Influence of mass multipole moments on the deflection of a light ray by an isolated axisymmetric body

TL;DR

This paper develops a method to calculate how the mass multipole moments of axisymmetric bodies affect light deflection, crucial for high-precision space astrometry missions aiming for microarcsecond accuracy.

Contribution

It introduces an explicit algorithm within the parametrized post-Newtonian framework to determine light deflection caused by mass multipoles of isolated bodies.

Findings

Derived formulae for light deflection including multipole effects

Special cases for sources and observers at infinity analyzed

Applicable to high-precision astrometry measurements

Abstract

Future space astrometry missions are planned to measure positions and/or parallaxes of celestial objects with an accuracy of the order of the microarcsecond. At such a level of accuracy, it will be indispensable to take into account the influence of the mass multipole structure of the giant planets on the bending of light rays. Within the parametrized post-Newtonian formalism, we present an algorithmic procedure enabling to determine explicitly this influence on a light ray connecting two points located at a finite distance. Then we specialize our formulae in the cases where 1) the light source is located at space infinity, 2) both the light source and the observer are located at space infinity. We examine in detail the cases where the unperturbed ray is in the equatorial plane or in a meridian plane.