Future gravitational physics tests from ranging to the BepiColombo Mercury planetary orbiter

Milani et al. recently have published careful and fundamental studies of the accuracy with which both gravitational physics information and the solar quadrupole moment can be obtained from Earth-Mercury distance data. To complement these results, a quite different analysis method is used in the present paper. We calculate the first-order corrections to the Keplerian motion of a single planet around the Sun due to the parameterized post-Newtonian theory parameters $\beta$, $\gamma$, ${\alpha }_1$, ${\alpha }_2$, and $\xi$, as well as corrections due to the solar quadrupole moment $J_2$ and a possible secular change in $G{M}_{\odot }$. The Nordtvedt parameter $\eta$ that is used in tests of the strong equivalence principle also is included in this analysis. The expected accuracies are given for 1 yr, 2 yr, and 8 yr mission durations, assuming that the planet-planet and asteroid-planet perturbations are accurately known. The “modified worst-case” error analysis method that we use is quite different from the usual covariance analysis method based on assumed uncorrelated random errors, plus a bias that is fixed or that changes in a prescribed way. We believe this is appropriate because systematic measurement errors are likely to be the main limitation on the accuracy of the results. Our final estimated uncertainties are one-third of the errors that would result if a 4.5-cm rms systematic error had the most damaging possible variation with time. We discuss the resulting uncertainties for several different subsets of orbital and relativity parameters.