Skip to main content

Orbital dynamics of the planetary system HD 196885


The orbital dynamics of the single known planet in the binary star system HD 196885 has been considered. The Lyapunov characteristic exponents and Lyapunov time of the planetary system have been calculated for possible values of the planetary orbit parameters. It has been shown that the dynamics of the planetary system HD 196885 is regular with the Lyapunov time of more than 5 × 104 years (the orbital period of the planet is approximately 3.7 years), if the motion occurs at a distance from the separatrix of the Lidov–Kozai resonance. The values of the planet’s orbital inclination to the plane of the sky and longitude of the ascending node lie either within ranges 30° < i p < 90° and 30° < Ωp < 90°, or 90° < i p < 180° and 180° < Ωp < 300°.

This is a preview of subscription content, access via your institution.


  • von Bremen, H.F., Udwadia, F.E., and Proskurowski, W., An efficient QR based method for the computation of Lyapunov exponents, Phys. D, 1997, vol. 101, pp. 1–16.

    MathSciNet  Article  MATH  Google Scholar 

  • Chauvin, G., Beust, H., Lagrange, A.-M., and Eggenberger, A., Planetary systems in close binary stars: The case of HD 196885. Combined astrometric and radial velocity study, Astron. Astrophys., 2011, vol. 528, art. ID A8.

  • Chauvin, G., Lagrange, A.-M., Udry, S., and Mayor, M., Characterization of the long-period companions of the exoplanet host stars: HD 196885, HD 1237 and HD 27442. VLT/NACO, and SINFONI near-infrared, follow-up imaging and spectroscopy, Astron. Astrophys., 2007, vol. 475, no. 2, pp. 723–727.

    ADS  Article  Google Scholar 

  • Chirikov, B.V., A universal instability of many-dimensional oscillator systems, Phys. Rep., 1979, vol. 52, no. 5, pp. 263–379.

    ADS  MathSciNet  Article  Google Scholar 

  • Cochran, W.D., Hatzes, A.P., Butler, R.P., and Marcy, G.W., The discovery of a planetary companion to 16 Cygni B, Astrophys. J., 1997, vol. 483, pp. 457–463.

    ADS  Article  Google Scholar 

  • Correia, A.C.M., Udry, S., Mayor, M., Eggenberger, A., Naef, D., Beuzit, J.-L., Perrier, C., Queloz, D., Sivan, J.-P., Pepe, F., Santos, N.C., and Ségransan, D., The ELODIE survey for northern extra-solar planets. IV. HD 196885, a close binary star with a 3.7-year planet, Astron. Astrophys., 2008, vol. 479, no. 1, pp. 271–275.

    ADS  Article  Google Scholar 

  • Duboshin, G.N., Spravochnoe rukovodstvo po nebesnoi mekhanike i astrodinamike (Handbook on Celestial Mechanics and Astrodynamics), Moscow: Nauka, 1976.

    Google Scholar 

  • Eggleton, P.P., Approximations to the radii of Roche lobes, Astrophys. J., 1983, vol. 268, pp. 368–369.

    ADS  Article  Google Scholar 

  • Giuppone, C.A., Morais, M.H.M., Boué, G., and Correia, A.C.M., Dynamical analysis and constraints for the HD 196885 system, Astron. Astrophys., 2012, vol. 541, art. ID A151.

  • Hairer, E., Nørsett, S.P., and Wanner, G., Solving Ordinary Differential Equations: I. Nonstiff Problems, Berlin: Springer-Verlag, 1987.

    Book  MATH  Google Scholar 

  • Holman, M., Touma, J., and Tremaine, S., Chaotic variations in the eccentricity of the planet orbiting 16 Cygni B, Nature, 1997, vol. 386, no. 6622, pp. 254–256.

    ADS  Article  Google Scholar 

  • Kouprianov, V.V. and Shevchenko, I.I., On the chaotic rotation of planetary satellites: The Lyapunov exponents and the energy, Astron. Astrophys., 2003, vol. 410, pp. 749–757.

    ADS  Article  MATH  Google Scholar 

  • Kozai, Y., Secular perturbations of asteroids with high inclination and eccentricity, Astron. J., 1962, vol. 67, no. 9, pp. 591–598.

    ADS  MathSciNet  Article  Google Scholar 

  • Lichtenberg, A.J. and Lieberman, M.A., Regular and Chaotic Dynamics, New York: Springer-Verlag, 1983.

    MATH  Google Scholar 

  • Lidov, M.L., Evolution of orbits of artificial satellites affected by gravitational perturbations of external bodies, Iskusstv. Sputniki Zemli, 1961, vol. 8, pp. 5–45.

    Google Scholar 

  • Maffione, N.P., Darriba, L.A., Cincotta, P.M., and Giordano, C.M., Chaos detection tools: application to a self-consistent triaxial model, Mon. Not. R. Astron. Soc., 2011, vol. 429, no. 3, pp. 2700–2717.

    ADS  Article  Google Scholar 

  • Marov, M.Ya. and Shevchenko, I.I., Exoplanets, Priroda (Moscow), 2014, no. 6, pp. 3–15.

    Google Scholar 

  • Melnikov, A.V., On the chaotic orbital dynamics of the planet in the system 16 Cyg, Astron. Lett., 2016, vol. 42, no. 2, pp. 115–125.

    ADS  Article  Google Scholar 

  • Mel’nikov, A.V., Orlov, V.V., and Shevchenko, I.I., Stability of the multiple star system ɩUMa (ADS 7114), Astron. Rep., 2014, vol. 58, no. 9, pp. 640–649.

    ADS  Article  Google Scholar 

  • Naoz, S., Farr, W., Lithwick, Y., Rasio, F.A., and Teyssandier, J., Hot Jupiter from secular planet-planet interactions, Nature, 2011, vol. 473, no. 7346, pp. 187–189.

    ADS  Article  Google Scholar 

  • Perryman, M.A.C., Lindegren, L., Kovalevsky, J., Hoeg, E., Bastian, U., Bernacca, P.L., Crézé, M., Donati, F., Grenon, M., Grewing, M., van Leeuwen, F., van der Marel, H., Mignard, F., Murray, C.A., Le Poole, R.S., et al., The HIPPARCOS catalogue, Astron. Astrophys., 1997, vol. 323, pp. L49–L52.

    ADS  Google Scholar 

  • Satyal, S., Hinse, T.C., Quarles, B., and Noyola, J.P., Chaotic dynamics of the planet in HD 196885 AB, Mon. Not. R. Astron. Soc., 2014, vol. 443, no. 2, pp. 1310–1318.

    ADS  Article  Google Scholar 

  • Satyal, S., Quarles, B., and Hinse, T.C., Application of chaos indicators in the study of dynamics of S-type extrasolar planets in stellar binaries, Mon. Not. R. Astron. Soc., 2013, vol. 433, no. 3, pp. 2215–2225.

    ADS  Article  Google Scholar 

  • Shevchenko, I.I. and Kouprianov, V.V., On the chaotic rotation of planetary satellites: The Lyapunov spectra and the maximum Lyapunov exponents, Astron. Astrophys., 2002, vol. 394, pp. 663–674.

    ADS  Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to A. V. Melnikov.

Additional information

Original Russian Text © A.V. Melnikov, 2017, published in Astronomicheskii Vestnik, 2017, Vol. 51, No. 4, pp. 357–364.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Melnikov, A.V. Orbital dynamics of the planetary system HD 196885. Sol Syst Res 51, 327–334 (2017).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • exoplanets
  • HD 196885
  • orbital dynamics
  • Lyapunov time
  • Lidov–Kozai resonance