Abstract
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, log in via an institution to check access.
Similar content being viewed by others
References
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.
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.
Chirikov, B.V., A universal instability of many-dimensional oscillator systems, Phys. Rep., 1979, vol. 52, no. 5, pp. 263–379.
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.
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.
Duboshin, G.N., Spravochnoe rukovodstvo po nebesnoi mekhanike i astrodinamike (Handbook on Celestial Mechanics and Astrodynamics), Moscow: Nauka, 1976.
Eggleton, P.P., Approximations to the radii of Roche lobes, Astrophys. J., 1983, vol. 268, pp. 368–369.
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.
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.
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.
Kozai, Y., Secular perturbations of asteroids with high inclination and eccentricity, Astron. J., 1962, vol. 67, no. 9, pp. 591–598.
Lichtenberg, A.J. and Lieberman, M.A., Regular and Chaotic Dynamics, New York: Springer-Verlag, 1983.
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.
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.
Marov, M.Ya. and Shevchenko, I.I., Exoplanets, Priroda (Moscow), 2014, no. 6, pp. 3–15.
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.
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.
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.
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.
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.
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.
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.V. Melnikov, 2017, published in Astronomicheskii Vestnik, 2017, Vol. 51, No. 4, pp. 357–364.
Rights and permissions
About this article
Cite this article
Melnikov, A.V. Orbital dynamics of the planetary system HD 196885. Sol Syst Res 51, 327–334 (2017). https://doi.org/10.1134/S0038094617040025
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0038094617040025