Planar Three-Body Problem: theoretical predictions and simulation results

Abstract

We investigate the statistical properties of the non-hierarchical planar three-body problem, relevant to astrophysical systems with nearly planar dynamics, including protoplanetary disks and AGN disks. Using the Flux-based statistical theory of the three-body problem, previously studied in three dimensions, we derive theoretical predictions for several statistical observables in the planar case. Focusing on ergodic disintegration outcomes, we compare these predictions directly with numerical simulations and contrast the results with the corresponding unconstrained three-dimensional case. Our analysis is based on one million simulations for each of eight distinct mass sets. We examine escape probabilities, properties of marginal escape events, eccentricity distributions, lifetime distributions, and relative prevalence of prograde and retrograde escapes. While several of the theoretical predictions are in good agreement with the simulations, others exhibit unexpected discrepancies. We discuss possible explanations for these deviations.