To test General Relativity with the tracking data of the BepiColombo Mercury orbiter we need relativistic models for the orbits of Mercury and of the Earth, for the light-time and for all the spatio-temporal reference frames involved, with accuracy corresponding to the measurements: ≃10 cm in range, ≃2 micron/s in range-rate, over 2 years.
For the dynamics we start from the Lagrangian post-Newtonian (PN) formulation, using a relativistic equation for the solar system barycenter to avoid rank deficiency. In the determination of the PN parameters, the difficulty in disentangling the effects of β from the ones of the Sun's oblateness is confirmed. We have found a consistent formulation for the preferred frame effects, although the center of mass is not an integral. For the identification of strong equivalence principle (SEP) violations we use a formulation containing both direct and indirect effects (through the modified position of the Sun in a barycentric frame).
In the light-time equations, the Shapiro effect is modeled to PN order 1 but with an order 2 correction compatible with (Moyer 2003). The 1.5-PN order corrections containing the Sun's velocity are not relevant at the required level of accuracy.
To model the orbit of the probe, we use a mercury-centric reference frame with its own “Mercury Dynamic Time”: this is the largest and the only relativistic correction required, taking into account the major uncertainties introduced by non-gravitational perturbations.
A delicate issue is the compatibility of our solution with the ephemerides for the other planets, and for the Moon, which cannot be improved by the BepiColombo data alone. Conversely, we plan to later export the BepiColombo measurements, as normal points, to contribute with their unprecedented accuracy to the global improvement of the planetary ephemerides.