Test of general relativity during the BepiColombo interplanetary cruise to Mercury

The theory of general relativity first introduced the concept that space-time is curved by the presence of masses. As a consequence, any signal between two sources passing by a massive body is deflected and therefore experiences a transmission time delay with respect to the straight-line propagation. In the parametrized Post-Newtonian formalism—which makes use of a set of post-Newtonian parameters to describe all metric theories of gravitation that assume Einstein equivalence principle—the curvature of space-time is accounted for by the parameter $\gamma$. In general relativity $\gamma$ is equal to unity. The measure of $\gamma$ is one of the most popular general relativity tests that have been undertaken since 1919. The current state-of-the-art measure of $\gamma$ is $\gamma =1+(2.1\pm 2.3)\times {10}^{-5}$, obtained by radio tracking of the NASA/ESA/ASI Cassini-Huygens satellite near solar superior conjunction (Superior Conjunction Experiment—SCE). The ESA/JAXA BepiColombo mission to Mercury will perform a SCE during its cruise-phase. Thanks to a more advanced telecommunication system, made up of a X/X, Ka/Ka, X/Ka multifrequency link, BepiColombo will allow range measurements as accurate as 15 cm at 300 s integration time and range-rate (or Doppler) measurements at the level of $1.5\mu \mathrm{m}/\mathrm{s}$ at 1000 s integration time, one-way. In this work we present the results of the numerical simulations of the BepiColombo SCE with the ORBIT14 orbit determination and parameter estimation software, developed at the University of Pisa. Our software is able to simulate measurements of range and range-rate of the BepiColombo probe during solar superior conjunction and obtain an estimate of $\gamma$ based on a non-linear least squares fit. Through a thorough and complete analysis, which includes the study of the impact of possible systematic errors in the range observables, we show that BepiColombo has the capability to improve the result yielded by Cassini up to a factor 10.