The gravitational time delay in the field of a slowly moving body with arbitrary multipoles

TL;DR

This paper extends the calculation of gravitational light time delay to bodies with arbitrary multipole moments in motion, providing new results for moving bodies with complex structures using the Time-Transfer-Function formalism.

Contribution

It introduces a novel method to compute gravitational time delay for moving bodies with arbitrary multipoles, generalizing previous static source models.

Findings

Results match existing literature for static cases.

New expressions derived for moving bodies with full multipole structure.

Method simplifies integration of time delay calculations.

Abstract

We calculate the time delay of light in the gravitational field of a slowly moving body with arbitrary multipoles (mass and spin multipole moments) by the Time-Transfer-Function (TTF) formalism. The parameters we use, first introduced by Kopeikin for a gravitational source at rest, make the integration of the TTF very elegant and simple. Results completely coincide with expressions from the literature. The results for a moving body (with constant velocity) with complete multipole-structure are new, according to our knowledge.