Rough Estimates of Solar System Gravitomagnetic Effects in Post-Newtonian Gravity

In order to properly describe the gravity interactions, including the mass currents, in gravitomagnetism, we construct four Maxwell-type gravitational equations that are shown to be analogs of the Maxwell equations in electromagnetism. Next, exploiting the Maxwell-type gravitational equations, we explicitly predict the mass magnetic fields for both the isolated system of the spinning Moon orbiting the spinning Earth and that of the Sun and solar system planets orbiting the spinning Sun, whose phenomenological values have not been evaluated in the preceding Newtonian gravity formalisms. In gravitomagnetism, we also phenomenologically investigate the mass magnetic general relativity (GR) forces associated with the mass magnetic fields, finding that they are extremely small but non-vanishing compared to the corresponding mass electric Newtonian forces. Moreover, the directions of the mass magnetic GR forces for the solar system planets, except Venus and Uranus, are shown to be anti-parallel to those of their mass electric Newtonian forces. Next, we investigate the mass magnetic dipole moment related to the B ring of Saturn to evaluate m→M(Ring)=−1.141×104m3s−1ω^, with ω^ being the unit vector along the axis direction of the spinning B ring. The predicted value of m→M(Ring) is shown to be directly related to the Cassini data on the total mass of the rings of Saturn.