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

The paper presents the principles of measuring the Earth’s global gravitational field (EGF) using a spacecraft (SC) equipped with a high-precision three-axis gravity gradiometer and located in low Earth orbit. Such a spacecraft is primarily designed to measure high-frequency EGF harmonics. Gradiometer measurements are not sensitive to low-order EGF harmonics, so to reconstruct the EGF in the entire frequency range, starting from =2, high-precision measurements of the SC orbit are required, which are performed by the onboard high-precision GNSS receiver. Theoretical aspects of satellite gradiometry are considered and the problem of reconstructing the EGF harmonics is solved based on model measurements. 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. A direct method is used to reconstruct the EGF: a matrix of conditional equations is compiled relative to the Stokes coefficients. Solving this system using the least squares method allows us to obtain corrections to the harmonics of the a priori (initial) EGF model, which used the EGM96 model. This way, the harmonics of the reconstructed field are formed. The quality criterion for the solution is the agreement between the difference in the amplitudes of the harmonics of the reconstructed model and the EGM2008 model. Based on the obtained model solutions, an optimal SC orbit was selected for carrying out gradiometric measurements, and estimates of the accuracy characteristics of the main key elements of the spacecraft onboard scientific instruments were obtained.