In physics, the gravitomagnetic clock effect is a deviation from Kepler's third law that, according to the weak-field and low-velocity approximation of general relativity, will be suffered by a particle in orbit around a (slowly) spinning body, such as a typical planet or star.
According to general relativity, in its weak-field and low-velocity linearized approximation, a slowly spinning body induces an additional component of the gravitational field that acts on a freely-falling test particle with a non-central, gravitomagnetic Lorentz-like force.
If the orbit of the particle is circular and lies in the equatorial plane of the central body, the correction is Particles orbiting in opposite directions experience gravitomagnetic corrections TGvm with opposite signs, so that the difference of their orbital periods would cancel the standard Keplerian terms and would add the gravitomagnetic ones.
[1][2][3][4][5][6][7][8][9][10][11][12][excessive citations] Note that the + sign occurs for particle's corotation with respect to the rotation of the central body, whereas the − sign is for counter-rotation.
That is, if the satellite orbits in the same direction as the planet spins, it takes more time to make a full orbit, whereas if it moves oppositely with respect to the planet's rotation its orbital period gets shorter.