Analysis of Orbital Stability in the Three-Body Problem

Abstract

Three body problem is one of the most complicated dynamical problems in classical mechanics; the difficulty comes from the nonlinear equations and sensitive initial conditions. In this paper, it reviews the disintegration process of Three body system in long-term evolution and discuss the application of statistical mechanics in explaining this phenomenon. Based on the theoretical model, numerical simulation, and observational results, it draws the following conclusions: The most frequent final state of a three-body system is the disintegration of a binary star and an escape star. This kind of mechanism comes from the energy and angular momentum’s homogenization, and it has been proved by the BN/KL region in Orion. Besides, the statistical model based on the microcanonical distribution and ergodicity assumption can predict the final state parameter’s distribution, which is consistent with the simulation results and provides a new way to explore chaotic systems. In the future, it will combine Gaia, gravitational wave observation, and high-precision numerical simulation to further complete the theory and application in the dynamics of compact objects.