In the end, like here on Earth, the moon will belong to whomever can hold it through force of arms.
I find it funny that they still teach that gravity directly causes fusion in the sun. Long before gravity can squish two protons together, hydrogen will be torn into it's basic components: protons and electrons. This occurs at a rather low energy state (relatively speaking).
Once that occurs, you now have the fact that protons are more than 1800 times the weight of electrons, so gravity causes the electrons and protons to separate. This results in HUGE electric fields inside the sun. It's these incredible electric fields that cause fusion to occur.
Instead of trying to make high-density plasmas, they should have been working on electric fusion devices, like the Farnsworth–Hirsch Fusor.