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. Since basic researches of Laplace, Legendre and Gauss in the theory of Newtonian potential, the classical Legendre-Laplace-Gauss-Maxwell representation of the Earth gravitational potential as a series of solid spherical functions has taken an interdisciplinary significance for the static and time-dependent fields of the Earth and planets. Note that this parameterization of the gravitational potential is not considered to be a standard only, but also as one of the best for modern scientific and applied problems of celestial mechanics, satellite geodesy, and global geodynamics. From 2000 to 2009 years were launched satellites CHAMP, GRACE and GOCE, which are classified as satellites LEO (Low Earth Orbit), the height of the orbit is lower than 500 km. The data from these satellites are LEO significantly clarified and expanded our knowledge of the Earth gravity field. The last achievements of the satellite geodesy is the project of European Space Agency – the GOCE satellite mission (Gravity of field and steady – state of Ocean Circulation Explorer) which is using the satellite gradientometry method. The choice of algorithm, which allows the determination of harmonic coefficients geopotential from gravity gradient tensor components, which is measured as part of the modern approach satellite mission GOCE gradientometry, became significant task for improving long and mean components of the gravitational field via data processing. As a result, in this paper two version of the corresponding harmonic coefficients Cnm, Snm (gravity field models GOCE-LP01s and GOCE-LP02s up to degree/order 250) were derived based on the second Neumann method including the construction of the corresponding Gauss grid.

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