Comparison of light-time formulations in the post-Newtonian framework for the BepiColombo MORE experiment

Abstract

The ESA/JAXA BepiColombo mission, launched on 20 October 2018, is currently in cruise toward Mercury. The Mercury Orbiter Radio-science Experiment (MORE), one of the 16 experiments of the mission, will exploit range and range-rate measurements collected during superior solar conjunctions to better constrain the post-Newtonian parameter $γ$. The MORE radio tracking system is capable of establishing a 5-leg link in X- and Ka-band to obtain 2-way range-rate measurements with an accuracy of $0.01 mm/s^-1$ @ 60 s sampling time and 2-way range measurements at centimeter level after a few seconds of integration time, at almost all solar elongation angles. In this paper, we investigate if the light-time formulation derived by Moyer, implemented in JPL's orbit determination code MONTE, is still a valid approximation, in light of the recent advancements in radiometric measurement performance. Several formulations of the gravitational time delay, expressed as an expansion in powers of $GM/c^2r$, are considered in this work. We quantified the contribution of each term of the light-time expansion for the first superior solar conjunction experiment of BepiColombo. The maximum 2-way error caused by Moyer approximation with respect to a complete second order expansion amounts to 17 mm. This is at the level of accuracy of the novel pseudo-noise (PN) ranging system at 24 Mcps used by MORE. A complete second order expansion is then recommended for present and future superior solar conjunction experiments. The perturbation caused by the planets in the Solar System is considered as well, resulting in significant effects due to the Jupiter, the Earth and the Saturn systems. For these bodies the classical Shapiro time delay is sufficient. The corrections due to the Sun oblateness and angular momentum are negligible.