New methods in the Newtonian potential theory. I - The representation of the potential energy of homogeneous gravitating bodies by converging bodies

Details New methods in the Newtonian potential theory. I - The representation of the potential energy of homogeneous gravitating bodies by converging bodies New methods in the Newtonian potential theory. I - The representation of the potential energy of homogeneous gravitating bodies by converging bodies

Jun 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993azh....70..583k&link_type=abstract

Astronomicheskij Zhurnal (ISSN 0004-6299), vol. 70, no. 3, p. 583-593.

Mathematics

1

Gravitation Theory, Newton Theory, Potential Theory, Series (Mathematics), Legendre Functions, Polynomials

Scientific paper

A method is developed for the representation of the potential energy of homogeneous gravitating, as well as electrically charged, bodies in the form of special series. These series contain members consisting of products of the corresponding coefficients appearing in the expansion of external and internal Newtonian potentials in Legendre polynomial series. Several versions of the representation of potential energy through these series are possible. A formula which expresses potential energy not as a volume integral, as is the convention, but as an integral over the body surface is derived. The method is tested for the particular cases of sphere and ellipsoid, and the convergence of the found series is shown.

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