Post-Newtonian orbital effects induced by the mass quadrupole and spin octupole moments of an axisymmetric body

TL;DR

This paper analytically derives post-Newtonian orbital effects caused by the mass quadrupole and spin octupole moments of an axisymmetric body, exploring potential measurements with spacecraft and stars near black holes.

Contribution

It provides new analytical formulas for orbital effects induced by higher multipole moments of an axisymmetric body, applicable to various orbital configurations.

Findings

Potential measurement of effects with a Juno-like spacecraft around Jupiter

Larger effects observed in less elliptical orbits

Possible constraints on mass distribution around Sgr A* using stellar orbits

Abstract

The post-Newtonian orbital effects induced by the mass quadrupole and spin octupole moments of an isolated, oblate spheroid of constant density that is rigidly and uniformly rotating on the motion of a test particle are analytically worked out for an arbitrary orbital configuration and without any preferred orientation of the body's spin axis. The resulting expressions are specialized to the cases of (a) equatorial and (b) polar orbits. The opportunity offered by a hypothetical new spacecraft moving around Jupiter along a Juno-like highly elliptical, polar orbit to measure them is preliminarily studied. Although more difficult to be practically implemented, also the case of a less elliptical orbit is considered since it yields much larger figures for the relativistic effects of interest. The possibility of using the S stars orbiting the supermassive black hole in Sgr A$^\ast$ at the Galactic Center as probes to potentially constrain some parameters of the predicted extended mass distribution surrounding the hole by means of the aforementioned orbital effects is briefly examined.