Future astrobiological activities and discoveries, along with other human activities in the transnational domain of outer space, will require the development of political institutions able legitimately to speak for humanity as a whole. I identify a range of possibilities, including the formation of a world space agency and a strengthening of the UN system; but I argue that ultimately the logic points in the direction of bringing space exploration within the remit of a federal world government, the creation of which would also be desirable for other reasons. Although, at present, humanity lacks a sufficiently strong sense of global community for the formation of strong global political institutions, I argue that the cosmic and evolutionary perspectives provided by astrobiology and related disciplines can help lay the psychological foundations on which such institutions may be built.