General relativistic spin-orbit and spin-spin effects on the motion of rotating particles in an external gravitational field

We analytically compute the orbital effects induced on the motion of a spinning particle geodesically traveling around a central rotating body by the general relativistic two-body spin-spin and spin-orbit leading-order interactions. Concerning the spin-orbit term, we compute the long-term variations due to the particle's spin by finding secular precessions for the inclination I of the particle's orbit, its longitude of the ascending node Omega and the longitude of pericenter omega. Moreover, we generalize the well-known Lense-Thirring precessions to a generic orientation of the source's angular momentum by obtaining an entirely new effect represented by a secular precession of I, and additional secular precessions of Omega and omega as well. The spin-spin interaction is responsible of gravitational effects a la Stern-Gerlach consisting of secular precessions of I, Omega, omega and the mean anomalyM. Such results are obtained without resorting to any approximations either in the particle's eccentricity e or in its inclination I; moreover, no preferred orientations of both the system's angular momenta are adopted. Their generality allows them to be applied to a variety of astronomical and astrophysical scenarios like, e. g., the Sun and its planets and the double pulsar PSR J0737-3039A/ B. It turns out that the orbital precessions caused by the spin-spin and the spin-orbit perturbations due to the less massive body are below the current measurability level, especially for the solar system and the Stern-Gerlach effects. Concerning the solar Lense-Thirring precessions, the slight misalignment of the solar equator with respect to the ecliptic reduces the gravitomagnetic node precession of Mercury down to a 0.08mas per century level with respect to the standard value of 1mas per century obtained by aligning the z axis with the Sun's angular momentum. The new inclination precession is as large as 0.06mas per century, while the perihelion's rate remains substantially unchanged, amounting to-2mas per century. Further studies may be devoted to the extrasolar planets which exhibit a rich variety of orbital and rotational configurations.