Testing general relativity with the BepiColombo radio science experiment

Abstract

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.

Symmetries and Rank Deficiency in the Orbit Determination around Another Planet

“…There are solutions to this problem, as discussed in Section symmetries.tex; 7/01/2002; 14:45; p.16 6, which allow to stabilize the solution and remove most of the negative effects, but the problem needs to be understood and taken into account in the design of the orbit determination algorithms, as in (Milani et al, 2001a), (Milani et al, 2001b).…”

“…The equations we consider to model the motion of the satellite around the planet are those of the perturbed two body problem, where the potential is now given by the sum of the general term U 0 and the perturbative term U 1 (Roy, 1978). We have…”

“…From the usual equations for the perturbations of the keplerian elements of an elliptical orbit, due to the secular perturbative potential (Roy, 1978), and from equation (15), we can derive the orbital elements at time t j , that is after k j ∆t from t 0 , our reference epoch. We have that the semi-major axis a, the eccentricity e and the inclination i change only for short periodic perturbations, thus by O¢ J 2 £ , while for the other elements we have…”

Light-time computations for the BepiColombo Radio Science Experiment

“…The planetary terms, similar to the solar one, can also be included but they are smaller than the accuracy needed for our measurements. Parameter γ is the only post-Newtonian parameter used for the light-time effect and, in fact, it could be best constraint during superior conjunction ( [8]). The total amount of the Shapiro effect in range is shown in Figure 3.…”

Commission 52: Relativity in Fundamental Astronomy

“…Considering the anticipated accuracy of the future relativistic experiments it is important to go beyond the standard least-square fits and to provide realistic errors of the achieved estimates of relativistic parameters. A sophisticated statistical analysis of the relativistic experiments with ESA's mission BepiColombo (Milani et al 2002) has been performed by Ashby, Bender & Wahr (2007).…”