The ESA mission BepiColombo will explore the planet Mercury with equipment allowing an extremely accurate tracking. While determining its orbit around Mercury, it will be possible to indirectly observe the motion of its center of mass, with an accuracy several orders of magnitude better than what is possible by radar ranging to the planet's surface. This is an opportunity to conduct a relativity experiment which will be a modern version of the traditional tests of general relativity, based upon Mercury's perihelion advance and the relativistic light propagation near the Sun. We define the mathematical methods to be used to extract from the data of the BepiColombo mission, as presently designed, the best constraints on the main post-Newtonian parameters, especially ␤,␥ and the Nordtvedt parameter , but also the dynamic oblateness of the Sun J 2᭪ and the preferred frame parameters ␣ 1 ,␣ 2 . We have performed a full cycle simulation of the BepiColombo radio science experiments, including this relativity experiment, with the purpose of assessing in a realistic ͑as opposed to formal͒ way the accuracy achievable on each parameter of interest. For ␥ the best constraint can be obtained by means of a dedicated superior conjunction experiment, with a realistic accuracy Ӎ2ϫ10 Ϫ6 . For ␤ the main problem is the very strong correlation with J 2᭪ ; if the Nordtvedt relationship ϭ4␤Ϫ␥Ϫ3 is used, as it is legitimate in the metric theories of gravitation, a realistic accuracy of Ӎ2ϫ10 Ϫ6 for ␤ and Ӎ2ϫ10 Ϫ9 for J 2᭪ can be achieved, while itself is constrained within Ӎ10 Ϫ5 . If the preferred frame parameters ␣ 1 ,␣ 2 are included in the analysis, they can be constrained within Ӎ8ϫ10 Ϫ6 and Ӎ10 Ϫ6 , respectively, at the price of some degradation in ␤, J 2᭪ and . It is also possible to test the change with time of the gravitational constant G, but the results are severely limited because of the problems of absolute calibration of the ranging transponder, to the point that the improvement as compared with other techniques ͑such as lunar laser ranging͒ is not so important.

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Abstract. We have defined new algorithms for the data processing of a satellite geodesy mission with gradiometer (such as the next European mission GOCE) to extract the information on the gravity field coefficients with a realistic estimate of their accuracy. The large scale data processing can be managed by a multistage decomposition. First the spacecraft position is determined, i.e., a kinematic method is normally used. Second we use a new method to perform the necessary digital calibration of the gradiometer. Third we use a multiarc approach to separately solve for the global gravity field parameters. Fourth we use an approximate resonant decomposition, that is we partition in a new way the harmonic coefficients of the gravity field. Thus the normal system is reduced to blocks of manageable size without neglecting significant correlations. Still the normal system is badly conditioned because of the polar gaps in the spatial distribution of the data. We have shown that the principal components of the uncertainty correspond to harmonic anomalies with very small signal in the region where GOCE is flying; these uncertainties cannot be removed by any data processing method. This allows a complete simulation of the GOCE mission with affordable computer resources. We show that it is possible to solve for the harmonic coefficients up to degree 200 ÷ 220 with error to signal ratio ≥ 1, taking into account systematic measurement errors. Errors in the spacecraft orbit, as expected from state of the art satellite navigation, do not degrade the solution. Gradiometer calibration is the main problem. By including a systematic error model, we have shown that the results are sensitive to spurious gradiometer signals at frequencies close to the lower limit of the measurement band. If these spurious effects grow as the inverse of the frequency, then the actual error is larger than the formal error only by a factor 2, that is the results are not compromised.