On the Euler-type gravitomagnetic orbital effects in the field of a precessing body

TL;DR

This paper analytically investigates how time-dependent gravitomagnetic effects from a precessing rotating mass influence the long-term orbital elements of a test particle, with potential significance near supermassive black holes.

Contribution

It derives general formulas for orbital element variations caused by precessing gravitomagnetic fields, applicable to any orbital configuration and orientation of the precession.

Findings

Orbital elements, except mean anomaly, undergo long-term variations.

Effects are small for spacecraft like Juno and pulsars but significant near supermassive black holes.

Potential for up to 7% semimajor axis change per year near a Kerr black hole.

Abstract

To the first post-Newtonian order, the gravitational action of mass-energy currents is encoded by the off-diagonal gravitomagnetic components of the spacetime metric tensor. If they are time-dependent, a further acceleration enters the equations of motion of a moving test particle. Let the source of the gravitational field be an isolated, massive body rigidly rotating whose spin angular momentum experiences a slow precessional motion. The impact of the aforementioned acceleration on the orbital motion of a test particle is analytically worked out in full generality. The resulting averaged rates of change are valid for any orbital configuration of the satellite; furthermore, they hold for an arbitrary orientation of the precessional velocity vector of the spin of the central object. In general, all the orbital elements, with the exception of the mean anomaly at epoch, undergo nonvanishing long-term variations which, in the case of the Juno spacecraft currently orbiting Jupiter and the double pulsar PSR J0737-3039 A/B turn out to be quite small. Such effects might become much more relevant in a star-supermassive black hole scenario; as an example, the relative change of the semimajor axis of a putative test particle orbiting a Kerr black hole as massive as the one at the Galactic Centre at, say, 100 Schwarzschild radii may amount up to about $7\%$ per year if the hole's spin precessional frequency is $10\%$ of the particle's orbital one.