Three body problem

By Alain Chenciner. Scholarpedia, 2007

556 citations recorded by the source corpus.

An isolated system consisting of two point masses exerting forces on one another — which is usually referred to as a two-body problem — can always be converted into an equivalent one-body problem. In particular, we can exactly solve a dynamical system containing two gravitationally interacting point masses. What about a system containing three gravitationally interacting point masses? Despite hundreds of years of research, no exact solution of this famous problem — which is generally known as the three-body problem — has ever been found. It is, however, possible to make some progress by restricting the problem’s scope.

Subfields: Aerospace Engineering, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/372650bb915cd7d0ccdb2ae9bfc27140cf6a1b94

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Aerospace Engineering

1. S. Naoz
2. B. Kocsis
3. Yi-sui Sun
4. Abraham Loeb
5. Dit-Yan Yeung
6. Gongjie Li
7. Mu Li
8. Yi Zhu

In Astronomy and Astrophysics

1. S. Naoz
2. D. Lai
3. B. Kocsis
4. Abraham Loeb
5. Gongjie Li
6. D. Muñoz
7. B. Liu
8. D. Lin

Citations in the corpus

• Eccentric Black Hole Mergers Forming in Globular Clusters (2017, unknown): “Its value can be analytically estimated by using that the normalized orbital energy distribution of binaries assembled in three-body interactions approximately follows [45, 57],”
• Post-oligarchic Evolution of Protoplanetary Embryos and the Stability of Planetary Systems (2007, background): “Based on the results from qualitative studies of the general three-body problem (e.g., Marchal 1990), Gladman (1993) investigated the stability of the two planet systems both analytically and numerically.”
• The Eccentric Kozai-Lidov Effect and Its Applications (2016, background): “…phenomena, it was limited to a narrow parts of the parameter space (favoring close to perpendicular initial orientation between the two orbits, e.g., Marchal 1990; Morbidelli 2002; Valtonen and Karttunen 2006; Fabrycky and Tremaine 2007) and produced only moderate eccentricity excitations.”
• Suppression of extreme orbital evolution in triple systems with short-range forces (2014, methodology): “Harrington (1968); Marchal et al. (1990); Krymolowski & Mazeh (1999); Ford et al. (2000b); Blaes et al. (2002) have derived the orbit-averaged Hamiltonian to octupole order and used the resulting equation of motion to explore some aspects of the evolution of triples.”
• Earthformer: Exploring Space-Time Transformers for Earth System Forecasting (2022, methodology): “We choose N 3 in the experiments so that the digits will follow the chaotic 3 -body motion [25].”
• ECCENTRICITY GROWTH AND ORBIT FLIP IN NEAR-COPLANAR HIERARCHICAL THREE-BODY SYSTEMS (2013, methodology): “2 degree due to the “Kozai resonance” (Thomas & Morbidelli 1996). Recently, Naoz et al. (2011, 2012) showed that relaxing either one of these assumptions, (i.e., an eccentric outer orbit, or non-negligible mass binary members) leads to qualitatively different behavior. In this case the z-component o”
• THE ECCENTRIC KOZAI MECHANISM FOR A TEST PARTICLE (2011, methodology): “To do so, we use the secular octupole Hamiltonian of Ford et al. (2000), which was apparently first derived by Harrington (1968) (as cited by Harrington 1969; see also Marchal 1990 and Krymolowski & Mazeh 1999 for derivations).”