High Order Relativistic Corrections To Keplerian Motion

TL;DR

This paper derives high-order relativistic corrections to Keplerian motion by calculating the spacetime metric's multipole moments, providing detailed insights into orbital precessions influenced by complex gravitational fields.

Contribution

It introduces a method to compute high-order multipole effects on orbital precession using Ernst potentials and invariant quantities, extending previous models.

Findings

Calculated up to seventh order in the radial coordinate.

Quantified the influence of multipoles on perihelion and node line precession.

Expressed results in terms of Geroch-Hansen multipoles and orbital parameters.

Abstract

The first terms of the general solution for an asymptotically flat stationary axisymmetric vacuum spacetime endowed with an equatorial symmetry plane are calculated from the corresponding Ernst potential up to seventh order in the radial pseudospherical coordinate. The metric is used to determine the influence of high order multipoles in the perihelion precession of an equatorial orbit and in the node line precession of a non-equatorial orbit with respect to a geodesic circle. Both results are written in terms of invariant quantities such as the Geroch-Hansen multipoles and the energy and angular momentum of the orbit.