Satellite Gradientometer: Principles of Measuring the Earth’s Gravitational Field

Abstract—The paper presents the principles of measuring the Earth’s gravitational field (EGF) using a spacecraft (SC) equipped with a high-precision three-axis gravity gradiometer and located in low Earth orbit. Such spacecraft are designed primarily for measuring high-frequency EGF harmonics. Gradiometric measurements are insensitive to low-order EGF harmonics; therefore, to reconstruct the EGF in the entire frequency range, starting from n = 2, high-precision measurements of the spacecraft orbit are required, which are done by an onboard high-precision GNSS receiver. The theoretical aspects of satellite gradiometry are considered, and the problem of reconstructing the EGF harmonics based on model measurements is solved. To calculate the “measured” components of the gravitational potential tensor, the EGM2008 EGF model was used. A program for numerical integration of the spacecraft orbit was also developed based on this model, including additional forces acting on the spacecraft. To reconstruct the EGF, a direct method is used: a matrix of conditional equations is compiled with respect to the Stokes coefficients. The solution of this system by the least squares method makes it possible to obtain corrections to the harmonics of the a priori (initial) EGF model, for which the EGM96 model was used. In this way, the harmonics of the reconstructed field are formed. The criterion for the quality of the solution is agreement between the difference in the amplitudes of the harmonics of the reconstructed model and EGM2008 model. Based on the obtained model solutions, an optimal spacecraft orbit was selected for gradiometric measurements and estimates of the accuracy characteristics of the main key elements of the spacecraft’s onboard scientific instruments were obtained.