Gravity field and rotation state of Mercury from the BepiColombo Radio Science Experiments

Abstract The ESA mission BepiColombo will include a Mercury Planetary Orbiter equipped with a full complement of instruments to perform Radio Science Experiments. Very precise range and range-rate tracking from Earth, on-board accelerometry, altimetry and accurate angular measurements with optical instruments will provide large data sets. From these it will be possible to study (1) the global gravity field of Mercury and its temporal variations due to tides, (2) the medium to short scale (down do 300≃400 km ) gravity anomalies, (3) the rotation state of the planet, in particular the obliquity and the libration with respect to the 3/2 spin orbit resonance and (4) the orbit of the center of mass of the planet. With the global gravity field and the rotation state it is possible to tightly constrain the internal structure of the planet, in particular to determine whether the solid surface of the planet is decoupled from the inner core by some liquid layer, as postulated by dynamo theories of Mercury's magnetic field. With the gravity anomalies and altimetry it is possible to study the geophysics of the planet's crust, mantle and impact basins. With the orbit of the planet closest to the Sun it is possible to constrain relativistic theories of gravitation. The possibility of achieving these scientific goals has been tested with a full cycle numerical simulation of the Radio Science Experiments. It includes the generation of simulated tracking and accelerometer data, and the determination, by least squares fit, of a long list of variables including the initial conditions for each observed arc, calibration parameters, gravity field harmonic coefficients, and corrections to the orbit of Mercury. An error budget has been deduced both from the formal covariance matrices and from the actual difference between the nominal values used in the data simulation and the solution. Thus the most complete error budget contains the effect of systematic measurement errors and is by far more reliable than a formal one. For the rotation experiment an error budget has been computed on the basis of dedicated studies on each separate error source. The results of the full cycle simulation are positive, that is the experiments are feasible at the required level of accuracy. However, the extraction of the full accuracy results from the data will be by no means trivial, and there are a number of open problems, both in the data processing (e.g., the selection of the orbital arc length) and in the mission scheduling (e.g., the selection of the target areas for the rotation experiment).