Solution of the planar problem of N fixed centers

Details Solution of the planar problem of N fixed centers Solution of the planar problem of N fixed centers

Sep 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977cemec..16...41a&link_type=abstract

Celestial Mechanics, vol. 16, Sept. 1977, p. 41-44. In Russian.

Mathematics

Celestial Mechanics, Gravitational Effects, Many Body Problem, Gravitational Fields, Quadratures, Satellite Orbits, Transformations (Mathematics)

Scientific paper

The planar problems of N fixed centers is formulated in oblate spheroidal coordinates, and the Aksenov transformations are used to reduce the solution to quadratures. Solutions for two special cases are obtained: (1) the masses of the fixed centers are equal and the fixed centers are even in number, being symmetrically arranged along one axis, and (2) the masses are equal and the centers are odd in number, with one center at the origin and the remaining centers symmetrically arranged about this one on an axis.

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