At least one author does describe it this way, but others state that "The Thomas precession comes into play for a gyroscope on the surface of the Earth ..., but not for a gyroscope in a freely moving satellite." An objection to the former interpretation is that the Thomas precession required has the wrong sign. The Fermi-Walker transport equation gives both the geodetic effect and Thomas precession and describes the transport of the spin 4-vector for accelerated motion in curved spacetime.
At least one writer portrays it in this manner, but others claim that "The Thomas precession applies to a gyroscope on the surface of the Earth ..., but not to a gyroscope in a freely moving satellite." A criticism of the former interpretation is that the required Thomas precession has the wrong sign. The Fermi-Walker transport equation accounts for both the geodetic effect and Thomas precession, describing the transport of the spin 4-vector for accelerated motion in curved spacetime.