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The ESA/JAXA BepiColombo mission, launched on 20 October 2018, is currentlyin cruise toward Mercury. The Mercury Orbiter Radio-science Experiment (MORE),one of the 16 experiments of the mission, will exploit range and range-ratemeasurements collected during superior solar conjunctions to better constrainthe post-Newtonian parameter ${\gamma}$. The MORE radio tracking system iscapable of establishing a 5-leg link in X- and Ka-band to obtain 2-wayrange-rate measurements with an accuracy of $0.01 mm/s^-1$ @ 60 s sampling timeand 2-way range measurements at centimeter level after a few seconds ofintegration time, at almost all solar elongation angles. In this paper, weinvestigate if the light-time formulation derived by Moyer, implemented inJPL's orbit determination code MONTE, is still a valid approximation, in lightof the recent advancements in radiometric measurement performance. Severalformulations of the gravitational time delay, expressed as an expansion inpowers of $GM/c^2r$, are considered in this work. We quantified thecontribution of each term of the light-time expansion for the first superiorsolar conjunction experiment of BepiColombo. The maximum 2-way error caused byMoyer approximation with respect to a complete second order expansion amountsto 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 isthen recommended for present and future superior solar conjunction experiments.The perturbation caused by the planets in the Solar System is considered aswell, resulting in significant effects due to the Jupiter, the Earth and theSaturn systems. For these bodies the classical Shapiro time delay issufficient. The corrections due to the Sun oblateness and angular momentum arenegligible.

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