Abstract
Numerical orbit integrations have been conducted to characterize the types of trajectories in the one-dimensional Newtonian three-body problem with equal masses and negative energy. Essentially three different types of motions were found to exist. They may be classified according to the duration of the bound three-body state. There are zero-lifetime predictable trajectories, finite lifetime apparently chaotic orbits, and infinite lifetime quasi-periodic motions. The quasi-periodic orbits are confined to the neighbourhood of Schubart's stable periodic orbit. For all other trajectories the final state is of the type binary + single particle in both directions of time. The boundaries of the different orbit-type regions seem to be sharp. We present statistical results for the binding energies and for the duration of the bound three-body state. Properties of individual orbits are also summarized in the form of various graphical maps in a two-dimensional grid of parameters defining the orbit.
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Supported by the Academy of Finland.
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Mikkola, S., Hietarinta, J. A numerical investigation of the one-dimensional newtonian three-body problem. Celestial Mech Dyn Astr 46, 1–18 (1989). https://doi.org/10.1007/BF02426707
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DOI: https://doi.org/10.1007/BF02426707