# гармонічна функція

## 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.

## Method for approximate construction of three-dimensional mass distribution function and gradient of an elipsoidal planet based on external gravitational field parameters

Purpose. To investigate the technique for constructing a three-dimensional distribution function for the masses of the interior of the Earth and its derivatives, coordinated with the parameters of the planet's gravitational field to fourth order inclusive. By using the mass distribution function constructed, to make an interpretation of the features of the internal structure of an ellipsoidal planet. Methodology. Based on the created initial approximation of the function, which includes a reference density model, further refinements are built.

## One option of constructing three-dimensional distribution of the mass and its derivatives for a spherical planet Earth

Purpose. To build a three-dimensional function of the mass distribution of the Earth's interior according to the parameters (Stokes constant to the second order inclusive) of the external gravitational field of the Earth without considering the minimum deviation from its known density models in geophysics. Methodology. The classic methods of constructing mass distribution use only the Stoke’s constants zero and second orders.

## On recovering the potential and its derivatives on the boundary of the area containing sources

In the work, the dual nature of the gravitational potential is investigated. It is proved, that the integral representation of the gravitational potential is a mirror reflection of the same images for the class of harmonic functions. The integrated equations, enabling to restore potential and it’s derivations on the boundary of sources-including areas was obtained.