Long-term effects of the Galactic tide on cometary dynamics

  • Marc Fouchard
  • Christiane Froeschlé
  • Giovanni Valsecchi
  • Hans Rickman
Conference paper


We introduce a model for integrating the effects of Galactic tides on Oort cloud comets, which involves two procedures, according to the values of the osculating semi-major axis a and eccentricity e. Ten simulations of the dynamics of 106 comets over 5 Gyr are performed using this model. We thus investigate the long-term effects of the Galactic tide with and without a radial component, the effects of the local density of the Galactic disk, and those of the Oort constants. Most of the results may be understood in terms of the integrability or non-integrability of the system. For an integrable system, which occurs for moderate semi-major axes with or without radial component, the dynamics is explained by periodic variation of the cometary perihelion, inducing the depletion of the outer region of the Oort cloud, a constant flux from the inner region after 500 Myr, and the quick formation of a reservoir of comets with argument of perihelion near 26.6°. When the system is non-integrable, the efficiency of the tide in reducing the cometary perihelion distance is enhanced both by replenishing the Oort cloud domain from which comets are sent toward the planetary system, and by reducing the minimal value that the perihelion distance may reach. No effects of varying the Oort constants were observed, showing that the flat rotation curve is a satisfactory approximation in Oort cloud dynamics.


Galactic dynamics Numerical model Long-period comets Oort cloud 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bahcall, J.N., Flynn, C., Gould, A.: Local dark matter from a carefully selected sample. ApJ 389, 234–250 (1992)CrossRefADSGoogle Scholar
  2. Bailey, M.E.: The structure and evolution of the solar system comet cloud. MNRAS 204, 603–633 (1983)ADSzbMATHGoogle Scholar
  3. Brasser, R.: Some properties of a two-body system under the influence of the Galactic tidal field. MNRAS 324, 1109–1116 (2001)CrossRefADSGoogle Scholar
  4. Breiter, S., Ratajczak, R.: Vectorial elements for the Galactic disc tide effects in cometary motion. MNRAS, 364, 1222–1228 (2005)CrossRefADSGoogle Scholar
  5. Breiter, S., Dybczyński, P.A., Elipe, A.: The action of the galactic disk on the Oort cloud comets. Qualitative study. A & A 315, 618–624 (1996)ADSGoogle Scholar
  6. Duncan, M., Quinn, T., Tremaine, S.: The formation and extent of the solar system comet cloud. AJ 94, 1330–1338 (1987)CrossRefADSGoogle Scholar
  7. Dybczyński, P.A.: Simulating observable comets II. Simultaneous stellar and galactic action. A & A 441, 783–790 (2005)ADSGoogle Scholar
  8. Elipe, A., Ferrer, S.: Reductions, relative equilibria, and bifurcations in the generalized van der Waals potential: relation to the integrable cases. Phys. Rev. Lett. 72, 985–988 (1994)CrossRefADSGoogle Scholar
  9. Everhart, E.: An efficient integrator that uses Gauss-Radau spacings. In: Carusi, A., Valsecchi, G.B. (eds.) Proc. IAU Colloq. 83, Dynamics of Comets: Their Origin and Evolution, p. 185, Reidel, Dordrecht (1985)Google Scholar
  10. Fouchard, M.: New fast models of the galactic tide. MNRAS 349, 347–356 (2004)CrossRefADSGoogle Scholar
  11. Fouchard, M., Froeschlé, C., Matese, J.J., Valsecchi, G.B.: Comparison between different models of the galactic tidal effects on cometary orbits. Celest. Mech. Dyn. Astron. 93, 231–264 (2005)CrossRefADSGoogle Scholar
  12. García-Sánchez, J., Weissman, P.R., Preston, R.A., Jones, D.L., Lestrade, J.-F., Latham, D.W., Stefanik, R.P., Paredes, J.M.: Stellar encounters with the solar system. A & A 379, 634–659 (2001)ADSGoogle Scholar
  13. Hills, J.G.: Comet showers and the steady-state infall of comets from the Oort cloud, Astron. J. 86, 1730–1740 (1981)CrossRefADSGoogle Scholar
  14. Heisler, J.: Monte Carlo simulations of the Oort comet cloud. Icarus 75, 104–121 (1990)CrossRefADSGoogle Scholar
  15. Heisler, J., Tremaine, S.: The influence of the galactic tidal field on the Oort comet cloud, Icarus 65, 13–26 (1986)CrossRefADSGoogle Scholar
  16. Holmberg, J., Flynn, C.: The local density of matter mapped by Hipparcos. MNRAS 313, 209–216 (2000)CrossRefADSGoogle Scholar
  17. Levison, H., Dones, L., Duncan, M.J.: The origin of Halley-type comets: probing the inner Oort cloud. Astron. J. 121, 2253–2267 (2001)CrossRefADSGoogle Scholar
  18. Matese, J.J., Lissauer, J.J.: Characteristics and frequency of weak stellar impulses of the Oort cloud. Icarus 157, 228–240 (2002)CrossRefADSGoogle Scholar
  19. Matese, J.J., Lissauer, J.J.: Perihelion evolution of observed new comets implies the dominance of the galactic tide in making Oort cloud comets discernable. Icarus 170, 508–513 (2004)CrossRefADSGoogle Scholar
  20. Matese, J.J., Whitman, P.G.: The galactic disk tidal field and the nonrandom distribution of observed Oort cloud comets. Icarus 82, 389–401 (1989)CrossRefADSGoogle Scholar
  21. Matese, J.J., Whitman, P.G.: A model of the galactic tidal interaction with the Oort comet cloud, Celest. Mech. Dyn. Astron. 54, 13–35 (1992)CrossRefADSGoogle Scholar
  22. Mignard, F.: Local galactic kinematics from Hipparcos proper motions. A & A 354, 522–536 (2000)ADSGoogle Scholar
  23. Neslušan, L., Jakubík, M.: Some characteristics of the outer Oort cloud as inferred from observations of new comets. A & A 437, 1093–1108 (2005)ADSGoogle Scholar
  24. Olling, R.P., Dehnen, W.: The Oort constants measured from proper motions. ApJ 599, 275–296 (2003)CrossRefADSGoogle Scholar
  25. Olling, R.P., Merrifield, M.R.: Refining the Oort and Galactic constants. MNRAS 297, 943–952 (1998)CrossRefADSGoogle Scholar
  26. Oort, J.H.: The structure of the cloud of comets surrounding the Solar System and a hypothesis concerning its origin. Bull. Astron. Inst. Neth. 11, 91–110 (1950)ADSGoogle Scholar
  27. Tommei, G: Canonical elements for Öpik theory. Celest. Mech. Dyn. Astron., 94, 173–195 (2006)CrossRefADSMathSciNetzbMATHGoogle Scholar
  28. Tremaine, S.: Canonical elements for collision orbits. Celest. Mech. Dyn. Astron. 79, 231–233 (2000)CrossRefADSGoogle Scholar
  29. Wiegert, P., Tremaine, S.: The evolution of long-period comets. Icarus 137, 84–121 (1999)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  • Marc Fouchard
    • 1
    • 2
  • Christiane Froeschlé
    • 3
  • Giovanni Valsecchi
    • 1
  • Hans Rickman
    • 4
  1. 1.INAF-IASFRomaItaly
  2. 2.Observatoire de ParisIMCCE/SYRTEParisFrance
  3. 3.Observatoire de la Côte d’Azur, UMR 6202Nice cedex 4France
  4. 4.Uppsala Astronomical ObservatoryUppsalaSweden

Personalised recommendations