Oscillations of a spin in a circular orbit in the schwarzschild and Lense-Thirring metrics

Abstract

A gyroscope in motion along a circular geodesic line oscillates with respect to a reference body because of the variability of the inclination of its orbit. Due to precession of the spin vector, these oscillations have the appearance of beats whose frequency is close to that of the orbital motion, and whose amplitude changes with a large period, so that the amplitude increases linearly during a long time. This phenomenon can be detected using symmetrical oscillations of gyroscopes with opposite spin vectors in an orbit around the Earth, or by observing the evolution of a planet orbit in the solar system.