Light propagation in the field of a moving axisymmetric body: theory and application to JUNO

TL;DR

This paper develops a relativistic model for light propagation around moving axisymmetric bodies, extending previous work, and applies it to improve the accuracy of JUNO mission observations in the Jovian system.

Contribution

It introduces a new formalism for modeling light propagation in the field of moving bodies, including an ensemble of arbitrarily moving masses, with practical application to space mission tracking.

Findings

Derived a space-time metric for moving bodies.

Provided a general integral expression for the Time Transfer Function.

Applied the model to analyze relativistic effects in JUNO's tracking data.

Abstract

Given the extreme accuracy of modern space science, a precise relativistic modeling of observations is required. We use the Time Transfer Functions formalism to study light propagation in the field of uniformly moving axisymmetric bodies, which extends the field of application of previous works. We first present a space-time metric adapted to describe the geometry of an ensemble of uniformly moving bodies. Then, we show that the expression of the Time Transfer Functions in the field of a uniformly moving body can be easily derived from its well-known expression in a stationary field by using a change of variables. We also give a general expression of the Time Transfer Function in the case of an ensemble of arbitrarily moving point masses. This result is given in the form of an integral easily computable numerically. We also provide the derivatives of the Time Transfer Function in this case, which are mandatory to compute Doppler and astrometric observables. We particularize our results in the case of moving axisymmetric bodies. Finally, we apply our results to study the different relativistic contributions to the range and Doppler tracking for the JUNO mission in the Jovian system.