Testing General Relativity with the Radio Science Experiment of the BepiColombo mission to Mercury

The relativity experiment is part of the Mercury Orbiter Radio science Experiment (MORE) on-board the ESA/JAXA BepiColombo mission to Mercury. Thanks to very precise radio tracking from the Earth and accelerometer, it will be possible to perform an accurate test of General Relativity, by constraining a number of post-Newtonian and related parameters with an unprecedented level of accuracy. The Celestial Mechanics Group of the University of Pisa developed a new dedicated software, ORBIT14, to perform the simulations and to determine simultaneously all the parameters of interest within a global least squares fit. After highlighting some critical issues, we report on the results of a full set of simulations, carried out in the most up-to-date mission scenario. For each parameter we discuss the achievable accuracy, in terms of a formal analysis through the covariance matrix and, furthermore, by the introduction of an alternative, more representative, estimation of the errors. We show that, for example, an accuracy of some parts in ${10}^{-6}$ for the Eddington parameter html-italic^>β and of ${10}^{-5}$ for the Nordtvedt parameter html-italic^>η can be attained, while accuracies at the level of $5\times {10}^{-7}$ and $1\times {10}^{-7}$ can be achieved for the preferred frames parameters ${\alpha }_1$ and ${\alpha }_2$, respectively.