Capture orbits and melnikov integrals in the planar three-body problem

Details Capture orbits and melnikov integrals in the planar three-body problem Capture orbits and melnikov integrals in the planar three-body problem

Sep 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990cemda..50..283e&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 50, Issue 3, pp.283-297

Astronomy and Astrophysics

Astronomy

1

Parabolic Orbit, Capture Orbit, Hyperbolic Homoclinic Orbit, Melnikov'S Method, Three-Body Problem

Scientific paper

The separatrix between bounded and unbounded orbits in the three-body problem is formed by the manifolds of forward and backward parabolic orbits. In an ideal problem these manifolds coincide and form the boundary between the sets of bounded and unbounded orbits. As a mass parameter increases the movement of the parabolic manifolds is approximated numerically and by Melnikov's method. The evidence indicates that for positive values of the mass parameter these manifolds no longer coincide, and that capture and oscillatory orbits exist.

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