Undoubtedly this will lead to Space Pirates of the Mark Watney (The Martian) kind:
“I’ve been thinking about laws on Mars. There’s an international treaty saying that no country can lay claim to anything that’s not on Earth. By another treaty if you’re not in any country’s territory, maritime law aplies. So Mars is international waters. Now, NASA is an American non-military organization, it owns the Hab. But the second I walk outside I’m in international waters. So Here’s the cool part. I’m about to leave for the Schiaparelli Crater where I’m going to commandeer the Ares IV lander. Nobody explicitly gave me permission to do this, and they can’t until on board the Ares IV. So I’m going to be taking a craft over in international waters without permission, which by definition… makes me a pirate. Mark Watney: Space Pirate.”
I would imagine that companies and people would also be prohibited from making these claims.
But I do believe that is going to be ineffective for the future. Progress would be very slow if there is nothing to claim on Mars, or another celestial body for that manner.
A very interesting discussion, as I do see this treaty changing in the future, but whether it will be country oriented or market oriented will be the big question that defines humanity's voyage outside earth
The Moon Treaty explicitly forbade private property on the moon, but by implication it means that private property is still possible under the Outer Space Treaty.
Also, the United States did not ratify the Moon Treaty. It is in force for the 13 signatory nations, but none are space powers.
“I’ve been thinking about laws on Mars. There’s an international treaty saying that no country can lay claim to anything that’s not on Earth. By another treaty if you’re not in any country’s territory, maritime law aplies. So Mars is international waters. Now, NASA is an American non-military organization, it owns the Hab. But the second I walk outside I’m in international waters. So Here’s the cool part. I’m about to leave for the Schiaparelli Crater where I’m going to commandeer the Ares IV lander. Nobody explicitly gave me permission to do this, and they can’t until on board the Ares IV. So I’m going to be taking a craft over in international waters without permission, which by definition… makes me a pirate. Mark Watney: Space Pirate.”