Skip to main content
SpringerLink
Log in

Long-term orbital dynamics of trans-Neptunian objects

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

Abstract

This article reviews the different mechanisms affecting the orbits of trans-Neptunian objects, ranging from internal perturbations (planetary scattering, mean-motion resonances, and secular effects) to external perturbations (galactic tides and passing stars). We outline the theoretical tools that can be used to model and study them, focussing on analytical approaches. We eventually compare these mechanisms to the observed distinct populations of trans-Neptunian objects and conclude on how they participate to the sculpting of the whole distribution.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Notes

  1. Unpublished results described in the web page: https://www.boulder.swri.edu/~davidn/kbmmr/kbmmr.html.

  2. For a slow scattering, the secular perturbations of the planets actually produce small oscillations of q and I, especially near \(I\approx 63^{\circ }\) and \(117^{\circ }\), as described in Sect. 4. Even without isolated mean-motion resonances, a small body can hence slowly diffuse vertically inside the chaotic volume.

  3. In Saillenfest et al. (2016), it is written that terms of order \(\xi =\varepsilon _\mathrm {P}^{1/2}\) are neglected, instead of \(\varepsilon _\mathrm {P}^{3/2}\). Indeed, their Hamiltonian was implicitly divided by \(\varepsilon _\mathrm {P}\).

  4. An early formation of the Oort cloud, during the planetary formation, is unlikely because gas drag prevents objects from being ejected onto such distant orbits (Brasser et al. 2007).

  5. Objects of the classical Kuiper belt are sometimes called “Cubewanos” in reference to their first observed member, 1992 QB\(_1\), now officially named (15760) Albion. See Sect. 2 for a historical perspective.

  6. Here again, the question of origin loses its meaning: most of the inner-Oort-cloud comets that become observable are actually first briefly transferred into the outer Oort cloud. Hence, the notion of origin largely depends on the time that we define as “time zero”.

References

  • Bailer-Jones, C.A.L.: Close encounters of the stellar kind. Astron. Astrophys. 575, 35 (2015)

    Article  ADS  Google Scholar 

  • Bailer-Jones, C.A.L.: The completeness-corrected rate of stellar encounters with the Sun from the first Gaia data release. Astron. Astrophys. 609, 8 (2018)

    Article  ADS  Google Scholar 

  • Bailer-Jones, C.A.L., Rybizki, J., Andrae, R., Fouesneau, M.: New stellar encounters discovered in the second Gaia data release. Astron. Astrophys. 616, 37 (2018)

    Article  ADS  Google Scholar 

  • Bannister, M.T., Shankman, C., Volk, K., Chen, Y.-T., Kaib, N., Gladman, B.J., et al.: OSSOS. V. Diffusion in the orbit of a high-perihelion distant solar system object. Astron. J. 153, 262 (2017)

    Article  ADS  Google Scholar 

  • Batygin, K., Brown, M.E.: Evidence for a distant giant planet in the solar system. Astron. J. 151, 22 (2016)

    Article  ADS  Google Scholar 

  • Batygin, K., Morbidelli, A.: Dynamical evolution induced by planet nine. Astron. J. 154, 229 (2017)

    Article  ADS  Google Scholar 

  • Batygin, K., Adams, F.C., Brown, M.E., Becker, J.C.: The planet nine hypothesis. Phys. Rep. 805, 1–53 (2019)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Berski, F.: Gliese 710 will pass the Sun even closer. Close approach parameters recalculated based on the first Gaia data release. Astron. Astrophys. 595, 10 (2016)

    Article  ADS  Google Scholar 

  • Beust, H.: Orbital clustering of distant Kuiper belt objects by hypothetical Planet 9. Secular or resonant? Astron. Astrophys. 590, L2 (2016)

    Article  ADS  Google Scholar 

  • Brasser, R.: Some properties of a two-body system under the influence of the Galactic tidal field. Mon. Not. R. Astron. Soc. 324, 1109–1116 (2001)

    Article  ADS  Google Scholar 

  • Brasser, R., Duncan, M.J., Levison, H.F.: Embedded star clusters and the formation of the Oort cloud. Icarus 184, 59–82 (2006)

    Article  ADS  Google Scholar 

  • Brasser, R., Duncan, M.J., Levison, H.F.: Embedded star clusters and the formation of the Oort cloud. II. The effect of the primordial solar nebula. Icarus 191, 413–433 (2007)

    Article  ADS  Google Scholar 

  • Brasser, R., Schwamb, M.E., Lykawka, P.S., Gomes, R.S.: An Oort cloud origin for the high-inclination, high-perihelion Centaurs. Mon. Not. R. Astron. Soc. 420, 3396–3402 (2012)

    Article  ADS  Google Scholar 

  • Breiter, S., Ratajczak, R.: Vectorial elements for the galactic disc tide effects in cometary motion. Mon. Not. R. Astron. Soc. 364, 1222–1228 (2005)

    Article  ADS  Google Scholar 

  • Breiter, S., Fouchard, M., Ratajczak, R., Borczyk, W.: Two fast integrators for the Galactic tide effects in the Oort cloud. Mon. Not. R. Astron. Soc. 377, 1151–1162 (2007)

    Article  ADS  Google Scholar 

  • Breiter, S., Fouchard, M., Ratajczak, R.: Stationary orbits of comets perturbed by Galactic tides. Mon. Not. R. Astron. Soc. 383, 200–208 (2008)

    Article  ADS  Google Scholar 

  • Brown, M.E., Trujillo, C., Rabinowitz, D.: Discovery of a candidate inner Oort cloud planetoid. Astrophys. J. 617, 645–649 (2004)

    Article  ADS  Google Scholar 

  • Callandreau, O.: Étude sur la théorie des comètes périodiques. Ann. l’Obs. Paris 20, 1–64 (1892)

    Google Scholar 

  • Carusi, A., Valsecchi, G.B., Greenberg, R.: Planetary close encounters—geometry of approach and post-encounter orbital parameters. Celest. Mech. Dyn. Astron. 49, 111–131 (1990)

    Article  ADS  MATH  Google Scholar 

  • Chirikov, B.V.: Resonance processes in magnetic traps. J. Nuclear Energy 1, 253–260 (1960)

    Article  ADS  Google Scholar 

  • Collins, B.F., Sari, R.: A unified theory for the effects of stellar perturbations and galactic tides on Oort cloud comets. Astron. J. 140, 1306–1312 (2010)

    Article  ADS  Google Scholar 

  • Duncan, M.J., Levison, H.F.: A disk of scattered icy objects and the origin of Jupiter-family comets. Science 276, 1670–1672 (1997)

    Article  ADS  Google Scholar 

  • Duncan, M., Quinn, T., Tremaine, S.: The formation and extent of the solar system comet cloud. Astron. J. 94, 1330 (1987)

    Article  ADS  Google Scholar 

  • Duncan, M., Quinn, T., Tremaine, S.: The origin of short-period comets. Astrophys. J. 328, 69–73 (1988)

    Article  ADS  Google Scholar 

  • Duncan, M.J., Levison, H.F., Budd, S.M.: The dynamical structure of the Kuiper belt. Astron. J. 110, 3073 (1995)

    Article  ADS  Google Scholar 

  • Dybczyński, P.A.: Impulse approximation improved. Celest. Mech. Dyn. Astron. 58, 139–150 (1994)

    Article  ADS  Google Scholar 

  • Dybczyński, P.A., Leto, G., Jakubík, M., Paulech, T., Neslušan, L.: The simulation of the outer Oort cloud formation. The first giga-year of the evolution. Astron. Astrophys. 487, 345–355 (2008)

    Article  ADS  MATH  Google Scholar 

  • Edgeworth, K.E.: The origin and evolution of the solar system. Mon. Not. R. Astron. Soc. 109, 600–609 (1949)

    Article  ADS  Google Scholar 

  • Eggers, S., Woolfson, M.M.: Stellar perturbations of inner core comets and the impulse approximation. Mon. Not. R. Astron. Soc. 282, 13–18 (1996)

    Article  ADS  Google Scholar 

  • Ellis, K.M., Murray, C.D.: The disturbing function in solar system dynamics. Icarus 147, 129–144 (2000)

    Article  ADS  Google Scholar 

  • Emel’Yanenko, V.V., Asher, D.J., Bailey, M.E.: The fundamental role of the Oort cloud in determining the flux of comets through the planetary system. Mon. Not. R. Astron. Soc. 381, 779–789 (2007)

    Article  ADS  Google Scholar 

  • Everhart, E.: The origin of short-period comets. Astrophys. Lett. 10, 131–135 (1972)

    ADS  Google Scholar 

  • Fernandez, J.A.: On the existence of a comet belt beyond Neptune. Mon. Not. R. Astron. Soc. 192, 481–491 (1980)

    Article  ADS  Google Scholar 

  • Fernandez, J.A., Ip, W.-H.: Some dynamical aspects of the accretion of Uranus and Neptune: the exchange of orbital angular momentum with planetesimals. Icarus 58, 109–120 (1984)

    Article  ADS  Google Scholar 

  • Fouchard, M.: New fast models of the Galactic tide. Mon. Not. R. Astron. Soc. 349, 347–356 (2004)

    Article  ADS  Google Scholar 

  • Fouchard, M.: Galactic environment and cometary flux from the Oort cloud. In: Fernandez, J.A., Lazzaro, D., Prialnik, D., Schulz, R. (eds.) Icy Bodies of the Solar System. IAU Symposium, vol. 263, pp. 57–66 (2010)

  • Fouchard, M., Froeschlé, C., Rickman, H., Valsecchi, G.B.: methods for the study of the dynamics of the Oort cloud comets I: modelling the stellar perturbations. In: Benest, D., Froeschle, C., Lega, E. (eds.) Lecture Notes in Physics, vol. 729, p. 257. Springer, Berlin (2007a)

    Google Scholar 

  • Fouchard, M., Froeschlé, C., Breiter, S., Ratajczak, R., Valsecchi, G.B., Rickman, H.: Methods for the study of the dynamics of the Oort cloud comets II: modelling the galactic tide. In: Benest, D., Froeschle, C., Lega, e (eds.) Lecture Notes in Physics, vol. 729, p. 273. Springer, Berlin (2007b)

    Google Scholar 

  • Fouchard, M., Froeschlé, C., Rickman, H., Valsecchi, G.B.: The key role of massive stars in Oort cloud comet dynamics. Icarus 214, 334–347 (2011a)

    Article  ADS  Google Scholar 

  • Fouchard, M., Rickman, H., Froeschlé, C., Valsecchi, G.B.: The last revolution of new comets: the role of stars and their detectability. Astron. Astrophys. 535, 86 (2011b)

    Article  ADS  Google Scholar 

  • Fouchard, M., Rickman, H., Froeschlé, C., Valsecchi, G.B.: Planetary perturbations for Oort Cloud comets. I. Distributions and dynamics. Icarus 222, 20–31 (2013)

    Article  ADS  MATH  Google Scholar 

  • Fouchard, M., Rickman, H., Froeschlé, C., Valsecchi, G.B.: Planetary perturbations for Oort cloud comets: II. Implications for the origin of observable comets. Icarus 231, 110–121 (2014)

    Article  ADS  Google Scholar 

  • Fouchard, M., Rickman, H., Froeschlé, C., Valsecchi, G.B.: On the present shape of the Oort cloud and the flux of “new” comets. Icarus 292, 218–233 (2017)

    Article  ADS  MATH  Google Scholar 

  • Fouchard, M., Higuchi, A., Ito, T., Maquet, L.: The “memory” of the Oort cloud. Astron. Astrophys. 620, 45 (2018)

    Article  ADS  Google Scholar 

  • Gabryszewski, R., Rickman, H.: On the dynamical evolution of scattered disk objects outside the planetary system. Acta Astron. 60, 373–385 (2010)

    ADS  Google Scholar 

  • Gallardo, T.: Atlas of the mean motion resonances in the solar system. Icarus 184, 29–38 (2006a)

    Article  ADS  Google Scholar 

  • Gallardo, T.: The occurrence of high-order resonances and Kozai mechanism in the scattered disk. Icarus 181, 205–217 (2006b)

    Article  ADS  Google Scholar 

  • Gallardo, T.: Orbital stability in the Solar system for arbitrary inclinations and eccentricities: planetary perturbations versus resonances. Mon. Not. R. Astron. Soc. 487, 1709–1716 (2019a)

    Article  ADS  Google Scholar 

  • Gallardo, T.: Strength, stability and three dimensional structure of mean motion resonances in the solar system. Icarus 317, 121–134 (2019b)

    Article  ADS  Google Scholar 

  • Gallardo, T., Hugo, G., Pais, P.: Survey of Kozai dynamics beyond Neptune. Icarus 220, 392–403 (2012)

    Article  ADS  Google Scholar 

  • 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. Astron. Astrophys. 379, 634–659 (2001)

    Article  ADS  Google Scholar 

  • Gladman, B., Holman, M., Grav, T., Kavelaars, J., Nicholson, P., Aksnes, K., Petit, J.-M.: Evidence for an extended scattered disk. Icarus 157, 269–279 (2002)

    Article  ADS  Google Scholar 

  • Gladman, B., Marsden, B.G., Vanlaerhoven, C.: Nomenclature in the outer solar system. In: Barucci, M.A., Boehnhardt, H., Cruikshank, D.P., Morbidelli, A., Dotson, R. (eds.) The Solar System Beyond Neptune, pp. 43–57. University of Arizona Press, Tucson (2008)

    Google Scholar 

  • Gomes, R.S.: The origin of the Kuiper Belt high-inclination population. Icarus 161, 404–418 (2003)

    Article  ADS  Google Scholar 

  • Gomes, R.S.: The origin of TNO 2004 XR \(_{190}\) as a primordial scattered object. Icarus 215, 661 (2011)

    Article  ADS  Google Scholar 

  • Gomes, R.S., Gallardo, T., Fernández, J.A., Brunini, A.: On the origin of the high-perihelion scattered disk: the role of the Kozai mechanism and mean motion resonances. Celest. Mech. Dyn. Astron. 91, 109–129 (2005)

    Article  ADS  MATH  Google Scholar 

  • Gomes, R.S., Soares, J.S., Brasser, R.: The observation of large semi-major axis Centaurs: Testing for the signature of a planetary-mass solar companion. Icarus 258, 37–49 (2015)

    Article  ADS  Google Scholar 

  • Gronchi, G.F.: Generalized averaging principle and the secular evolution of planet crossing orbits. Celest. Mech. Dyn. Astron. 83, 97–120 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Hadden, S., Li, G., Payne, M.J., Holman, M.J.: Chaotic dynamics of trans-Neptunian objects perturbed by planet nine. Astron. J. 155(6), 249 (2018)

    Article  ADS  Google Scholar 

  • Hamilton, C., Rafikov, R.R.: Secular dynamics of binaries in stellar clusters II: dynamical evolution. Mon. Not. R. Astron. Soc. 488, 5512–5535 (2019)

    Article  ADS  Google Scholar 

  • Hartmann, W.K., Tholen, D.J., Meech, K.J., Cruikshank, D.P.: 2060 Chiron: colorimetry and cometary behavior. Icarus 83, 1–15 (1990)

    Article  ADS  Google Scholar 

  • Heisler, J., Tremaine, S.: The influence of the galactic tidal field on the Oort comet cloud. Icarus 65, 13–26 (1986)

    Article  ADS  Google Scholar 

  • Henrard, J.: A semi-numerical perturbation method for separable Hamiltonian systems. Celest. Mech. Dyn. Astron. 49, 43–67 (1990)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Henrard, J.: Dynamics Reported—Expositions in Dynamical Systems: The Adiabatic Invariant in Classical Mechanics, vol. 2, pp. 117–235. Springer, Berlin (1993)

    MATH  Google Scholar 

  • Henrard, J., Morbidelli, A.: Slow crossing of a stochastic layer. Phys. D Nonlinear Phenomena 68, 187–200 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Higuchi, A., Kokubo, E.: Effect of stellar encounters on comet cloud formation. Astron. J. 150, 26 (2015)

    Article  ADS  Google Scholar 

  • Higuchi, A., Kokubo, E., Kinoshita, H., Mukai, T.: Orbital evolution of planetesimals due to the galactic tide: formation of the comet cloud. Astron. J. 134, 1693–1706 (2007)

    Article  ADS  Google Scholar 

  • Hills, J.G.: Comet showers and the steady-state infall of comets from the Oort cloud. Astron. J. 86, 1730–1740 (1981)

    Article  ADS  Google Scholar 

  • Jewitt, D., Luu, J.: Discovery of the candidate Kuiper belt object 1992 QB1. Nature 362, 730–732 (1993)

    Article  ADS  Google Scholar 

  • Jílková, L., Portegies Zwart, S., Pijloo, T., Hammer, M.: How Sedna and family were captured in a close encounter with a solar sibling. Mon. Not. R. Astron. Soc. 453, 3157–3162 (2015)

    Article  ADS  Google Scholar 

  • Kaib, N.A., Quinn, T.: Reassessing the source of long-period comets. Science 325, 1234 (2009)

    Article  ADS  Google Scholar 

  • Kaib, N.A., Becker, A.C., Jones, R.L., Puckett, A.W., Bizyaev, D., Dilday, B., Frieman, J.A., Oravetz, D.J., Pan, K., Quinn, T., Schneider, D.P., Watters, S.: 2006 SQ\(_{372}\): a likely long-period comet from the inner Oort cloud. Astrophys. J. 695, 268–275 (2009)

    Article  ADS  Google Scholar 

  • Kaib, N.A., Roškar, R., Quinn, T.: Sedna and the Oort cloud around a migrating Sun. Icarus 215, 491–507 (2011)

    Article  ADS  Google Scholar 

  • Kaib, N.A., Pike, P., Lawler, S., Kovalik, M., Brown, C., Alexandersen, M., et al.: OSSOS. XV. Probing the distant solar system with observed scattering TNOs. Astron. J. 158(1), 43 (2019)

    Article  ADS  Google Scholar 

  • Kenyon, S.J., Bromley, B.C.: Stellar encounters as the origin of distant solar system objects in highly eccentric orbits. Nature 432, 598–602 (2004)

    Article  ADS  Google Scholar 

  • Knezevic, Z., Milani, A., Farinella, P., Froeschle, C., Froeschle, C.: Secular resonances from 2 to 50 AU. Icarus 93, 316–330 (1991)

    Article  ADS  Google Scholar 

  • Kokaia, G., Davies, M.B.: Stellar encounters with giant molecular clouds. Mon. Not. R. Astron. Soc. 489, 5165–5180 (2019)

    Article  ADS  Google Scholar 

  • Kotoulas, T., Voyatzis, G.: Comparative Study of the 2:3 and 3:4 resonant motion with neptune: an application of symplectic mappings and low frequency analysis. Celest. Mech. Dyn. Astron. 88, 343–363 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Kowal, C.T., Liller, W., Marsden, B.G.: The discovery and orbit of (2060) Chiron. In: Duncombe, R.L. (ed.) Dynamics of the Solar System. IAU Symposium, vol. 81, pp. 245–250. Cambridge University Press, Cambridge (1979)

    Chapter  Google Scholar 

  • Kozai, Y.: Secular perturbations of asteroids with high inclination and eccentricity. Astron. J. 67, 591 (1962)

    Article  ADS  MathSciNet  Google Scholar 

  • Kuiper, G.P.: On the origin of the solar system. Proc. Natl. Acad. Sci. 37, 1–14 (1951)

    Article  ADS  Google Scholar 

  • Lan, L., Malhotra, R.: Neptune’s resonances in the scattered disk. Celest. Mech. Dyn. Astron. 131, 39 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  • Laskar, J.: The chaotic motion of the solar system—a numerical estimate of the size of the chaotic zones. Icarus 88, 266–291 (1990)

    Article  ADS  Google Scholar 

  • Lawler, S.M., Pike, R.E., Kaib, N., Alexandersen, M., Bannister, M.T., Chen, Y.-T., et al.: OSSOS. XIII. Fossilized resonant dropouts tentatively confirm Neptune’s migration was grainy and slow. Astron. J. 157, 253 (2019)

    Article  ADS  Google Scholar 

  • Leto, G., Jakubík, M., Paulech, T., Neslušan, L.: A model of the current stellar perturbations on the Oort Cloud. Contrib. Astron. Obser. Skalnaté Pleso 37, 161–172 (2007)

    ADS  MATH  Google Scholar 

  • Levison, H.F.: Comet taxonomy. In: Rettig, T., Hahn, J.M. (eds.) Completing the Inventory of the Solar System. Astronomical Society of the Pacific Conference Series, vol. 107, pp. 173–191 (1996)

  • Levison, H.F., Stern, S.A.: Possible origin and early dynamical evolution of the Pluto-Charon binary. Icarus 116, 315–339 (1995)

    Article  ADS  Google Scholar 

  • Levison, H.F., Duncan, M.J.: From the Kuiper belt to Jupiter-family comets: the spatial distribution of ecliptic comets. Icarus 127, 13–32 (1997)

    Article  ADS  Google Scholar 

  • Levison, H.F., Dones, L., Duncan, M.J.: The origin of Halley-type comets: probing the inner Oort cloud. Astron. J. 121, 2253–2267 (2001)

    Article  ADS  Google Scholar 

  • Levison, H.F., Duncan, M.J., Dones, L., Gladman, B.J.: The scattered disk as a source of Halley-type comets. Icarus 184, 619–633 (2006)

    Article  ADS  Google Scholar 

  • Levison, H.F., Morbidelli, A., Gomes, R., Backman, D.: Planet migration in planetesimal disks. In: Reipurth, B., Jewitt, D., Keil, K. (eds.) Protostars and Planets V, p. 669 (2007)

  • Li, G., Hadden, S., Payne, M., Holman, M.J.: The secular dynamics of TNOs and planet nine interactions. Astron. J. 156(6), 263 (2018)

    Article  ADS  Google Scholar 

  • Lidov, M.L.: The evolution of orbits of artificial satellites of planets under the action of gravitational perturbations of external bodies. Planet. Space Sci. 9, 719–759 (1962)

    Article  ADS  Google Scholar 

  • Luu, J., Marsden, B.G., Jewitt, D., Trujillo, C.A., Hergenrother, C.W., Chen, J., Offutt, W.B.: A new dynamical class of object in the outer solar system. Nature 387, 573–575 (1997)

    Article  ADS  Google Scholar 

  • Lykawka, P.S., Mukai, T.: Dynamical classification of trans-Neptunian objects: probing their origin, evolution, and interrelation. Icarus 189, 213–232 (2007a)

    Article  ADS  Google Scholar 

  • Lykawka, P.S., Mukai, T.: Resonance sticking in the scattered disk. Icarus 192, 238–247 (2007b)

    Article  ADS  Google Scholar 

  • Malhotra, R.: The origin of Pluto’s peculiar orbit. Nature 365, 819–821 (1993)

    Article  ADS  Google Scholar 

  • Malhotra, R.: The origin of Pluto’s orbit: implications for the solar system beyond Neptune. Astron. J. 110, 420 (1995)

    Article  ADS  Google Scholar 

  • Malhotra, R.: The phase space structure near neptune resonances in the Kuiper belt. Astron. J. 111, 504 (1996)

    Article  ADS  Google Scholar 

  • Malhotra, R., Lan, L., Volk, K., Wang, X.: Neptune’s 5:2 resonance in the Kuiper belt. Astron. J. 156, 55 (2018)

    Article  ADS  Google Scholar 

  • Malyshkin, L., Tremaine, S.: The Keplerian map for the planar restricted three-body problem as a model of comet evolution. Icarus 141, 341–353 (1999)

    Article  ADS  Google Scholar 

  • Martínez-Barbosa, C.A., Jílková, L., Portegies Zwart, S., Brown, Brown: The rate of stellar encounters along a migrating orbit of the Sun. Mon. Not. R. Astron. Soc. 464, 2290–2300 (2017)

    Article  ADS  Google Scholar 

  • Milani, A., Baccili, S.: Dynamics of earth-crossing asteroids: the protected Toro orbits. Celest. Mech. Dyn. Astron. 71, 35–53 (1998)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Morbidelli, A.: Chaotic diffusion and the origin of comets from the 2/3 resonance in the Kuiper belt. Icarus 127, 1–12 (1997)

    Article  ADS  Google Scholar 

  • Morbidelli, A., Levison, H.F.: Scenarios for the origin of the orbits of the trans-Neptunian objects 2000 CR\(_{105}\) and 2003 VB\(_{12}\) (Sedna). Astron. J. 128, 2564–2576 (2004)

    Article  ADS  Google Scholar 

  • Morbidelli, A., Nesvorný, D.: Kuiper belt: formation and evolution. In: Prialnik, D., Barucci, A., Young, L. (eds.) The Trans-Neptunian Solar System. Elsevier, Berlin (2019)

    Google Scholar 

  • Morbidelli, A., Thomas, F., Moons, M.: The resonant structure of the Kuiper belt and the dynamics of the first five trans-Neptunian objects. Icarus 118, 322–340 (1995)

    Article  ADS  Google Scholar 

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

    MATH  Google Scholar 

  • Murray, N.W., Holman, M.: Diffusive chaos in the outer asteroid belt. Astron. J. 114, 1246–1259 (1997)

    Article  ADS  Google Scholar 

  • Murray, N.W., Lieberman, M.A., Lichtenberg, A.J.: Corrections to quasilinear diffusion in area-preserving maps. Phys. Rev. A 32, 2413–2424 (1985)

    Article  ADS  Google Scholar 

  • Nesvorný, D., Morbidelli, A.: Statistical study of the early solar system’s instability with four, five, and six giant planets. Astron. J. 144, 117 (2012)

    Article  ADS  Google Scholar 

  • Nesvorný, D., Roig, F.: Mean motion resonances in the trans-Neptunian region. I. The 2:3 resonance with Neptune. Icarus 148, 282–300 (2000)

    Article  ADS  Google Scholar 

  • Nesvorný, D., Roig, F.: Mean motion resonances in the trans-Neptunian region. Part II: the 1:2, 3:4, and weaker resonances. Icarus 150, 104–123 (2001)

    Article  ADS  Google Scholar 

  • Nesvorný, D., Vokrouhlický, D.: Neptune’s orbital migration was grainy. Not Smooth. Astrophys. J. 825, 94 (2016)

    Article  ADS  Google Scholar 

  • Nesvorný, D., Vokrouhlický, D., Dones, L., Levison, H.F., Kaib, N., Morbidelli, A.: Origin and evolution of short-period comets. Astrophys. J. 845, 27 (2017)

    Article  ADS  Google Scholar 

  • Newton, H.A.: On the capture of comets by planets, especially their capture by Jupiter. Mem. Natl. Acad. Sci. 6, 5–23 (1893)

    Google Scholar 

  • 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)

    ADS  Google Scholar 

  • Öpik, E.: Note on stellar perturbations of nearly parabolic orbits. Proc. Am. Acad. Arts Sci. 67, 169–183 (1932)

    Article  MATH  Google Scholar 

  • Pan, M., Sari, R.: A generalization of the Lagrangian points: studies of resonance for highly eccentric orbits. Astron. J. 128, 1418–1429 (2004)

    Article  ADS  Google Scholar 

  • Pichierri, G., Morbidelli, A., Lai, D.: Extreme secular excitation of eccentricity inside mean motion resonance. Small bodies driven into star-grazing orbits by planetary perturbations. Astron. Astrophys. 605, 23 (2017)

    Article  ADS  Google Scholar 

  • Rickman, H.: Stellar perturbations of orbits of long-period comets and their significance for cometary capture. Bull. Astron. Inst. Czechoslov. 27, 92–105 (1976)

    ADS  Google Scholar 

  • Rickman, H., Froeschlé, C., Froeschlé, C., Valsecchi, G.B.: Stellar perturbations on the scattered disk. Astron. Astrophys. 428, 673–681 (2004)

    Article  ADS  MATH  Google Scholar 

  • Rickman, H., Fouchard, M., Valsecchi, G.B., Froeschlé, C.: Algorithms for stellar perturbation computations on Oort cloud comets. Earth Moon Planets 97, 411–434 (2005)

    Article  ADS  MATH  Google Scholar 

  • Rickman, H., Fouchard, M., Froeschlé, C., Valsecchi, G.B.: Injection of Oort Cloud comets: the fundamental role of stellar perturbations. Celest. Mech. Dyn. Astron. 102, 111–132 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Robutel, P., Laskar, J.: Frequency map and global dynamics in the solar system I. Short period dynamics of massless particles. Icarus 152, 4–28 (2001)

    Article  ADS  Google Scholar 

  • Saillenfest, M., Lari, G.: The long-term evolution of known resonant trans-Neptunian objects. Astron. Astrophys. 603, 79 (2017)

    Article  ADS  Google Scholar 

  • Saillenfest, M., Fouchard, M., Tommei, G., Valsecchi, G.B.: Long-term dynamics beyond Neptune: secular models to study the regular motions. Celest. Mech. Dyn. Astron. 126, 369–403 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  • Saillenfest, M., Fouchard, M., Tommei, G., Valsecchi, G.B.: Non-resonant secular dynamics of trans-Neptunian objects perturbed by a distant super-Earth. Celest. Mech. Dyn. Astron. 129, 329–358 (2017a)

    Article  ADS  MathSciNet  Google Scholar 

  • Saillenfest, M., Fouchard, M., Tommei, G., Valsecchi, G.B.: Study and application of the resonant secular dynamics beyond Neptune. Celest. Mech. Dyn. Astron. 127, 477–504 (2017b)

    Article  ADS  MathSciNet  Google Scholar 

  • Saillenfest, M., Fouchard, M., Ito, T., Higuchi, A.: Chaos in the inert Oort cloud. Astron. Astrophys. 629, A95 (2019)

    Article  ADS  Google Scholar 

  • Schubart, J.: Long-period effects in nearly commensurable cases of the restricted three-body problem. Spec. Rep. Smithson. Astrophys. Obs. 149, 6 (1964)

    ADS  Google Scholar 

  • Sheppard, S.S., Trujillo, C.A., Tholen, D.J., Kaib, N.: A new high perihelion trans-Plutonian inner Oort cloud object: 2015 TG387. Astron. J. 157, 139 (2019)

    Article  ADS  Google Scholar 

  • Shevchenko, I.I.: On the Lyapunov exponents of the asteroidal motion subject to resonances and encounters. In: Near Earth Objects, Our Celestial Neighbors: Opportunity and Risk. IAU Symposium, vol. 236, pp. 15–30 (2007)

  • Shevchenko, I.I.: The Kepler map in the three-body problem. New Astron. 16, 94–99 (2011)

    Article  ADS  Google Scholar 

  • Šidlichovský, M.: A non-planar circular model for the 4/7 resonance. Celest. Mech. Dyn. Astron. 93, 167–185 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Sidorenko, V.V.: Evolution of asteroid orbits at the 3:1 their mean motion resonance with Jupiter (planar problem). Cosmic Res. 44, 440–455 (2006)

    Article  ADS  Google Scholar 

  • Sidorenko, V.V.: Dynamics of “jumping” Trojans: a perturbative treatment. Celest. Mech. Dyn. Astron. 130, 67 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  • Sidorenko, V.V., Neishtadt, A.I., Artemyev, A.V., Zelenyi, L.M.: Quasi-satellite orbits in the general context of dynamics in the 1:1 mean motion resonance: perturbative treatment. Celest. Mech. Dyn. Astron. 120, 131–162 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Thomas, F., Morbidelli, A.: The Kozai resonance in the outer solar system and the dynamics of long-period comets. Celest. Mech. Dyn. Astron. 64, 209–229 (1996)

    Article  ADS  MATH  Google Scholar 

  • Tisserand, M.F.: Mémoires et observations. Sur la théorie de la capture des comètes périodiques. Bull. Astron. Sér. I 6, 241–257 (1889a)

    MATH  Google Scholar 

  • Tisserand, M.F.: Mémoires et observations. Sur la théorie de la capture des comètes périodiques [suite et fin]. Bull. Astron. Sér. I 6, 289–292 (1889b)

    Google Scholar 

  • Torbett, M.V.: Chaotic motion in a comet disk beyong Neptune: the delivery of short-period comets. Astron. J. 98, 1477–1481 (1989)

    Article  ADS  Google Scholar 

  • Torbett, M.V., Smoluchowski, R.: Chaotic motion in a primordial comet disk beyond Neptune and comet influx to the Solar System. Nature 345, 49–51 (1990)

    Article  ADS  Google Scholar 

  • Torres, S., Cai, M.X., Brown, A.G.A., Zwart, S.P.: Galactic tide and local stellar perturbations on the Oort cloud: creation of interstellar comets. Astron. Astrophys. 629, A139 (2019)

    Article  ADS  Google Scholar 

  • Touma, J.R., Tremaine, S., Kazandjian, M.V.: Gauss’s method for secular dynamics, softened. Mon. Not. R. Astron. Soc. 394, 1085–1108 (2009)

    Article  ADS  Google Scholar 

  • Valsecchi, G.B., Froeschlé, C., Gonczi, R.: Modelling close encounters with Öpik’s theory. Planet. Space Sci. 45, 1561–1574 (1997)

    Article  ADS  Google Scholar 

  • Valsecchi, G.B., Milani, A., Gronchi, G.F., Chesley, S.R.: The distribution of energy perturbations at planetary close encounters. Celest. Mech. Dyn. Astron. 78, 83–91 (2000)

    Article  ADS  MATH  Google Scholar 

  • Valsecchi, G.B., Milani, A., Gronchi, G.F., Chesley, S.R.: Resonant returns to close approaches: analytical theory. Astron. Astrophys. 408, 1179–1196 (2003)

    Article  ADS  Google Scholar 

  • Valsecchi, G.B., Alessi, E.M., Rossi, A.: Cartography of the \(b\)-plane of a close encounter I: semimajor axes of post-encounter orbits. Celest. Mech. Dyn. Astron. 130, 8 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Vokrouhlický, D., Nesvorný, D., Dones, L.: Origin and evolution of long-period comets. Astron. J. 157, 181 (2019)

    Article  ADS  Google Scholar 

  • Wang, J.-H., Brasser, R.: An Oort cloud origin of the Halley-type comets. Astron. Astrophys. 563, 122 (2014)

    Article  Google Scholar 

  • Weissman, P.R.: The Kuiper belt. Ann. Rev. Astron. Astrophys. 33, 327–358 (1995)

    Article  ADS  Google Scholar 

  • Whipple, F.L.: A comet model. I. The acceleration of Comet Encke. Astrophys. J. 111, 375–394 (1950)

    Article  ADS  Google Scholar 

  • Wisdom, J.: A perturbative treatment of motion near the 3/1 commensurability. Icarus 63, 272–289 (1985)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

I thank Marc Fouchard for his support during the redaction of this review article. I am also very grateful to the two anonymous referees for their careful reading of the manuscript and their expert suggestions. This work was supported by the Programme National de Planétologie (PNP) of CNRS/INSU, co-funded by CNES.

Author information

Authors and Affiliations

  1. IMCCE, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Université, LAL, Université de Lille, 75014, Paris, France

    Melaine Saillenfest

Authors
  1. Melaine Saillenfest
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Melaine Saillenfest.

Additional information

This article is dedicated to Giovanni B. Valsecchi.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article is part of the topical collection on Trans-Neptunian Objects.

Guest Editors: David Nesvorný and Alessandra Celletti.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Saillenfest, M. Long-term orbital dynamics of trans-Neptunian objects. Celest Mech Dyn Astr 132, 12 (2020). https://doi.org/10.1007/s10569-020-9954-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10569-020-9954-9

Keywords

Search

Navigation