Derivation of the radial gradient of the gravity based on non-full tensor satellite gravity gradients

The formula for computing the radial gradient of the gravity is derived from the gravity gradients. Since GOCE satellite attitude has such property that one axis in the gradiometer almost has the same direction as the radial one of the earth, the formula can be used to compute the radial derivative of second order of the disturbing potential. This means that the boundary value problem (BVP) with the radial gradient of the gravity can be established on the satellite orbit. Hence, the recovery of the gravity field from GOCE data can be realized by solving the BVP. In order to examine the accuracy of the BVP, an arithmetic example is given, the computational results of which illustrate that the efficient degrees/orders of the gravity field model recovered by the BVP can satisfy the requirements of the satellite gravity gradients. In addition, a gravity field model is solved out from the BVP by using actual GOCE data.

► The boundary condition of radial gradients is established for gravity field recovery using GOCE data whose gradient observations are non-full tensors.
► The influence of non-full tensors is analyzed in detail by using actual orbit and attitude data.
► Compared to the value of radial gradients, relative error from non-full tensors is around 3%.
► The experiment on gravity field recovery using simulated data proves the effectiveness of the method based on the BVP.
► A gravity field model is derived from actual GOCE data, whose accuracy is nearly consistent with models from ESA in high degrees.