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On the determination of the collinear double points in the averaged plane elliptic restricted three-body problem. (English) Zbl 0685.70007

Summary: The essential of Rein’s scheme for the “simplified semiaveraged” plane elliptic restricted three-body problem is briefly presented. The equations for the double points of zero velocity curves are established and the relations for finding the abscissae of the collinear double points are deduced in a general form. Three applications are given: The Sun-Jupiter case (for comparison with Rein’s results), the Earth-Moon case, and the case of the binary system Beta Persei.

MSC:

70F07 Three-body problems
70F15 Celestial mechanics
70F99 Dynamics of a system of particles, including celestial mechanics
70-08 Computational methods for problems pertaining to mechanics of particles and systems
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