Chaos in the Kepler System

TL;DR

This paper explores how gravitational radiation influences the long-term dynamics of a Keplerian binary system, revealing phenomena like transient chaos, sensitivity to initial conditions, and chaotic transitions in three dimensions.

Contribution

It extends previous planar chaos results to three-dimensional Kepler systems, analyzing the effects of radiation damping and oblique radiation on orbital evolution.

Findings

Orbital inclination varies significantly during resonance capture.

Chaotic transitions can occur due to gravitational radiation effects.

Sensitivity to initial conditions affects long-term orbital behavior.

Abstract

The long-term dynamical evolution of a Keplerian binary orbit due to the emission and absorption of gravitational radiation is investigated. This work extends our previous results on transient chaos in the planar case to the three dimensional Kepler system. Specifically, we consider the nonlinear evolution of the relative orbit due to gravitational radiation damping as well as external gravitational radiation that is obliquely incident on the initial orbital plane. The variation of orbital inclination, especially during resonance capture, turns out to be very sensitive to the initial conditions. Moreover, we discuss the novel phenomenon of chaotic transition.