The three-body problem
Authors:
- 1 June 2014
- journal article
- review article
- Published by IOP Publishing in Reports on Progress in Physics
- Vol. 77 (6) , 065901
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 and searching for periodic orbits and resonances. We apply the results to some interesting problems of celestial mechanics. We also provide a brief presentation of the general and restricted relativistic three-body problems, and discuss their astronomical applications.Keywords
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