Mapping the three-body system - decay time and reversibility

TL;DR

This study analyzes the predictability and decay times of Newtonian three-body systems, revealing fractal decay distributions, localized instabilities, and the emergence of an Arrow of Time despite deterministic initial conditions.

Contribution

It provides a comprehensive quantitative mapping of three-body system behaviors, including decay times, stability regions, and time asymmetry, using extensive numerical simulations.

Findings

Decay time distribution is fractal.

Localized narrow instability strips exist within stable regions.

Time asymmetry observed despite symmetric initial conditions.

Abstract

In this paper we carry out a quantitative analysis of the three-body systems and map them as a function of decaying time and intial conguration, look at this problem as an example of a simple deterministic system, and ask to what extent the orbits are really predictable. We have investigated the behavior of about 200 000 general Newtonian three body systems using the simplest initial conditions. Within our resolution these cover all the possible states where the objects are initially at rest and have no angular momentum. We have determined the decay time-scales of the triple systems and show that the distribution of this parameter is fractal in appearance. Some areas that appear stable on large scales exhibit very narrow strips of instability and the overall pattern, dominated by resonances, reminds us of a traditional Maasai warrior shield. Also an attempt is made to recover the original starting conguration of the three bodies by backward integration. We find there are instances where the evolution to the future and to the past lead to different orbits, in spite of time symmetric initial conditions. This implies that even in simple deterministic systems there exists an Arrow of Time.