Transformation between $\tau$ and TCB for Deep Space Missions under IAU Resolutions

TL;DR

This paper presents an analytic method to transform proper time to barycentric coordinate time for deep space missions, accounting for gravitational and velocity effects, with applications demonstrated for a Mars orbiter.

Contribution

An analytic approach for transforming spacecraft proper time to TCB under IAU resolutions, improving clarity and computational efficiency for deep space navigation.

Findings

Method is effective for a Mars orbiter over one year.

Main effects are from the Sun's gravity and spacecraft velocity.

Time transformation differences are at the sub-second level.

Abstract

For tracking a spacecraft and doing radio science, the transformation between the proper time $\tau$ given by a clock carried on board a spacecraft and the barycentric coordinate time (TCB) is investigated under IAU resolutions. In order to show more clearly physical pictures and improve computational efficiency, an analytic approach is adopted. After numerical checks, it shows this method is qualified for a Mars orbiter during one year, especially being good at describing the influence from perturbing bodies. Further analyses demonstrate that there are two main effects in the transformation: the gravitational field of the Sun and the velocity of the spacecraft in the barycentric coordinate reference system (BCRS). The whole contribution of them is at the level of a few sub-seconds.