, after all.
Furthermore, yes, rotational inertia can be applied to this to say that even if it is hollow then it must be much less hollow which means that unobtanium is much less dense and thus probably much weaker structurally (density and strength are at least loosely related) and would be even more prone to collapsing.
A side note: As far as the universe cares, we are insignificant yet surprisingly arrogant little apes. We are, as far as we know, in no way special. The probabilities that more advanced alien life exists out there are staggeringly high, the fact that we haven't encountered them yet is merely a testament to "Space is big". The chance that they care about us in particular, on the other hand, is staggeringly low. What if they're Tyranids? Scary thought.
Last edited by suomynona; Jan 8, 2011 at 07:35 PM.
Reason: Spelling.