Skip to main content
Log in

On the stability of dust orbits in mean-motion resonances perturbed by from an interstellar wind

  • Original Article
  • Published:
Celestial Mechanics and Dynamical Astronomy Aims and scope Submit manuscript

Abstract

Circumstellar dust particles can be captured in a mean-motion resonance (MMR) with a planet and simultaneously be affected by non-gravitational effects. It is possible to describe the secular variations of a particle orbit in the MMR analytically using averaged resonant equations. We derive the averaged resonant equations from the equations of motion in near-canonical form. The secular variations of the particle orbit depending on the orientation of the orbit in space are taken into account. The averaged resonant equations can be derived/confirmed also from Lagrange’s planetary equations. We apply the derived theory to the case when the non-gravitational effects are the Poynting–Robertson effect, the radial stellar wind, and an interstellar wind. The analytical and numerical results obtained are in excellent agreement. We found that the types of orbits correspond to libration centers of the conservative problem. The averaged resonant equations can lead to a system of equations which holds for stationary points in a subset of resonant variables. Using this system we show analytically that for the considered non-gravitational effects, all stationary points should correspond to orbits which are stationary in interplanetary space after an averaging over a synodic period. In an exact resonance, the stationary orbits are stable. The stability is achieved by a periodic repetition of the evolution during the synodic period. Numerical solutions of this system show that there are no stationary orbits for either the exact or non-exact resonances.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  • Alouani-Bibi, F., Opher, M., Alexashov, D., Izmodenov, V., Toth, G.: Kinetic versus multi-fluid approach for interstellar neutrals in the heliosphere: exploration of the interstellar magnetic field effects. Astrophys. J. 734, 45 (2011)

    Article  ADS  Google Scholar 

  • Baines, M.J., Williams, I.P., Asebiomo, A.S.: Resistance to the motion of a small sphere moving through a gas. Mon. Not. R. Astron. Soc. 130, 63–74 (1965)

    Article  ADS  Google Scholar 

  • Belyaev, M.A., Rafikov, R.R.: The dynamics of dust grains in the outer solar system. Astrophys. J. 723, 1718–1735 (2010)

    Article  ADS  Google Scholar 

  • Bate, R.R., Mueller, D.D., White, J.E.: Fundamentals of Astrodynamics. Dover Publications, New York (1971)

    Google Scholar 

  • Beaugé, C.: Asymmetric librations in exterior resonances. Celest. Mech. Dyn. Astron. 60, 225–248 (1994)

    Article  MATH  ADS  Google Scholar 

  • Beaugé, C., Ferraz-Mello, S.: Resonance trapping in the primordial solar nebula: the case of a Stokes drag dissipation. Icarus 103, 301–318 (1993)

    Article  ADS  Google Scholar 

  • Beaugé, C., Ferraz-Mello, S.: Capture in exterior mean-motion resonances due to Poynting–Robertson drag. Icarus 110, 239–260 (1994)

    Article  ADS  Google Scholar 

  • Brouwer, D., Hori, G.I.: Theoretical evaluation of atmospheric drag effects in the motion of an artificial satellite. Astron. J. 66, 193–225 (1961)

    Article  MathSciNet  ADS  Google Scholar 

  • Brownlee, D.E.: The ring around us. Nature 369, 706 (1994)

    Article  ADS  Google Scholar 

  • Buenzli, E., Thalmann, C., Vigan, A., Boccaletti, A., Chauvin, G., Augereau, J.C., Meyer, M.R., Ménard, F., Desidera, S., Messina, S., Henning, T., Carson, J., Montagnier, G., Beuzit, J.L., Bonavita, M., Eggenberger, A., Lagrange, A.M., Mesa, D., Mouillet, D., Quanz, S.P.: Dissecting the Moth: discovery of an off-centered ring in the HD 61005 debris disk with high-resolution imaging. Astron. Astrophys. 524, L1 (2010)

    Article  ADS  Google Scholar 

  • Danby, J.M.A.: Fundamentals of Celestial Mechanics, 2nd edn. Willmann-Bell, Richmond (1988)

    Google Scholar 

  • Debes, J.H., Weinberger, A.J., Kuchner, M.J.: Interstellar medium sculpting of the HD 32297 debris disk. Astrophys. J. 702, 318–326 (2009)

    Article  ADS  Google Scholar 

  • Dermott, S.F., Jayaraman, S., Xu, Y.L., Gustafson, B.A.S., Liou, J.-C.: A circumsolar ring of asteroidal dust in resonant lock with the Earth. Nature 369, 719–723 (1994)

    Article  ADS  Google Scholar 

  • Dermott, S.F., Grogan, K., Durda, D.D., Jayaraman, S., Kehoe, T.J.J., Kortenkamp, S.J., Wyatt, M.C.: Orbital evolution of interplanetary dust. In: Grün, E., Gustafson, B.A.S., Dermott, S.F., Fechtig, H. (eds.) Interplanetary Dust, pp. 569–639. Springer, Berlin (2001)

    Chapter  Google Scholar 

  • Dohnanyi, J.S.: Particle dynamics. In: McDonnell, J.A.M. (ed.) Cosmic Dust, pp. 527–605. Wiley-Interscience, Chichester (1978)

    Google Scholar 

  • Frisch, P.C., Bzowski, M., Grün, E., Izmodenov, V., Krüger, H., Linsky, J.L., McComas, D.J., Möbius, E., Redfield, S., Schwadron, N., Shelton, R., Slavin, J.D., Wood, B.E.: The galactic environment of the sun: interstellar material inside and outside of the heliosphere. Space Sci. Rev. 146, 235–273 (2009)

    Article  ADS  Google Scholar 

  • Golimowski, D.A., Krist, J.E., Stapelfeldt, K.R., Chen, C.H., Ardila, D.R., Bryden, G., Clampin, M., Ford, H.C., Illingworth, G.D., Plavchan, P., Rieke, G.H., Su, K.Y.L.: Hubble and Spitzer Space Telescope observations of the debris disk around the nearby K dwarf HD 92945. Astrophys. J. 142, 30 (2011)

    ADS  Google Scholar 

  • Gomes, R.S.: The effect of nonconservative forces on resonance lock: stability and instability. Icarus 115, 47–59 (1995)

    Article  ADS  Google Scholar 

  • Gomes, R.S.: Orbital evolution in resonance lock. I. The restricted 3-body problem. Astron. J. 114, 2166–2176 (1997)

    Article  ADS  Google Scholar 

  • Gustafson, B.A.S.: Physics of zodiacal dust. Annu. Rev. Earth Planet. Sci. 22, 553–595 (1994)

    Article  ADS  Google Scholar 

  • Hines, D.C., Schneider, G., Hollenbach, D., Mamajek, E.E., Hillenbrand, L.A., Metchev, S.A., Meyer, M.R., Carpenter, J.M., Moro-Martín, A., Silverstone, M.D., Kim, J.S., Henning, T., Bouwman, J., Wolf, S.: The Moth: an unusual circumstellar structure associated with HD 61005. Astrophys. J. 671, L165–L168 (2007)

    Article  ADS  Google Scholar 

  • Kirkwood, D.: Meteoric Astronomy: A Treatise on Shooting-Stars, Fireballs, and Aerolites. Lippincott, Philadelphia (1867)

    Google Scholar 

  • Klačka, J., Kómar, L., Pástor, P., Petržala, J.: The non-radial component of the solar wind and motion of dust near mean motion resonances with planets. Astron. Astrophys. 489, 787–793 (2008)

    Article  ADS  Google Scholar 

  • Klačka, J., Petržala, J., Pástor, P., Kómar, L.: Solar wind and motion of dust grains. Mon. Not. R. Astron. Soc. 421, 943–959 (2012)

    Article  ADS  Google Scholar 

  • Klačka, J., Petržala, J., Pástor, P., Kómar, L.: The Poynting–Robertson effect: a critical perspective. Icarus 232, 249–262 (2014)

    Article  ADS  Google Scholar 

  • Lallement, R., Quémerais, E., Bertaux, J.L., Ferron, S., Koutroumpa, D., Pellinen, R.: Deflection of the interstellar neutral hydrogen flow across the heliospheric interface. Science 307, 1447–1449 (2005)

    Article  ADS  Google Scholar 

  • Leinert, C., Grün, E.: Interplanetary dust. In: Schwen, R., Marsch, E. (eds.) Physics of the Inner Heliosphere I, pp. 207–275. Springer, Berlin (1990)

    Chapter  Google Scholar 

  • Liou, J.-C., Zook, H.A.: Evolution of interplanetary dust particles in mean motion resonances with planets. Icarus 128, 354–367 (1997)

    Article  ADS  Google Scholar 

  • Maness, H.L., Kalas, P., Peek, K.M.G., Chiang, E.I., Scherer, K., Fitzgerald, M.P., Graham, J.R., Hines, D.C., Schneider, G., Metchev, S.A.: Hubble Space Telescope optical imaging of the eroding debris disk HD 61005. Astrophys. J. 707, 1098–1114 (2009)

    Article  ADS  Google Scholar 

  • Margheri, A., Ortega, R., Rebelo, C.: Some analytical results about periodic orbits in the restricted three body problem with dissipation. Celest. Mech. Dyn. Astron. 113, 279–290 (2012)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Marzari, F.: Interstellar medium perturbations on transport-dominated debris discs in binary star systems. Mon. Not. R. Astron. Soc. 421, 3431–3442 (2012)

    Article  ADS  Google Scholar 

  • Marzari, F., Thébault, P.: On how optical depth tunes the effects of the interstellar medium on debris discs. Mon. Not. R. Astron. Soc. 416, 1890–1899 (2011)

    Article  ADS  Google Scholar 

  • Murray, C.D., Dermott, S.F.: Solar System Dynamics. Cambridge University Press, New York (1999)

    MATH  Google Scholar 

  • Pástor, P.: Influence of fast interstellar gas flow on the dynamics of dust grains. Celest. Mech. Dyn. Astron. 112, 23–45 (2012a)

    Article  ADS  Google Scholar 

  • Pástor, P.: Orbital evolution under the action of fast interstellar gas flow with a non-constant drag coefficient. Mon. Not. R. Astron. Soc. 426, 1050–1060 (2012b)

    Article  ADS  Google Scholar 

  • Pástor, P.: Dust particles in mean motion resonances influenced by an interstellar gas flow. Mon. Not. R. Astron. Soc. 431, 3139–3149 (2013)

    Article  ADS  Google Scholar 

  • Pástor, P., Klačka, J., Kómar, L.: Motion of dust in mean motion resonances with planets. Celest. Mech. Dyn. Astron. 103, 343–364 (2009)

    Article  MATH  Google Scholar 

  • Pástor, P., Klačka, J., Kómar, L.: Orbital evolution under the action of fast interstellar gas flow. Mon. Not. R. Astron. Soc. 415, 2637–2651 (2011)

    Article  Google Scholar 

  • Pástor, P., Klačka, J., Petržala, J., Kómar, L.: Eccentricity evolution in mean motion resonance and non-radial solar wind. Astron. Astrophys. 501, 367–374 (2009)

    Article  MATH  Google Scholar 

  • Poynting, J.M.: Radiation in the solar system: its effect on temperature and its pressure on small bodies. Philos. Trans. R. Soc. Lond. Ser. A 202, 525–552 (1904)

    Article  MATH  ADS  Google Scholar 

  • Reach, W.T., Franz, B.A., Welland, J.L., Hauser, M.G., Kelsall, T.N., Wright, E.L., Rawley, G., Stemwedel, S.W., Splesman, W.J.: Observational confirmation of a circumsolar dust ring by the COBE satellite. Nature 374, 521–523 (1995)

    Article  ADS  Google Scholar 

  • Robertson, H.P.: Dynamical effects of radiation in the solar system. Mon. Not. R. Astron. Soc. 97, 423–438 (1937)

    Article  MATH  ADS  Google Scholar 

  • Rodigas, T.J., Hinz, P.M., Leisenring, J., Vaitheeswaran, V., Skemer, A.J., Skrutskie, M., Su, K.Y.L., Bailey, V., Schneider, G., Close, L., Mannucci, F., Esposito, S., Arcidiacono, C., Pinna, E., Argomedo, J., Agapito, G., Apai, D., Bono, G., Boutsia, K., Briguglio, R., Brusa, G., Busoni, L., Cresci, G., Currie, T., Desidera, S., Eisner, J., Falomo, R., Fini, L., Follette, K., Fontana, A., Garnavich, P., Gratton, R., Green, R., Guerra, J.C., Hill, J.M., Hoffmann, W.F., Jones, T.J., Krejny, M., Kulesa, C., Males, J., Masciadri, E., Mesa, D., McCarthy, D., Meyer, M., Miller, D., Nelson, M.J., Puglisi, A., Quiros-Pacheco, F., Riccardi, A., Sani, E., Stefanini, P., Testa, V., Wilson, J., Woodward, C.E., Xompero, M.: The gray needle: large grains in the HD 15115 debris disk from LBT/PISCES/ Ks and LBTI/LMIRcam/ L’ adaptive optics imaging. Astrophys. J. 752, 57 (2012)

    Article  ADS  Google Scholar 

  • Whipple, F.L.: A comet model III. The zodiacal light. Astrophys. J. 121, 750–770 (1955)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

I would like to thank the referees of this paper for their useful comments and suggestions.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pavol Pástor.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pástor, P. On the stability of dust orbits in mean-motion resonances perturbed by from an interstellar wind. Celest Mech Dyn Astr 120, 77–104 (2014). https://doi.org/10.1007/s10569-014-9558-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10569-014-9558-3

Keywords

Navigation