The project of European Space Agency and a recent achievement in satellite geodesy, the GOCE satellite mission (Gravity of Field and Steady-State of Ocean Circulation Explorer) exploits a method of satellite gradientometry. Gravitational field of the Earth is usually represented as a finite series of spherical harmonic functions, the model containing a finite number of coefficients, Cnm, Snm. The coefficients Cnm, Snm are derived in our work, based on the second method of Neumann and the Gauss-Legandre quadrature decomposition.
Objectives. The method of satellite altimetry as a relatively new approach to precise satellite surveying, which provides the different Earth sciences by a most complete information about the state of the ocean and its changes over time. In particular this method uses in scientific researches of geodesy, oceanography and climatology. The models of ocean dynamic topography are based on the altimetry data also. Methodology.
The last achievements of the physical geodesy is the project of European Space Agency – the GOCE satellite (Gravity of field and steady – state of Ocean Circulation Explorer) which uses the satellite gradientometry method. The gravitational field of the Earth is represented traditionally as a series of spherical harmonic functions, i.e. to model the gravitational field of the finite number of parameters, the so–called coefficients Cnm, Snm. In this paper we analyze the basic relationships for the determination of these coefficients.
As well-known, one of the oldest geodetic problems has today a new development. There is the method of satellite gradientometry allowing essentially improvement of the Earth's gravity field. So, the development of geodesy together with the expansion of various types of measurements is characterized by traditional increase of their level of accuracy and solving the basic problems of geodesy – definition of shape and gravity field of the Earth on the new level.