A numerical investigation of the one-dimensional newtonian three-body problem II. Positive energies

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 positive energy. At positive energies the basic types of motions are “binary + single particle’ and ‘ionization’, and when time goes from −∞ to +∞ all possible transitions between these states can take place. Properties of individual orbits have been summarized in the form of graphical maps in a two-dimensional grid of initial values. The basic motion types exist at all positive energies, but the binary + single particle configuration is obtained only in a narrow region of initial values if the total energy is large. At very large energies the equations of motion can be solved approximately, and this asymptotic result, exact in the limit of infinite energy, is presented.