Celestial Mechanics and Dynamical Astronomy

, Volume 129, Issue 3, pp 329–358 | Cite as

Non-resonant secular dynamics of trans-Neptunian objects perturbed by a distant super-Earth

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


We use a secular model to describe the non-resonant dynamics of trans-Neptunian objects in the presence of an external ten-Earth-mass perturber. The secular dynamics is analogous to an “eccentric Kozai mechanism” but with both an inner component (the four giant planets) and an outer one (the eccentric distant perturber). By the means of Poincaré sections, the cases of a non-inclined or inclined outer planet are successively studied, making the connection with previous works. In the inclined case, the problem is reduced to two degrees of freedom by assuming a non-precessing argument of perihelion for the perturbing body. The size of the perturbation is typically ruled by the semi-major axis of the small body: we show that the classic integrable picture is still valid below about 70 AU, but it is progressively destroyed when we get closer to the external perturber. In particular, for \(a>150\) AU, large-amplitude orbital flips become possible, and for \(a>200\) AU, the Kozai libration islands at \(\omega =\pi /2\) and \(3\pi /2\) are totally submerged by the chaotic sea. Numerous resonance relations are highlighted. The most large and persistent ones are associated with apsidal alignments or anti-alignments with the orbit of the distant perturber.


Secular model Trans-Neptunian object (TNO) Poincaré section 



We thank two anonymous referees who helped us to improve the paper. This work was partly funded by Paris Sciences et Lettres (PSL).


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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  • Melaine Saillenfest
    • 1
    • 2
    • 3
    Email author
  • Marc Fouchard
    • 1
    • 3
  • Giacomo Tommei
    • 2
  • Giovanni B. Valsecchi
    • 4
    • 5
  1. 1.IMCCEParisFrance
  2. 2.Dipartimento di MatematicaUniversità di PisaPisaItaly
  3. 3.PSL Research University, CNRS, Sorbonne Universités, UPMC Université Paris 06, LAL, Université de LilleParis/LilleFrance
  4. 4.IAPS-INAFRomeItaly
  5. 5.IFAC-CNRSesto FiorentinoItaly

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