Dozens of people have historically claimed ownership of planets, stars and more. Some notable examples including Dennis Hope successfully turned it into a full-fledged business and made a fortune. However most claims were made in an era in which no one was actually living on the objects being traded. That might soon no longer be the case and space colonialism may become a reality.
When some individual or company decides to actually build structures and/or send humans to live in the moon, are they obliged to research the entity that "purchased" the piece of land from Hope or others and buy ownership? If they ignore those and occupy the land anyway, can the "owners" file a lawsuit and prevent them from doing so? Are the "rightful owners" authorized to use force to repel machinery and unrecognized people from entering their land?
What international body, if any, would settle extraterrestrial property disputes between multiple people from different countries? For example, US citizen X's claim that they own a specific portion of Mars holds up in a US court. Russian citizen Y's claim to the same region holds up in a Russian court. Both send unmanned vehicles to probe the land and prepare for further colonization. The two vehicles contest the area. Which body should they contact to decide who owns the land? Would the owner be whoever landed faster? Do their vehicles fight until one is fully destroyed? Or are both claims void according to the UN's Outer Space Treaty of 1967?