The three-body problem
arXiv:1508.02312 · doi:10.1088/0034-4885/77/6/065901
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, 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.
49 pages, 10 figures, Published in Reports on Progress in Physics
References in corpus (13)
- DHP Framework: Digital Health Passports Using Blockchain -- Use case on international tourism during the COVID-19 pandemic
- Transit timing effects due to an exomoon
- KOI-126: A Triply-Eclipsing Hierarchical Triple with Two Low-Mass Stars
- TTVFast: An efficient and accurate code for transit timing inversion problems
- Stability Limits in Extra-solar Planetary Systems
- Three Classes of Newtonian Three-Body Planar Periodic Orbits
- Habitability of Earth-type Planets and Moons in the Kepler-16 System
- Collinear solution to the general relativistic three-body problem
- Choreographic solution to the general relativistic three-body problem
- Secular dynamics of coplanar, non-resonant planetary system under the general relativity and quadrupole moment perturbations
- Post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem
- Uniqueness of collinear solutions for the relativistic three-body problem
- Stability of Circular Orbits in General Relativity: A Phase Space Analysis
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