Problem of three fixed centers

Details Problem of three fixed centers Problem of three fixed centers

Jun 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976azh....53..639a&link_type=abstract

Astronomicheskii Zhurnal, vol. 53, May-June 1976, p. 639-646. In Russian.

Mathematics

Complex Variables

2

Celestial Mechanics, Fixed Points (Mathematics), Four Body Problem, Gravitational Effects, Planetary Orbits, Satellite Orbits, Complex Variables, Dependent Variables, Differential Equations, Equations Of Motion, Integral Equations, Kinetic Theory, Quadratures

Scientific paper

Exact solutions are obtained for three variants of the plane problem of three fixed centers. The analysis considers the motion of a passively gravitating material point subjected to the Newtonian gravitational attraction of three fixed material centers, two of which may have complex masses. Two variants of the case of complex masses are analyzed in oblate spheroidal coordinates, and the case of three real masses is analyzed in prolate spheroidal coordinates. The equations of motion of a satellite are reduced to a separate system of differential equations for each variant; all the systems have a kinetic-energy integral and an area integral. It is shown that these systems give the solutions for the three variants in quadratures.

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