Periodic solutions of circular-elliptic type in the planar n-body problem

Details Periodic solutions of circular-elliptic type in the planar n-body problem Periodic solutions of circular-elliptic type in the planar n-body problem

May 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978cemec..17..331a&link_type=abstract

Celestial Mechanics, vol. 17, May 1978, p. 331-355.

Mathematics

4

Circular Orbits, Equations Of Motion, Many Body Problem, Orbit Perturbation, Determinants, Ellipses, Periodic Functions, Transformations (Mathematics)

Scientific paper

Let n mass points, where n is at least 2, with arbitrary masses move circularly on a rotating straight-line central-configuration; i.e., on a particular solution of relative equilibrium of the n-body problem. By replacing one of the mass points by a close pair of mass points (with mass conservation), it is shown that the resulting N-body problem (N = n + 1) has solutions, which are periodic in a rotating coordinate system and describe precessing nearly elliptic motion of the binary and nearly circular collinear motion of its center of mass and the other bodies; it is also assumed that the mass ratio of the binary is small.

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