The geodetic precession as a 3D Schouten precession and a gravitational Thomas precession

The Gravity Probe B (GP-B) experiment measured the geodetic precession due to parallel transport in a curved space-time metric, as predicted by de Sitter, Fokker, and Schiff. The Schiff treatment included Thomas precession and argued that it should be zero in a free fall orbit. We review the existing interpretations regarding the relation between the Thomas precession and the geodetic precession for a gyroscope in a free fall orbit. Schiff and Parker had contradictory views on the status of the Thomas precession in a free fall orbit, a contradiction that continues to exist in the literature. In the second part of this paper we derive the geodetic precession as a global Thomas precession by use of the equivalent principle and some elements of hyperbolic geometry, a derivation that allows the treatment of GP-B physics in between special and general relativity courses. (author)