I spent a lot of time thinking about this recently; writing new material, reading books and binge watching TV shows.

If space exploration and planetary settlement is spearheaded by private industry (and partially paid for my Earth governments) there will employment contracts and confidentiality agreements, not a Constitution, dictating how those venturing off world life. Space and other worlds (moons and asteroids) would be equal to international waters, lawless places where might makes right and what happened is what whoever with that might say happened. Law will be what a corporation determines it to be. Tyrannical rule akin to saddam hussein could/would flourish as the food, water, communication and even the very air a person breathes is tightly regulated and can be withheld (under voluntary agreement of course) at the discretion of the company.

I contend that freedom in any meaningful capacity would be dead. The idea of Objectivism may be present in space but the practice, like freedom, like the individual and free will, would essentially be dead.