On some gravitomagnetic spin-spin effects for astronomical bodies

TL;DR

This paper investigates the post-Newtonian gravitomagnetic spin-spin interactions between astronomical bodies, analyzing their effects on orbital parameters and discussing potential detectability in astrophysical systems like binary pulsars.

Contribution

It provides a detailed calculation of gravitomagnetic spin-spin effects on orbital dynamics, highlighting long-term harmonic influences and potential astrophysical observations.

Findings

Long-term harmonic effects on orbital elements due to spin-spin interactions.

Undetectability of these effects within the Solar System.

Possible future detection in binary millisecond pulsar systems.

Abstract

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 $\mathcal{O}(c^{-2})$ on the trajectory of a spinning particle with proper angular momentum ${\bf s}$ moving in the external gravitomagnetic field generated by a central spinning mass with proper angular momentum ${\bf J}$. It turns out that, at order $\mathcal{O}(e)$ 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 that in an astrophysical context like that of the binary millisecond pulsars there will be some hopes of measuring them in the future.