From Tensor to Vector of Gravitation

Abstract

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 Txy. 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 Tzz, Txz and Tyz 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 Ty from Tyz. Larger cap sizes than 5 on is recommended for recovering Tx and Tz but smaller ones for Ty.

Application of Gravity Gradients in the Process of GOCE Orbit Determination

“…Bobojü and DroĪyner (2003) showed the possibility of using the gravity gradient tensor components to improve simulated low Earth-orbiting (LEO) satellite orbits. An interesting idea of the application of dynamical aspect of gravity gradients for a satellite orbit determination is given by Eshagh (2014). The satellite acceleration vector is derived from gravity gradients in order to determine an orbit by the numerical integration (Eshagh 2014).…”

“…An interesting idea of the application of dynamical aspect of gravity gradients for a satellite orbit determination is given by Eshagh (2014). The satellite acceleration vector is derived from gravity gradients in order to determine an orbit by the numerical integration (Eshagh 2014).…”