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On the chaotic orbital dynamics of the planet in the system 16 Cyg

Abstract

The chaotic orbital dynamics of the planet in the wide visual binary star system 16 Cyg is considered. The only planet in this system has a significant orbital eccentricity, e = 0.69. Previously, Holman et al. suggested the possibility of chaos in the orbital dynamics of the planet due to the proximity of 16 Cyg to the separatrix of the Lidov–Kozai resonance. We have calculated the Lyapunov characteristic exponents on the set of possible orbital parameters for the planet. In all cases, the dynamics of 16 Cyg is regular with a Lyapunov time of more than 30 000 yr. The dynamics is considered in detail for several possible models of the planetary orbit; the dependences of Lyapunov exponents on the time of their calculation and the time dependences of osculating orbital elements have been constructed. Phase space sections for the system dynamics near the Lidov–Kozai resonance have been constructed for all models. A chaotic behavior in the orbital motion of the planet in 16 Cyg is shown to be unlikely, because 16 Cyg in phase space is far from the separatrix of the Lidov–Kozai resonance at admissible orbital parameters, with the chaotic layer near the separatrix being very narrow.

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Correspondence to A. V. Melnikov.

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Original Russian Text © A.V. Melnikov, 2016, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2016, Vol. 42, No. 2, pp. 136–147.

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Melnikov, A.V. On the chaotic orbital dynamics of the planet in the system 16 Cyg. Astron. Lett. 42, 115–125 (2016). https://doi.org/10.1134/S1063773716010059

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  • DOI: https://doi.org/10.1134/S1063773716010059

Keywords

  • 16 Cyg
  • multiple stars
  • exoplanets
  • stability of motion
  • Lyapunov exponents
  • Lyapunov time
  • Lidov–Kozai resonance