Explicit formulae for the two way time-transfer in the T2L2 experiment including the J2 contribution to the Earth potential in a relativistic framework

TL;DR

This paper derives explicit relativistic formulae for two-way time transfer between ground stations and satellites, including Earth's J2 potential contribution, to improve precision in experiments like T2L2.

Contribution

It provides the first explicit relativistic formulae for two-way time transfer that incorporate Earth's J2 potential term, enhancing accuracy for high-precision timing experiments.

Findings

Explicit formulae for distance and offset problems are derived.

The J2 contribution to Earth's potential is explicitly included.

Results improve the precision of time transfer measurements.

Abstract

The topic of this paper is to study the two way time-transfer problem between a ground based station and a low orbit Earth's satellite, in the aim of an application to the T2L2 experiment. The sudy is driven in a fully relativistic framework. Because of the rapid increase in clock's precision/measurements, the first term beyond the Earth's potential monopolar term is explicitly taken into account. Explicit formulae, for both the distance and offset problems (definitions in the text) are proposed for the relevant applications.