The European Physical Journal Special Topics

, Volume 186, Issue 1, pp 67–89 | Cite as

Dynamics of small bodies in the solar system

  • K. TsiganisEmail author


In this chapter we review key results on the dynamics of small solar-system bodies, such as asteroids and comets. We begin by presenting the main populations of small bodies in the solar system, in terms of their orbital characteristics. We define the different types of resonant interactions for small bodies, relating them to the orbital structure of the main belts. In the next section, we present the basic theoretical background on the dynamics of small bodies, referring to applications in selected problems. First, we introduce the reader to the basics of the three-body and N(>3)-body problem with a central mass, using a Hamiltonian framework. We then analyze the expansion of the disturbing function and discuss the classification of terms. Elements of canonical perturbation theory, with the use of Lie series, are also given. The analytical solution of the linearized secular problem (Lagrange-Laplace theory) and the definition of proper elements is then presented. The extension to higher-order/degree secular theories is discussed. Subsequently, we present a derivation of low-order resonant normal forms, suitable for studying motion in mean motion resonances (MMRs, averaged Hamiltonians). The single-resonance model and MMR multiplets (in two-body and three-body MMRs) are then analyzed. We show that the application of the resonance-overlap criterion explains the origin of chaos and chaotic diffusion in resonances; an analytical description of the different diffusion regimes is also given. This section ends with a discussion on extended chaos in the outer asteroid belt and on the origin of the Kirkwood gaps. In the last part of this chapter, we discuss the evolution of small-body reservoirs during the early phases of solar system evolution, namely the epoch of planet migration. We present different models of planet migration (i.e. “smooth vs. chaotic”) and discuss resonant capture, which can explain the origin of different small-body resonant populations. These results show how the observed orbital distribution of small bodies, combined with suitable dynamical modeling, can be used as a proxy to unveil the evolutionary history of the Solar System. A short discussion devoted to open problems concludes this chapter.


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  1. 1.
    C. Beaugé, F. Roig, Icarus 153, 391 (2001)CrossRefADSGoogle Scholar
  2. 2.
    N. Borderies, P. Goldreich, Celestial Mechanics 32, 127 (1984)zbMATHCrossRefADSMathSciNetGoogle Scholar
  3. 3.
    W.F. Bottke, A. Morbidelli, R. Jedicke, J. Petit, H.F. Levsion, P. Michel, T.S. Metcalfe, Icarus 156, 399 (2002)CrossRefADSGoogle Scholar
  4. 4.
    B.V. Chirikov, Phys. Rep. 52, 263 (1979)CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    M. Duncan, Sp. Sci. Rev. 138, 109 (2008)CrossRefADSGoogle Scholar
  6. 6.
    P. Farinella, D. Vokrouhlický, Science 283, 1507 (1999)CrossRefADSGoogle Scholar
  7. 7.
    J.A. Fernandez, W.-H. Ip, Icarus 58, 109 (1984)CrossRefADSGoogle Scholar
  8. 8.
    S. Ferraz-Mello, Canonical Perturbation Theories: Degenerate Systemss and Resonance, ASSL 345 (Springer US, 2007)Google Scholar
  9. 9.
    S. Ferraz-Mello, T.A. Michtchenko, D. Nesvorný, et al., Plan. Space Sci. 46, 1425 (1998)CrossRefADSGoogle Scholar
  10. 10.
    R.S. Gomes, Astron. J. 116, 2590 (1998)CrossRefADSGoogle Scholar
  11. 11.
    R.S. Gomes, A. Morbidelli, H.F. Levison, Icarus 170, 492 (2004)CrossRefADSGoogle Scholar
  12. 12.
    R. Gomes, H.F. Levison, K. Tsiganis, A. Morbidelli, Nature 435, 466 (2005)CrossRefADSGoogle Scholar
  13. 13.
    M. Guzzo, M. Morbidelli, Cel. Mech. Dyn. Astr. 66, 255 (1997)zbMATHCrossRefADSMathSciNetGoogle Scholar
  14. 14.
    J.D. Hadjidemetriou, Cel. Mech. Dyn. Astr. 56, 563 (1993)zbMATHCrossRefADSMathSciNetGoogle Scholar
  15. 15.
    J.M. Hahn, R. Malhotra, Astron. J. 117, 3041 (1999)CrossRefADSGoogle Scholar
  16. 16.
    J. Henrard, Celestial Mechanics 27, 3 (1982)zbMATHCrossRefADSMathSciNetGoogle Scholar
  17. 17.
    J. Henrard, A. Lemaitre, Celestial Mechanics 30, 197 (1983)zbMATHCrossRefADSMathSciNetGoogle Scholar
  18. 18.
    J. Henrard, N. Caranicolas, Cel. Mech. Dyn. Astr. 47, 99 (1990)CrossRefADSMathSciNetGoogle Scholar
  19. 19.
    M.J. Holman, N.W. Murray, Astron. J. 112, 1278 (1996)CrossRefADSGoogle Scholar
  20. 20.
    Z. Knežević, A. Milani, P. Farinella, Ch. Froeschlé, C. Froeschlé, Icarus 93, 316 (1991)CrossRefADSGoogle Scholar
  21. 21.
    Z. Knežević, A. Lemaître, A. Milani, In Asteroids III (University of Arizona Press, Tucson, 2002), p. 603Google Scholar
  22. 22.
    A. Lemaitre, A. Morbidelli, Cel. Mech. Dyn. Astron. 60, 29 (1994)zbMATHCrossRefADSGoogle Scholar
  23. 23.
    H.F. Levison, A. Morbidelli, Nature 426, 419 (2003)CrossRefADSGoogle Scholar
  24. 24.
    H.F. Levison, A. Morbidelli, C. Vanlaerhoven, R. Gomes, K. Tsiganis, Icarus 196, 258 (2008)CrossRefADSGoogle Scholar
  25. 25.
    H.F. Levison, W.F. Bottke, M. Gounelle, A. Morbidelli, D. Nesvorný, K. Tsiganis, Nature 460, 364 (2009)CrossRefADSGoogle Scholar
  26. 26.
    R. Malhotra, Astron. J. 110, 420 (1995)CrossRefADSGoogle Scholar
  27. 27.
    P. Michel, Icarus 129, 348 (1997)CrossRefADSGoogle Scholar
  28. 28.
    P. Michel, Ch. Froeschlé, P. Farinella, Cel. Mech. Dyn. Astron. 69, 133 (1998)zbMATHCrossRefADSGoogle Scholar
  29. 29.
    A. Milani, Z. Knežević, Cel. Mech. Dyn. Astr. 49, 347 (1990)zbMATHCrossRefADSGoogle Scholar
  30. 30.
    A. Milani, Z. Knežević, Icarus 98, 211 (1992)CrossRefADSGoogle Scholar
  31. 31.
    A. Milani, A.M. Nobili, Nature 357, 569 (1992)CrossRefADSGoogle Scholar
  32. 32.
    A. Milani, Cel. Mech. Dyn. Astr. 57, 59 (1993)CrossRefADSMathSciNetGoogle Scholar
  33. 33.
    O. Miloni, S. Ferraz-Mello, C. Beaugé, Cel. Mech. Dyn. Astron. 92, 89 (2005)zbMATHCrossRefADSGoogle Scholar
  34. 34.
    M. Moons, Cel. Mech. Dyn. Astr. 65, 175 (1997)zbMATHCrossRefADSMathSciNetGoogle Scholar
  35. 35.
    M. Moons, A. Morbidelli, Icarus 114, 33 (1995)CrossRefADSGoogle Scholar
  36. 36.
    A. Morbidelli, D. Nesvorný, Icarus 139, 295 (1999)CrossRefADSGoogle Scholar
  37. 37.
    A. Morbidelli, Modern Celestial Mechanics: Aspects of Solar System Dynamics (Taylor & Francis, London, 2002)Google Scholar
  38. 38.
    A. Morbidelli, M. Moons, Icarus 102, 316 (1993)CrossRefADSGoogle Scholar
  39. 39.
    A. Morbidelli, W.F. Bottke, Ch. Froeschlé, P. Michel, In Asteroids III (University of Arizona Press, Tucson, 2002), p. 409Google Scholar
  40. 40.
    A. Morbidelli, H.F. Levison, K. Tsiganis, R. Gomes, Nature 435, 462 (2005)CrossRefADSGoogle Scholar
  41. 41.
    A. Morbidelli, K. Tsiganis, A. Crida, H.F. Levison, R. Gomes, Astron. J. 134, (2007)Google Scholar
  42. 42.
    A. Morbidelli, R. Brasser, K. Tsiganis, R. Gomes, H.F. Levison, Astron Astrophys. 507, 1041 (2009)CrossRefADSGoogle Scholar
  43. 43.
    C.D. Murray, S.F. Dermott, Solar System Dynamics (Cambridge University Press, Cambridge, UK, 2002)Google Scholar
  44. 44.
    N. Murray, M. Holman, Astron. J. 114, 1246 (1997)CrossRefADSGoogle Scholar
  45. 45.
    N. Murray, M. Holman, M. Potter, Astron. J. 116, 2583 (1998)CrossRefADSGoogle Scholar
  46. 46.
    A.I. Neishtadt, Prikl. Mat. Mekh. 51, 750 (1987a)MathSciNetGoogle Scholar
  47. 47.
    A.I. Neishtadt, Sov. Phys. Dokl. 32, 47 (1987b)Google Scholar
  48. 48.
    D. Nesvorný, A. Morbidelli, Astron. J. 116, 3029 (1998)CrossRefADSGoogle Scholar
  49. 49.
    D. Nesvorný, A. Morbidelli, Cel. Mech. Dyn. Astron. 71, 243 (1999)CrossRefADSGoogle Scholar
  50. 50.
    D. Nesvorný, S. Ferraz-Mello, M. Holman, et al., In Asteroids III (University of Arizona Press, Tucson, 2002), p. 379Google Scholar
  51. 51.
    D. Nesvorný, D. Vokrouhlický, Astron. J. 137, 5003 (2009)CrossRefADSGoogle Scholar
  52. 52.
    D. Nesvorný, D. Vokrouhlický, A. Morbidelli, Astron. J. 133, 1962 (2007)CrossRefADSGoogle Scholar
  53. 53.
    B. Novaković, K. Tsiganis, Z. Knežević, Mon. Not. R. Astr. Soc. 402, 1263 (2010)CrossRefADSGoogle Scholar
  54. 54.
    A.C. Quillen, P. Faber, Mon. Not. R. Astr. Soc. 373, 1245 (2006)CrossRefADSGoogle Scholar
  55. 55.
    P. Robutel, J. Bodossian, Mon. Not. R. Astr. Soc. 399, 69 (2009)CrossRefADSGoogle Scholar
  56. 56.
    F. Tera, D.A. Papanastassiou, G.J. Wasserburg, Earth Plan. Sci. Lett. 22, 1 (1974)CrossRefADSGoogle Scholar
  57. 57.
    K. Tsiganis, H. Varvoglis, J.D. Hadjidemetriou, Icarus 146, 240 (2000)CrossRefADSGoogle Scholar
  58. 58.
    K. Tsiganis, H. Varvoglis, J.D. Hadjidemetriou, Icarus 155, 454 (2002a)CrossRefADSGoogle Scholar
  59. 59.
    K. Tsiganis, H. Varvoglis, J.D. Hadjidemetriou, Icarus 159, 284 (2002b)CrossRefADSGoogle Scholar
  60. 60.
    K. Tsiganis, R. Gomes, A. Morbidelli, H.F. Levison, Nature 435, 459 (2005)CrossRefADSGoogle Scholar
  61. 61.
    K. Tsiganis, Z. Knežević, H. Varvoglis, Icarus 186, 484 (2007)CrossRefADSGoogle Scholar
  62. 62.
    K. Tsiganis, Lect. Notes. Phys. 729, 111 (2008)CrossRefMathSciNetGoogle Scholar
  63. 63.
    D. Vokrouhličký, M. Brož, W.F. Bottke, et al., in Dynamics of Populations of Planetary Systems, Proceedings of IAU Colloquium 197 (Cambridge University Press, 2005), p. 145Google Scholar
  64. 64.
    J. Wisdom, Astron. J. 85, 1122 (1980)CrossRefADSGoogle Scholar
  65. 65.
    J. Wisdom, Icarus 56, 51 (1983)CrossRefADSGoogle Scholar
  66. 66.
    J. Wisdom, Icarus 63, 272 (1985)CrossRefADSGoogle Scholar

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© EDP Sciences and Springer 2010

Authors and Affiliations

  1. 1.Unit of Mechanics and Dynamics, Section of Astrophysics, Astronomy & Mechanics, Department of Physics, Aristotle University of ThessalonikiThessalonikiGreece

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