Law doesn't come from (or shouldn't come from) unqualified legislators guessing about what the future will be like and what problems will be there. Law comes from when somebody has a grievance against somebody else, and society steps in to resolve it. Could you imagine how bad it would be if Congress got excited about the potential for internet crime in 1985, tried to guess the form of the problems that would arise,…
Is it much different than the laws of the sea? Sometimes laws spur innovation. If the law is: first one to establish a base owns it then there will be a lot of effort put into establishing a base.
Personally, I think land ownership claims around unmanned probes, rovers, and stationary facilities should be kept small, and claims around manned homesteads should not be more than about a mile radius or so, probably less. In the beginning, I think it's good to have policies that encourage settlements with different owners to be located close together, without anyone becoming a real-estate baron. The best land should go to those who have the ability to actually use it, not real-estate speculators.
See also: https://xkcd.com/2125/ as an example of how land claims shouldn't work.