TL;DR
This paper reviews the historical and modern developments of the three-body problem, covering analytical and numerical methods, stability analysis, periodic orbits, and applications in astronomy and space dynamics.
Contribution
It provides a comprehensive overview of the three-body problem, including recent advances in analytical, numerical, and relativistic approaches, and discusses their practical applications.
Findings
Overview of analytical and numerical solution methods
Discussion of stability and periodic orbits
Application to astronomical and space systems
Abstract
The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more than 300 years. In this paper, we present a review of the three-body problem in the context of both historical and modern developments. We describe the general and restricted (circular and elliptic) three-body problems, different analytical and numerical methods of finding solutions, methods for performing stability analysis, search for periodic orbits and resonances, and application of the results to some interesting astronomical and space dynamical settings. We also provide a brief presentation of the general and restricted relativistic three-body problems, and discuss their astronomical applications.
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