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Dynamics of Two Planets in the 3/2 Mean-motion Resonance: Application to the Planetary System of the Pulsar PSR B1257+12

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Abstract

This paper considers the dynamics of two planets, as the planets B and C of the pulsar PSR B1257+12, near a 3/2 mean-motion resonance. A two-degrees-of-freedom model, in the framework of the general three-body planar problem, is used and the solutions are analyzed through surfaces of section and Fourier techniques in the full phase space of the system.

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References

  • Beaugé C., Callegari N. Jr., Ferraz-Mello S., Michtchenko T.A. Resonances and stability of extra-solar planetary systems. In: Z. Knežević and A. Milani (eds.) IAU Colloq. 197, 3–18 (2005)

  • Callegari Jr., N. Ressonâncias 2:1 e 3:2 em sistemas planetários. Dr. Thesis, Univ. Sao Paulo, SP (2003)

  • Callegari Jr., N., Michtchenko, T.A., Ferraz-Mello, S. Dynamics of two planets in resonances: the 2:1, 3:2 and 5:2 cases. Inst. Appl. Astron. RAS, Transactions. 8, 47–52 (2002)

    Google Scholar 

  • Callegari N. Jr., Michtchenko T.A., Ferraz-Mello S. (2004) Dynamics of two planets in the 2/1 mean-motion resonance. Celest. Mech. Dyn. Astr. 89, 201–234

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Ferraz-Mello S., Michtchenko T.A. (2002) Extra-solar planetary system. Rev. Mex. A. A. Conf. Ser. 14, 7–10

    ADS  Google Scholar 

  • Ferraz-Mello, S., Michtchenko, T.A., Beaugé, C. Regular motions in extra-solar planetary systems. astro-ph/0402335 (2004)

  • Ferraz-Mello, S., Michtchenko, T.A., Beaugé, C., Callegari, N. Jr.: Extra-solar planetary systems. In: R. Dvorak et al. (eds.), Lect. Notes Phys. 683, 219–271 (2005)

  • Goździewski K., Konacki M., Wolszczan A. (2005) Long-term stability and dynamical environment of the PSR 1257+12 planetary system. Astroph. J. 619, 1084–1097

    Article  ADS  Google Scholar 

  • Hori, G. Mutual perturbations of 1:1 commensurable small bodies with the use of canonical relative coordinates. Part I. In: S. Ferraz-Mello and W. Sessin (eds.) Resonances in the Motion of the Planets, Satellites and Asteroids, IAG/USP, Sao Paulo, pp. 33–66 (1985)

  • Konacki M., Maciejewski A.J. (1996) A method of verification of the existence of planets around planets. Icarus 122, 347–358

    Article  ADS  Google Scholar 

  • Konacki M., Maciejewski A.J., Wolszczan A. (1999) Resonance in PSR B1257+12 planetary system. Astroph. J. 513, 471–476

    Article  ADS  Google Scholar 

  • Konacki M., Wolszczan A. (2003) Masses and orbital inclinations of planets in the PSR B1257+12 system. Astroph. J. 591, L147–L150

    Article  ADS  Google Scholar 

  • Malhotra R., Black D., Eck A., Jackson A. (1992) Resonant orbital evolution in the putative planetary system of PSR1257 +12. Nature 356, 583–585

    Article  ADS  Google Scholar 

  • Malhotra R. (1993) Three body effects in the PSR 1257+12 planetary system. Astroph. J. 407, 266–275

    Article  ADS  Google Scholar 

  • Michtchenko T.A., Ferraz-Mello S. (2001a) Modeling the 5:2 Mean-motion resonance in the jupiter-saturn planetary system. Icarus. 149, 357–374

    Article  ADS  Google Scholar 

  • Michtchenko T.A., Ferraz-Mello S. (2001b) Resonant structure of the solar system in the neighborhood of the planets. Astron. J. 122, 474–481

    Article  ADS  Google Scholar 

  • Peale S.J. (1993) On the verification of the planetary system around PSR 1257+12. Astron. J. 105, 1562–1570

    Article  ADS  Google Scholar 

  • Poincaré H. (1987) Une forme nouvelle des équations du problème des trois corps. Bull. Astron. 14, 53–67

    Google Scholar 

  • Quintana, E.V., Rivera, E.J., Lissauer, J.J. Dynamical stability of the PSR1257+12 and HD83433 Extrasolar Planetary System. In: O. C. Winter and A. F. B. A. Prado (eds.) Adv. Space Dynam. INPE, 2, 82–88 (2002)

  • Rasio F.A., Nicholson P.D., Shapiro S.L., Teukolsky S.A. (1992) An observational test for the existence of a planetary system orbiting PSR 1257+12. Nature 355, 325–326

    Article  ADS  Google Scholar 

  • Tittemore W., Wisdom J. (1988) Tidal evolution of the uranian satellites I. Passage of Ariel and Umbriel through the 5:3 Mean-Motion Commensurability. Icarus 74, 172–230

    Article  ADS  Google Scholar 

  • Wolszczan A., Frail D.A. (1992) A planetary system around the millisecond pulsar PSR 1257+12. Nature 355, 145–147

    Article  ADS  Google Scholar 

  • Wolszczan A. (1994) Confirmation of earth-mass planets orbiting the millisecond pulsar PSR B1257+12. Science 264, 538–542

    Article  ADS  Google Scholar 

  • Wolszczan A., Doroshenko O., Konacki M., Kramer M., Jessner A., Wielebinski R., Camilo F., Nice D.J., Taylor J.H. (2000) Timing observations of four millisecond pulsars with the Arecibo and Effelsberg radiotelescopes. Astroph. J. 528, 907–912

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. DEMAC, UNESP, Av. 24A, Rio Claro, Brasil

    N. Callegari Jr

  2. Instituto de Astronomia, Geofí sica e Ciências Atmosféricas, Universidade de São Paulo, Rua do Matão, 1226, São Paulo, Brasil

    S. Ferraz-Mello & T. A. Michtchenko

Authors
  1. N. Callegari Jr
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  2. S. Ferraz-Mello
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  3. T. A. Michtchenko
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Corresponding author

Correspondence to N. Callegari Jr.

Additional information

On the possibility of existence of a fourth planet in distant orbit, see Wolszczan et al., 2000

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Callegari, N., Ferraz-Mello, S. & Michtchenko, T.A. Dynamics of Two Planets in the 3/2 Mean-motion Resonance: Application to the Planetary System of the Pulsar PSR B1257+12. Celestial Mech Dyn Astr 94, 381–397 (2006). https://doi.org/10.1007/s10569-006-9002-4

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  • DOI: https://doi.org/10.1007/s10569-006-9002-4

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