Abstract
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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Easton, R.W. Capture orbits and melnikov integrals in the planar three-body problem. Celestial Mech Dyn Astr 50, 283–297 (1990). https://doi.org/10.1007/BF00048768
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DOI: https://doi.org/10.1007/BF00048768