Who Owns The Moon?

The flags of two countries hang unfurled — not by any breeze but by metal wiring — over the desolate, eerily still surface of the moon. One is the stars and stripes of the United States; the other, the crimson of China. But if you ask any official from these countries, they will tell you that these flags do not represent a property claim of any kind. They're more like extraterrestrial graffiti.

But if planting a flag on the moon doesn't count as a property claim, then what does? And when you get down to it, can anyone actually own the moon? Does anyone have sovereignty over the moon?