Study of Gravitomagnetic Clock Effect Due To Gravitational Spin-Orbit Coupling

General relativity predicts that two freely counter-revolving test particles in the exterior field of a central body take different periods is usually termed as the gravitomagnetic clock effect [1]. The general relativistic derivation of this effect for a general orbit is quit complicated. The gravitomagnetic clock effect arises from the differences in orbital period in prograde and retrograde orbits. Prograde orbit is one where the sense of orbital motion of the test body is same as the sense of rotation of the central body. In retrograde orbit the situation is opposite. The period difference is 4πa/c, which is the expression for gravitomagnetic clock effect. Clearly, the retrograde orbit is faster than the prograde orbit.