Outer space, including the moon and other celestial bodies, is not subject to national appropriation by claim of sovereignty, by means of use or occupation, or by any other means.
Basically, all countries realistically capable of trying to enforce such a claim are party to the treaty.
So as things stand, nobody can really own any celestial bodies outside Earth.
I imagine that if humanity survives and spreads and starts to have interest in resources elsewhere, that that may change, but as things stand, the effective value of everything up there is pretty much zero, because you can’t own anything other than spacecraft that you launch.
Most countries in the world are party to the Outer Space Treaty:
https://en.wikipedia.org/wiki/Outer_Space_Treaty
Basically, all countries realistically capable of trying to enforce such a claim are party to the treaty.
So as things stand, nobody can really own any celestial bodies outside Earth.
I imagine that if humanity survives and spreads and starts to have interest in resources elsewhere, that that may change, but as things stand, the effective value of everything up there is pretty much zero, because you can’t own anything other than spacecraft that you launch.