The Treaty on Principles Governing the Activities of States in the Exploration and Use of Outer Space, including the Moon and Other Celestial Bodies (the "Outer Space Treaty"), adopted by the General Assembly in its resolution 2222 (XXI), opened for signature on 27 January 1967, entered into force on 10 October 1967;
States Parties to the Treaty shall bear international responsibility for national activities in outer space…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… shall require authorization and continuing supervision by the appropriate State Party to the Treaty. (Art. VI).
A State Party to the Treaty on whose registry an object launched into outer space is carried shall retain jurisdiction and control over such object, and personnel, while in outer space or on a celestial body. Ownership of objects … is not affected by their presence in outer space or on a celestial body or by their return to the Earth. (Art. VIII).
The above parts of the Outer Space Treaty were the precursor for the Registration Convention which further outlines the responsibility of nations who send objects and people into space.
The Convention on Registration of Objects Launched into Outer Space (the "Registration Convention"), adopted by the General Assembly in its resolution 3235 (XXIX), opened for signature on 14 January 1975, entered into force on 15 September 1976;This treaty was developed to provide for the national registration of objects launched into outer space, establish a central register of objects launched into outer space, and provide additional means and procedures to assist in the identification of space objects.
[T]he launching State shall register the space object by means of an entry in an appropriate registry which it shall maintain. Each launching State shall inform the Secretary-General of the United Nations of the establishment of such a registry. (Art. II).
The contents of each registry and the conditions under which it is maintained shall be determined by the State of registry concerned. (Art. II)
In 1984 the U.S. Congress passed the Commercial Space Launch Act, Pub. L. No. 98-575, 98 Stat. 3055 (1984). This Act and its amendments were codified in Title 49 of the U.S. Code. Then in December 2010 Congress consolidated all U.S. space laws into the new Title 51 National and Commercial Space Programs, Pub. L. No. 111-314, 124 Stat. 3328 (2010). The Commercial Space Launch Act is now codified in chapter 509 of title 51. This is where the Department of Transportation is designated to regulate the commercial launch industry. The Office of Commercial Space Transportation (AST) was transferred to the Federal Aviation Administration (FAA) in 1995.
The regulations based on the Commercial Space Launch Act are codified in the Code of Federal Regulations (CFR) in Title 14, chapter 3 (14 C.F.R. § 400.1 (2012)). Here is a list of where to find the various regulations within Title 14:
Part 413-LICENSE APPLICATION PROCEDURESPart 414-SAFETY APPROVALS
Part 415-LAUNCH LICENSE
Part 417-LAUNCH SAFETY
Part 420-LICENSE TO OPERATE A LAUNCH SITE
Part 431-LAUNCH AND REENTRY OF A REUSABLE LAUNCH VEHICLE (RLV)
Part 433-LICENSE TO OPERATE A REENTRY SITE
Part 435-REENTRY OF A REENTRY VEHICLE OTHER THAN A REUSABLE LAUNCH
Part 437-EXPERIMENTAL PERMITS
Part 440-FINANCIAL RESPONSIBILITY
Part 460-HUMAN SPACE FLIGHT REQUIREMENTS
It appears that the FAA's jurisdiction is over the launch and reentry of space vehicles and not over activities once in orbit.