Decomposition of the Coplanar Potential of the Gauss Ring in a Series in Degrees of Eccentricityстатья
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Дата последнего поиска статьи во внешних источниках: 8 сентября 2021 г.
Аннотация:Abstract—The problem of expanding the potential of an almost circular elliptic Gaussian ring in a series in powers of eccentricity is posed and solved. The gravitational potential of the ring is represented by a power series up to the terms inclusively on the entire set of points of the principal plane of the ring. The mainresult: two sets of coefficients for the power series of the potential inside and outside the ring are obtained, which are expressed in terms of complete elliptic integrals of the first and second kind. To control the formulas,the Landen transforms are used. It is proved that at the point of active focus of the ring, the four coefficients of the first set vanish. The calculation results are used to construct the equipotentials of the Gaussian rings that simulate the orbits of the planets of the Solar System.