Investigation of the asymmetry of the Earth's gravitational field using the representation of potentials of disks

The paper considers representations of the Earth external gravitational field, supplementing its traditional approximation by series in spherical functions. The necessity for additional means of describing the external potential is dictated by the need to study and use it at points in space close to the Earth's surface. It is in such areas that the need arises to investigate the convergence of series with respect to spherical functions and to adequately determine the value of the potential.

The gradient construction approach analysis of the three-dimensional mass distribution function of the ellipsoidal planet

Purpose. To investigate the features of the algorithm implementation for finding the derivatives of the spatial distribution function of the planet's masses with the use of high-order Stokes constants and, on the basis of this, to find its analytical expression. According to the given methodology, to carry out calculations with the help of which to carry on the study of dynamic phenomena occurring inside an ellipsoidal planet.

The methodology of approximate construction of the three-dimensional mass distribution function and its gradient for the ellipsoidal planet subsidies

Purpose. To create an algorithm for constructing a three-dimensional masses distribution function of the planet and its derivatives taking into account the Stokes constants of arbitrary orders. Being based on this method, the task is to perform the research on the internal structure of the Earth. Methodology. The derivatives of the inhomogeneous mass distribution are presented by linear combinations of biorthogonal polynomials which coefficients are obtained from the system of equations.


It is considered the main ideologically motivated urban reforms that the Ukrainian village underwent in the twentieth century during the socialist era, in the field of standardization of the area of land plots for rural estates. It is also analysed the implementation of these reforms in master plans and Хdetailed planning of rural settlements in Ukraine and, as a consequence, how these reforms affected agricultural production, social and demographic structure of rural population, the structure of households and life and psychology of peasants in general.

Determining of permissible values of area land plots mean square errors outside settlements

Was made an analysis of standard acts that are regulating the realization of geodetic measurements for national landscape cadastre purposes. The research have touched upon the influence of quadratic mean mistakes of boundary-marks coordinates determination on quadratic mean mistake of determination of land parcels areas outside the boundaries of settlements.