There is not much of a government in Prometheus; they are too far away from Earth to send messages, and the only authority is the company that funded the expedition. By current laws, they are still beholden to their State government. Article VI of the Outer Space Treaty States:
States Parties to the Treaty shall bear international responsibility for national activities in outer space, including the Moon and other celestial bodies, whether such activities are carried on by governmental agencies or by non-governmental entities, and for assuring that national activities are carried out in conformity with the provisions set forth in the present Treaty. The activities of non-governmental entities in outer space, including the Moon and other celestial bodies, shall require authorization and continuing supervision by the appropriate State Party to the Treaty. When activities are carried on in outer space, including the Moon and other celestial bodies, by an international organization, responsibility for compliance with this Treaty shall be borne both by the international organization and by the States Parties to the Treaty participating in such organization.1 (emphasis mine)
However, even in current times, ships at sea don’t really have much legal oversight. A New York Times article describes how “laws are … often weak, contradictory and easily skirted by criminals. National and international agencies usually have neither the inclination nor resources to enforce them.” 2 Given that Prometheus takes place 35 light-years, or 2 years travel, from Earth, the actual likelihood of enforcement is extremely small. From this, we conclude that there can be no issues with “Privacy and the Government”, as there is no government. For privacy issues in general, see Information Privacy.
Treaty on Principles Governing the Activities of States in the Exploration and Use of Outer Space, Including the Moon and Other Celestial Bodies, Jan. 27, 1967. Retrieved September 17, 2017, from https://www.state.gov/t/isn/5181.htm ↩
Urbina, I. (2015, July 17). Stowaways and Crimes Aboard a Scofflaw Ship. Retrieved September 17, 2017, from https://www.nytimes.com/2015/07/19/world/stowaway-crime-scofflaw-ship.html ↩