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Generalized problem of two and four Newtonian centers. (English) Zbl 1129.70010
Summary: We consider integrable spherical analog of the Darboux potential, which appear in the problem (and its generalizations) of the planar motion of a particle in the field of two and four fixed Newtonian centers. The obtained results can be useful when constructing a theory of motion of satellites in the field of an oblate spheroid in constant curvature spaces.

MSC:
70F10 \(n\)-body problems
70F15 Celestial mechanics
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