Escape Orbits in the Three-Body Problem

Abstract

The escape orbit in the three-body system is a crucial topic in the field of astrophysics, helping people to research the chaotic system, stimulate the evolution of some complex celestial systems, and design the spacecraft trajectory. Extensive research has been conducted on this topic, but there are still some limitations. This paper focuses on reviewing and analyzing escape orbits in the problem of three bodies. Specifically, this paper explains the basic mechanics conditions and analyzes findings from the general and restricted three-body problems (CRTBP and ERTBP). Key tools such as Poincaré sections, ergodic hypothesis, and fractal basin boundaries are introduced to explain escape mechanisms. The study also highlights recent progress in the escape of a celestial body: spacecraft escape orbit design, relativistic effects on escape, and statistical analysis. The review of gravity-assist and low-energy escape orbit design in this paper provides theoretical support for space missions. Future research should include more comprehensive models, initial conditions, and higher-order physical effects.