Light propagation in the gravitational field of N arbitrarily moving bodies in the 1.5PN approximation for high-precision astrometry

TL;DR

This paper derives an analytical solution for light propagation in the gravitational field of arbitrarily moving bodies in the Solar system at 1.5PN order, crucial for ultra-precise astrometry at sub-micro-arcsecond accuracy.

Contribution

It presents a novel 1.5PN analytical model accounting for arbitrary motion and complex structure of Solar system bodies, enhancing high-precision astrometric data analysis.

Findings

Analytical solution for light trajectory in 1.5PN approximation.

Estimation of time delay and light deflection for multipoles.

Framework for high-precision astrometric data reduction.

Abstract

High-precision astrometry on sub-micro-arcsecond level in angular resolution requires accurate determination of the trajectory of a light-signal from the celestial light source through the gravitational field of the Solar system toward the observer. In this investigation the light trajectory in the gravitational field of N moving bodies is determined in the 1.5 post-Newtonian approximation. In the approach presented two specific issues of particular importance are accounted for: (1) According to the recommendations of International Astronomical Union, the metric of the Solar system is expressed in terms of intrinsic mass-multipoles and intrinsic spin-multipoles of the massive bodies, allowing for arbitrary shape, inner structure and rotational motion of the massive bodies of the Solar system. (2) The Solar system bodies move along arbitrary worldlines which can later be specified by Solar system ephemeris. The presented analytical solution for light trajectory is a primary requirement for extremely high-precision astrometry on sub-micro-arcsecond level of accuracy and associated massive computations in astrometric data reduction. An estimation of the numerical magnitude for time delay and light deflection of the leading multipoles is given.