In this paper we look at the gravitational spin-spin interaction between macroscopic astronomical bodies. In particular, we calculate their post-Newtonian orbital effects of order O(c(-2)) on the trajectory of a spinning particle with proper angular momentum s moving in the external gravitomagnetic field generated by a central spinning mass with proper angular momentum J. It turns out that, at order O(e) in the orbiter's eccentricity, the eccentricity the pericenter and the mean anomaly rates of the moving particle are affected by long-term harmonic effects. If, on one hand, they are undetectable in the Solar System, on the other, maybe in an astrophysical context like that of the binary millisecond pulsars there will be some hopes of measuring them in the future, provided that substantial improvements in the accuracy of the detection of the periastron rate will occur. [References: 25]
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