Celestial Mechanics and Dynamical Astronomy

, Volume 127, Issue 4, pp 477–504 | Cite as

Study and application of the resonant secular dynamics beyond Neptune

  • Melaine SaillenfestEmail author
  • Marc Fouchard
  • Giacomo Tommei
  • Giovanni B. Valsecchi
Original Article


We use a secular representation to describe the long-term dynamics of transneptunian objects in mean-motion resonance with Neptune. The model applied is thoroughly described in Saillenfest et al. (Celest Mech Dyn Astron, doi: 10.1007/s10569-016-9700-5, 2016). The parameter space is systematically explored, showing that the secular trajectories depend little on the resonance order. High-amplitude oscillations of the perihelion distance are reported and localised in the space of the orbital parameters. In particular, we show that a large perihelion distance is not a sufficient criterion to declare that an object is detached from the planets. Such a mechanism, though, is found unable to explain the orbits of Sedna or \(2012\text {VP}_{113}\), which are insufficiently inclined (considering their high perihelion distance) to be possibly driven by such a resonant dynamics. The secular representation highlights the existence of a high-perihelion accumulation zone due to resonances of type 1:k with Neptune. That region is found to be located roughly at \(a\in [100;300]\) AU, \(q\in [50;70]\) AU and \(I\in [30;50]^{\circ }\). In addition to the flux of objects directly coming from the Scattered Disc, numerical simulations show that the Oort Cloud is also a substantial source for such objects. Naturally, as that mechanism relies on fragile captures in high-order resonances, our conclusions break down in the case of a significant external perturber. The detection of such a reservoir could thus be an observational constraint to probe the external Solar System.


Secular model Mean-motion resonance Transneptunian object (TNO) High-perihelion TNOs Resonant secular model 



The authors thank the two anonymous referees for their wise and very stimulating comments. They brought a valuable contribution to the article, allowing a deeper understanding in several parts of the work.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Melaine Saillenfest
    • 1
    • 2
    Email author
  • Marc Fouchard
    • 1
    • 3
  • Giacomo Tommei
    • 2
  • Giovanni B. Valsecchi
    • 4
    • 5
  1. 1.IMCCEObservatoire de ParisParisFrance
  2. 2.Dipartimento di MatematicaUniversità di PisaPisaItaly
  3. 3.LAL-IMCCEUniversité de LilleLilleFrance
  4. 4.IAPS-INAFRomeItaly
  5. 5.IFAC-CNRSesto FiorentinoItaly

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