I don't think this is going to happen, not in the near future, because of planetary protection issues. If he has a way of dealing with those issues, he hasn't shared it yet.

But I can answer generally - is the same on the Moon or anywhere. No there are no property rights in space.

Even for space mining - you don't get a "stake" on your mine. So far there is no legislation at all to protect space mining. The US bill recently passed just says the US government will stand by their citizens if they mine in space. But it says that it is subject to its obligations by international treaty.

And the US can't claim territory in space either, or support anyone else in territory claims in space, by the OST. I'm not sure the bill actually says anything at all of any substance. It is also a bill that was passed under US constitution using principles that can't be applied in other jurisdictions so doesn't really seem a basis for international law either. Maybe the similar attempt in Luxembourg will be clearer, if it comes to anything because that wouldn't use the US constitution which is rather problematical as a basis for international law.

At any rate it really needs to be an international treaty and so far the only one we have is the OST. And then also the Moon treaty which though it has not been ratified by many countries, still has enough support to count as international law and is the only other treaty we have to help clarify the OST so far, until more treaties are passed.

Anyway property rights are just not possible at all in space, not for celestial bodies. There may however be a possibility of safety zones. The ISS has a safety zone around it - so as long as you live there you have some kind of a safety zone where you are in control of any approaching spaceships. And future law may also establish some kind of a functional right, e.g. to a mine, to keep mining it.

Apart from that, the only thing we have at present is that you own your habitats.

But the habitats may well be the most valuable thing you have. Most places in space are so inhospitable, it really hardly makes any difference whether you own it or not. It's like owning a piece of the Antarctic ice sheet - indeed that would be much more valuable than many places in space.

But habitats - they are very valuable. If you set up a greenhouse on the Moon say - or a telerobotically operated greenhouse using hydroponics on Mars (that much may be consistent with planetary protection if it is done carefully so as not to introduce Earth microbes to Mars) - well the greenhouse is the thing you want to own, not the rocky landscape outside it, lifeless, useless for anything that humans need.

So - those are already yours under the Outer Space Treaty.

The only thing is there is one rather awkward feature. If you leave a habitat on the Moon say, go back to Earth for a holiday - well according to the Outer Space Treaty - other parties can return it to Earth so long as they give it back to you. So if that clause was taken literally - you might find that someone else removes it helpfully, returns it to Earth and gives it to you - deposits it outside your home in Florida or whatever - where it is not much use to you. So - but surely common sense will prevail there. And hopefully in the future additional law can be added to clarify the situation.

I'm sure that in the future there will be much more legislation about this. But that's the situation as present. And it is very difficult to get countries to sign in space legislation. So it's not likely that we will repeal the Outer Space Treaty - the only space law that is passed by all the space faring countries, and ones with space aspirations, even North Korea - with the one exception of Syria which has signed it but not yet ratified it. And most of the non space faring countries have signed it also.

That's a major achievement. So as we move forward we need to work within it.

As I said, it's not nearly so much a drawback as you might think at first, given the harsh nature of space and the value of habitats in space. And the plus side is that nobody needs to worry that the Russians or Chinese or Indians or Japanese or the Americans or Europeans or anyone else will turn around and tell everyone else that they have claimed the Moon or some other celestial body for themselves. That's prohibited in the OST and I think it is good that it is and best it stays that way. It helps with peaceful exploration of space. Before the OST was signed, right up until it was signed, the US had secret plans to build a military base on the Moon which they would man and use to defend the Moon against the Russians.

It may not have been very practical, and it's possible, maybe even probable that they would have never built that base quite as described - but without the treaty then that background suggests that the US would surely have claimed the Moon for themselves when they landed, and it would have lead to a very different future as space history played itself out in that alternative timeline.

I'm glad we are in the timeline where the OST was signed!