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.
arXiv comment49 pages, 10 figures, Published in Reports on Progress in Physics
References in corpus (55)
- Shrinking binary and planetary orbits by Kozai cycles with tidal friction
- Planet Occurrence within 0.25 AU of Solar-type Stars from Kepler
- The false positive rate of Kepler and the occurrence of planets
- Long-Term Stability of Planets in Binary Systems
- DHP Framework: Digital Health Passports Using Blockchain -- Use case on international tourism during the COVID-19 pandemic
- On detecting terrestrial planets with timing of giant planet transits
- Coalescing binary systems of compact objects to (post)$^{5/2}-Newtonian order. V. Spin Effects
- Kepler-16: A Transiting Circumbinary Planet
- A Closely-Packed System of Low-Mass, Low-Density Planets Transiting Kepler-11
- Validation of Kepler's Multiple Planet Candidates. III: Light Curve Analysis & Announcement of Hundreds of New Multi-planet Systems
- Kepler-36: A Pair of Planets with Neighboring Orbits and Dissimilar Densities
- Orbital perturbations on transiting planets: A possible method to measure stellar quadrupoles and to detect Earth-mass planets
- Transit timing effects due to an exomoon
- KOI-126: A Triply-Eclipsing Hierarchical Triple with Two Low-Mass Stars
- Validation of Kepler's Multiple Planet Candidates. II: Refined Statistical Framework and Descriptions of Systems of Special Interest
- Overstable Librations can account for the Paucity of Mean Motion Resonances among Exoplanet Pairs
- Formation of the Widest Binaries from Dynamical Unfolding of Triple Systems
- The Hunt for Exomoons with Kepler (HEK): I. Description of a New Observational Project
- The Detection and Characterization of a Nontransiting Planet by Transit Timing Variations
- KOI-142, the King of Transit Variations, is a Pair of Planets near the 2:1 Resonance
- TTVFast: An efficient and accurate code for transit timing inversion problems
- How not to build Tatooine: the difficulty of in situ formation of circumbinary planets Kepler 16b, Kepler 34b and Kepler 35b
- Stability Limits in Extra-solar Planetary Systems
- Long-term planetary integration with individual time steps
- Three Classes of Newtonian Three-Body Planar Periodic Orbits
- Circumbinary Planet Formation in the Kepler-16 system. I. N-body Simulations
- The Hunt for Exomoons with Kepler (HEK): II. Analysis of Seven Viable Satellite-Hosting Planet Candidates
- Calculating the Habitable Zone of Binary Star Systems I: S-Type Binaries
- Calculating the Habitable Zone of Binary Star Systems II: P-Type Binaries
- Prospects for Extrasolar "Earths" in Habitable Zones
- Application of the MEGNO technique to the dynamics of Jovian irregular satellites
- Light curve modelling for mutual transits
- The Hunt for Exomoons with Kepler (HEK): III. The First Search for an Exomoon around a Habitable-Zone Planet
- On the Habitable Zones of Circumbinary Planetary Systems
- An Analytic Method to determine Habitable Zones for S-Type Planetary Orbits in Binary Star Systems
- A Dynamical Analysis of the 47 UMa Planetary System
- S-Type and P-Type Habitability in Stellar Binary Systems: A Comprehensive Approach. I. Method and Applications
- Habitability of Earth-type Planets and Moons in the Kepler-16 System
- The contribution of secondary eclipses as astrophysical false positives to exoplanet transit surveys
- A dynamical analysis of the Kepler-11 planetary system
- Stability analysis of single planet systems and their habitable zones
- Collinear solution to the general relativistic three-body problem
- The Stability of the Suggested Planet in the nu Octantis System: A Numerical and Statistical Study
- Testing a hypothesis of the νOctantis planetary system
- 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
- Application of chaos indicators in the study of dynamics of S-type extrasolar planets in stellar binaries
- Stable 1:2 Resonant Periodic Orbits in Elliptic Three-Body Systems
- The dynamics of the elliptic Hill problem : Periodic orbits and stability regions
- Post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem
- Uniqueness of collinear solutions for the relativistic three-body problem
- The Instability Transition for the Restricted 3-Body Problem. III. The Lyapunov Exponent Criterion
- Planetary Dynamics and Habitable Planet Formation In Binary Star Systems
- On the Possibility of Habitable Moons in the System of HD 23079: Results from Orbital Stability Studies
- Stability of Circular Orbits in General Relativity: A Phase Space Analysis
Cited by in corpus (28)
- Hydrodynamics of circumbinary accretion: Angular momentum transfer and binary orbital evolution
- More than six hundreds new families of Newtonian periodic planar collisionless three-body orbits
- Orbital Stability of Circumstellar Planets in Binary Systems
- Outer solar system possibly shaped by a stellar fly-by
- Calcium-Rich Gap Transients: Tidal Detonations of White Dwarfs?
- Gravitational wave forms, polarizations, response functions and energy losses of triple systems in Einstein-Aether theory
- Orbital Stability of Exomoons and Submoons with Applications to Kepler 1625b-I
- Effects of inclined star-disk encounter on protoplanetary disk size
- Flux-based statistical prediction of three-body outcomes
- On the conservation of the Jacobi integral in the post-Newtonian circular restricted three-body problem
- Switching and amplifying three-body Casimir effects
- Trajectory of the stellar flyby that shaped the outer solar system
- Orbital dynamics in the post-Newtonian planar circular Sun-Jupiter system
- From star-disc encounters to numerical solutions for a subset of the restricted three-body problem
- Saddle Transport and Chaos in the Double Pendulum
- Inclination Excitation of Solar System Debris Disk due to Stellar Flybys
- Improved Analysis of Clarke Exobelt Detectability
- DESTINY: Database for the Effects of STellar encounters on dIsks and plaNetary sYstems
- Climatological and UV-based Habitability of Possible Exomoons in F-star Systems
- Integral field spectroscopy with the solar gravitational lens
- Chaotic dynamics in the planar gravitational many-body problem with rigid body rotations
- Irregular moons possibly injected from the outer solar system by a stellar flyby
- Guiding Video Prediction with Explicit Procedural Knowledge
- Periodic orbits of the two fixed centers problem with a variational gravitational field
- On the stability of planetary orbits in binary star systems I. The S-type orbits
- Tidal disruptions of close white dwarf binaries by intermediate mass black holes
- Newtonian restricted three-body gravitational problem with positive and negative point masses
- LieDetect: Detection of representation orbits of compact Lie groups from point clouds