Covariance Analysis Applied to the MESSENGER and BepiColombo Relativity Experiments

MESSENGER (MErcury Surface, Space ENvironment, GEochemistry, and Ranging) and BepiColombo are joint NASA and ESA/JAXA missions devoted to the exploration of Mercury. MESSENGER operated between 2008 and 2015, while BepiColombo will be launched in October 2018 and will orbit around Mercury for at least one year starting from March 2026. Both missions have the aim to study characteristics of Mercury in terms of its geology, magnetosphere, exosphere, etc. BepiColombo will improve some of the MESSENGER results regarding the rotation state and gravity field of Mercury and it will perform important tests of the General Relativity. In this work we investigate the benefits of the joint dataset of the two missions for the Relativity experiment. The very large baseline (about 19 years) together with BepiColombo's high precision measurements will be a key factor for the improvement of the accuracies. To this aim, we developed a semi-analytical model for a covariance analysis to estimate the formal uncertainties of the parameters of our interest: post-Newtonian parameters, Nordtvedt parameter, the Sun's GM, its rate of change and the Sun's gravitational oblateness. Non-gravitational forces have also been modeled. Finally, particular attention has been paid to the repercussions on the Relativity experiment due to the uncertainties on the GMs and ephemerides of planets and minor bodies of the Solar System.