Orbital dynamics in the post-Newtonian planar circular Sun-Jupiter system

TL;DR

This paper investigates the complex orbital dynamics of a test particle in the Sun-Jupiter system using post-Newtonian theory, revealing intricate basin structures and differences from classical models.

Contribution

It introduces a detailed numerical analysis of the post-Newtonian restricted three-body problem, highlighting the impact on orbital classifications and basin structures compared to classical approaches.

Findings

High complexity in orbital dynamics with fractal basin boundaries.

Significant differences between classical and post-Newtonian orbit outcomes.

Strong dependence of basin properties on the Jacobi constant.

Abstract

The theory of the post-Newtonian (PN) planar circular restricted three-body problem is used for numerically investigating the orbital dynamics of a test particle (e.g., a comet, asteroid, meteor or spacecraft) in the planar Sun-Jupiter system with a scattering region around Jupiter. For determining the orbital properties of the test particle, we classify large sets of initial conditions of orbits for several values of the Jacobi constant in all possible Hill region configurations. The initial conditions are classified into three main categories: (i) bounded, (ii) escaping and (iii) collisional. Using the smaller alignment index chaos indicator (SALI), we further classify bounded orbits into regular, sticky or chaotic. In order to get a spherical view of the dynamics of the system, the grids of the initial conditions of the orbits are defined on different types of two-dimensional planes. We locate the different types of basins and we also relate them with the corresponding spatial distributions of the escape and collision time. Our thorough analysis exposes the high complexity of the orbital dynamics and exhibits an appreciable difference between the final states of the orbits in the classical and PN approaches. Furthermore, our numerical results reveal a strong dependence of the properties of the considered basins with the Jacobi constant, along with a remarkable presence of fractal basin boundaries. Our outcomes are compared with earlier ones, regarding other planetary systems.