Presentation of the gravity field of celestial bodies using the potentials of flat ellipsoidal disks

Abstract

One of the possible ways for representing the external gravitational field of the planet by the potentials of flat discs, based on the classical potential theory, is proposed. At the same time, the potentials of a single- and double-layer are used for the description with the placement of the integration regions in the equatorial plane. The coefficients of the series expansion of these functions are linear combinations of the Stokes constants of the gravitational field and are uniquely expressed in terms of them. Series terms are single- or double-layer potentials. This makes it possible to calculate these terms using the results of the ellipsoid potential theory. The convergence of such a series, in contrast to the traditional one for spherical functions, is much wider and practically covers the effect of the external potential excluding the region of integration, including in the superficial parts of the surface. Since there is no problem with the convergence of the obtained expansions, we can interpret the obtained results more fully. The construction of flat density distributions for the potentials of a single and double layer is an additional tool in the study of the internal structure of the celestial body, as it is essentially a projection of the volume density of the planet’s interior onto the equatorial plane. Therefore, the extrema of these functions combine the features of the three-dimensional distribution function of the planet’s interior.