The problem of three fixed centers
Abstract
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 kineticenergy integral and an area integral. It is shown that these systems give the solutions for the three variants in quadratures.
 Publication:

Astronomicheskii Zhurnal
 Pub Date:
 June 1976
 Bibcode:
 1976AZh....53..639A
 Keywords:

 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;
 Astronomy