From Tensor to Vector of Gravitation

Different gravitational force models are used for determining the satellites’ orbits. The satellite gravity gradiometry (SGG) data contain this gravitational information and the satellite accelerations can be determined from them. In this study, we present that amongst the elements of the gravitational tensor in the local north-oriented frame, all of the elements are suitable for this purpose except T_xy. Three integral formulae with the same kernel function are presented for recovering the accelerations from the SGG data. The kernel of these integrals is well-behaving which means that the contribution of the far-zone data is not very significant to their integration results; but this contribution is also dependent on the type of the data being integrated. Our numerical studies show that the standard deviations of the differences between the accelerations recovered from T_zz, T_xz and T_zy and those computed by an existing Earth´s gravity model reduce by increasing the cap size of integration. However, their root mean squared errors increase for recovering T_y from T_yz. Larger cap sizes than 5 on is recommended for recovering T_x and T_z but smaller ones for T_y.