While the laws of physics most often govern what happens in outer space, there is also some international law that applies. The "Outer Space Treaty," which was signed and ratified by the United States and many other countries in 1967, limits its signatories' ability to place nuclear weapons and other weapons of mass destruction into orbit around Earth and other celestial bodies. It also reserves Earth's moon and other celestial bodies for peaceful purposes. Although seemingly aspirational in nature, the Treaty has been honored over the last 49 years allowing the U.S. and Russia - occasional terrestrial enemies - to collaborate in space.
For more on this document, visit the Outer Space Treaty page from the U.S. Department of State. You can also see a reproduction of the Treaty and the signatures of several member countries in the Law Library's lobby throughout Space Law Month - August 2016.