Correlation of macroscopic instability and Lyapunov times in the general three-body problem

Abstract

We conducted extensive numerical experiments of equal mass three-body systems until they became disrupted. The system lifetimes, as a bound triple, and the Lyapunov times show a correlation similarto what has been earlier obtained for small bodies in the Solar System. Numerical integrations of several sets of differently randomised initial conditions produced the same relationship of the instability time and Lyapunov time. Marginal probability densities of the various times in the three-body experiments are also discussed. Our high accuracy numerical method for three-body orbit computations and Lyapunov time determinations is concisely described.Comment: 4 pages, 7 figures. accepted for publication in MNRA