1 Kluykov A.A.
2 Yashkin S.N.

Astronomy Institute, RAS


Moscow State University of Geodesy and Cartography (MIIGAiK)

The determination of parameters of the Earth’s gravitational field model by using the satellite gravity projects CHAMP, GRACE, GOCE is carried out on the basis of mathematical processing of measurement information of sensor systems installed on board of a spacecraft. Each of these sensor systems realizes its coordinate system, in which measurements are performed. Measured parameters, as a rule, are related to the coordinate system of the sensory system, and the required parameters refer to the Earth’s coordinate system (EFRF). Therefore, to determine the required parameters, it is necessary to perform the conversion of the measured parameter from one system to another. In this paper we obtain formulas that allow us to calculate the first and second derivatives of the gravitational potential in spherical, rectangular and local rectangular coordinate systems. Matrices are also obtained, with the help of which the transformation from one coordinate system to another is carried out. The formulas given in the article are necessary for performing mathematical processing of gradientometric measurements in order to determine the parameters of the Earth’s gravitational field.
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Kluykov A.A., 
Yashkin S.N., 
(2017) Computation of first and second order derivatives gravity potential in different coordinate systems. Geodesy and cartography = Geodezia i Kartografia, 78(7), pp. 15-22. (In Russian). DOI: 10.22389/0016-7126-2017-926-8-15-22
Publication History
Received: 18.04.2017
Accepted: 06.06.2017
Published: 18.08.2017


2017 July DOI: