Periodic orbits in the free-fall three-body problem

Орлов, В. В.; Titov, V. B.; Shombina, L. A.

doi:10.1134/s1063772916110056

Cited by 9 publications

(10 citation statements)

References 14 publications

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“…Tokovinin (2001) presented the statistics of catalogued multiple systems in the form N i /N i−1 = 0.11, 0.22, 0.20, 0.36 for i = 3, 4, 5, 6, respectively, where N i is the number of systems of the ith multiplicity. These results are in accordance with the conclusions made by Orlov & Titov (1994) in their study of multiple objects in the immediate (d ≤ 25 pc) solar vicinity. Later on, Tokovinin (2014) studied hierarchical systems among F and G dwarfs in the solar neighborhood and found the fraction of multiple systems with 1, 2, 3, ... components to be 54:33:8:4:1.…”

Section: Catalogues Of Double and Multiple Systemssupporting

confidence: 93%

“…1. It can be seen that the most complete catalogue, WDS, satisfactory images the Orlov & Titov (1994) and Tokovinin (2001) distributions, while the newer and deeper study by Tokovinin (2014) demonstrates a surplus of triple and higher-multiplicity systems in comparison with the catalogued systems (or, conversely, WDS contains superfluous, obviously optical, double stars).…”

Section: Catalogues Of Double and Multiple Systemsmentioning

confidence: 98%

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On Utmost Multiplicity of Hierarchical Stellar Systems

et al. 2016

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Abstract. According to theoretical considerations, multiplicity of hierarchical stellar systems can reach, depending on masses and orbital parameters, several hundred, while observational data confirm the existence of at most septuple (seven-component) systems. In this study, we cross-match the stellar systems of very high multiplicity (six and more components) in modern catalogues of visual double and multiple stars to find among them the candidates to hierarchical systems. After cross-matching the catalogues of closer binaries (eclipsing, spectroscopic, etc.), some of their components were found to be binary/multiple themselves, what increases the system's degree of multiplicity. Optical pairs, known from literature or filtered by the authors, were flagged and excluded from the statistics. We compiled a list of hierarchical systems with potentially very high multiplicity that contains ten objects. Their multiplicity does not exceed 12, and we discuss a number of ways to explain the lack of extremely high multiplicity systems.

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Section: Catalogues Of Double and Multiple Systemssupporting

confidence: 93%

Section: Catalogues Of Double and Multiple Systemsmentioning

confidence: 98%

On Utmost Multiplicity of Hierarchical Stellar Systems

et al. 2016

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“…Yasko and Orlov [30] found three collisionless periodic orbits while searching periodic free-fall three-body orbits. Orlov et al [31] investigated periodic orbits of the free-fall three-body system with equal mass. In summary, so far, only four collisionless periodic orbits in the free-fall three-body problem have been found.…”

Section: Introductionmentioning

confidence: 99%

Collisionless periodic orbits in the free-fall three-body problem

Liao

2019

New Astronomy

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Although the free-fall three-body problem have been investigated for more than one century, however, only four collisionless periodic orbits have been found. In this paper, we report 234 collisionless periodic orbits of the free-fall three-body system with some mass ratios, including three known collisionless periodic orbits. Thus, 231 collisionless free-fall periodic orbits among them are entirely new. In theory, we can gain periodic orbits of the free-fall three-body system in arbitrary ratio of mass. Besides, it is found that, for a given ratio of masses of two bodies, there exists a generalized Kepler's third law for the periodic three-body system. All of these would enrich our knowledge and deepen our understanding about the famous three-body problem as a whole.

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“…Besides, they also found 313 new families of collisionless periodic orbits for the free-fall triple system with different ratios of masses 30 (there were only 4 trajectories reported before 31,32 ).…”

Section: Introductionmentioning

confidence: 97%

Can machine learning really solve the three-body problem?

Li¹,

Li²,

Liao³

2020

Preprint

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Machine learning is becoming one of most rapidly growing technical fields, benefiting tremendous areas in science and industry. Recently, Breen et al demonstrated a new study with a multi-layered deep artificial neural network (ANN) on a chaotic three-body system and claimed that it can bring “success in accurately reproducing the results of a chaotic system” with “up to 100 million times faster than numerical integrator”. Here, we use their trained ANN model to predict periodic orbits of the same three-body system, but the detailed comparisons are disappointing. It might be due to the butterfly-effect of chaotic systems, i.e. very sensitive to tiny disturbance, but in practice nearly all ML algorithms derive their solutions statistically and probabilistically and therefore are rarely possible to train them to 100% accuracy. We illustrate here that the current accuracy of the machine learning is not precise enough for correct prediction of periodic orbits of a chaotic three-body system in a long enough duration. Thus, it is still a great challenge for machine learning to solve chaotic systems, such as the famous three-body problem. Without doubt, studies in machine learning on chaotic systems might greatly deepen and enrich our understandings not only on chaos but also on machine learning itself.

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Periodic orbits in the free-fall three-body problem

Cited by 9 publications

References 14 publications

On Utmost Multiplicity of Hierarchical Stellar Systems

On Utmost Multiplicity of Hierarchical Stellar Systems

Collisionless periodic orbits in the free-fall three-body problem

Can machine learning really solve the three-body problem?

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