It will only matter when it matters, and then all the blathering people did when it didn’t matter won’t matter.
No, we’re not going to give Elon Musk ownership of Mars just because he lands a probe on Mars. We’re also not going to give Elon Musk ownership of Mars even if he lands there in person.
Setting foot on a place doesn’t mean you own that place. And neither did that rule apply in the Colonial Era. What mattered was whether you had an army and navy ready to enforce your land claim. Lots of explorers landed in lots of places and claimed those places for lots of places. Didn’t mean a thing until guys with guns showed up.
Ownership isn’t a metaphysical property. It’s a question of whether you can effectively control a thing yourself or with the help of your friends. If you can, then you own it, because nobody else can do anything about it. If you can’t, then you can complain about it, but if you can’t convince the rest of us to help you then your ownership claims don’t mean a thing.
So I can declare I own Mars tomorrow, and even type up a nice certificate. And that means what? It means nothing. It means nothing today because there’s no dispute over Mars or parts of Mars that can be resolved. If I could call the cops and they’d go over to NASA and arrest the engineers putting together Mars missions, then my claim would mean something. But since I can’t, it doesn’t.
And if Elon Musk lands on Mars the day after tomorrow, the cops aren’t going to march over to NASA to arrest anyone either. He can claim Mars, but unless there’s a dispute between people that other people care about, his claims mean nothing.
It’s when you have two Mars bases and they argue over who gets to mine in which canyon that property rights on Mars matter. And what really matters is what the guys on Mars actually do. If a court on Earth rules that Mars Base Alpha owns a particular crater, but the guys at Utopia Planitia Commons don’t listen to that court, then the rulings of that court are irrelevant. The court has to have some way of enforcing their ruling that the guys at Utopia Planitia will listen to.
And so the current state of property rights in outer space are that most countries have agreed for the time being that they will not recognize any such rights. So if you want to set up a mining operation on the Moon, you’re going to have to enforce your claim yourself, because no government on Earth will do it for you. The good news is that if you set up a mining colony on Mare Crisium, there isn’t anybody who can stop you either.