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 apparatus for approximating a piecewise continuous function in the middle of the ellipse is used for the representation of the Earth external gravitational field by the simple and double layer integrals. This makes it possible to expand the convergence region for the series supplying the potential to the entire space outside the integration ellipse. Therefore, as a result, the value of the gravitational potential coincides with the values of these series outside the body containing the interior masses (except for the integration ellipse). It becomes possible to evaluate the gravitational field behavior in surface areas and to carry out studies of geodynamic processes with greater reliability. Approximation of the gravitational field with the help of surface integrals also determines the geophysical aspect of the problem. Indeed, in the process of solving the problem we constructed two-dimensional integrands, which are uniquely determined by a set of Stokes constants. In this case, their expansion coefficients into series are defined by linear combinations of their function power moments. The resulting function schedules can be used to study the external gravitational field features, e.g., to study its asymmetry with respect to the equatorial plane.

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