Технология определения параметров гравитационного поля Земли по градиентометрическим измерениям 6. Вычисление компонент тензора гравитационного потенциала в земной пространственной прямоугольной системе координат

Abstract

This is the sixth one in a series of articles describing the technology of determining the Earth’s gravitational field parameters through gradiometric measurements performed with an onboard satellite electrostatic gradiometer. It provides formulas for calculating the components of the gravitational potential tensor in a geocentric spatial rectangular earth coordinate system in order to convert them into a gradiometric one and obtain a free term for the equations of correcting gradiometric measurements when determining the parameters of the Earth’s gravitational field. The components of the gravitational gradient tensor are functions of test masses accelerations measured by accelerometers and relate to the gradiometer coordinate system, while the desired parameters of the Earth’s gravitational field model relate to the Earth’s coordinate one. The components of the gravitational gradient tensor are the second derivatives of the gravitational potential in rectangular coordinates. The calculated values of the gravitational potential tensor components in the earth’s spatial rectangular coordinate system are obtained through double differentiation of the gravitational potential formula. Basing on the obtained formulas, an algorithm and a program in the Fortran algorithmic language were developed. Using this program, experimental calculations were performed, the results of which were compared with the data of the EGG_TRF_2 product.