My own personal belief is that no particular nation has any right to claim land or sovereignty anywhere in space.
Any claim on any unclaimed/uninhabited Moon/planet/asteroid etc or even region of space, needs to be made in the name of all the people of Planet Earth.
When it comes to space, there should be no 'Americans' or 'Russians' or 'Chinese' or 'Indians' etc.
In space we are Earthlings (or Terrans).
But it won't happen
The problem is that because America is losing its status as the so called 'Policemen of the World', they want to establish themselves as the Policemen of Space.