The long-term evolution of known resonant trans-Neptunian objects

Abstract

Aims. Numerous trans-Neptunian objects are known to be in mean-motion resonance with Neptune. We aim to describe their longterm orbital evolution (both past and future) by means of a one-degree-of-freedom secular model. In this paper, we focus only on objects with a semi-major axis larger than 50 astronomical units (au). Methods. For each resonant object considered, a 500 000-year numerical integration is performed. The output is digitally filtered to get the parameters of the resonant secular model. Their long-term (Giga-year) orbital evolution is then represented by the level curves of the secular Hamiltonian. Results. For the majority of objects considered, the mean-motion resonance has little impact on the long-term trajectories (the secular dynamics is similar to a non-resonant one). However, a subset of objects is strongly affected by the resonance, producing moderatelyhigh-amplitude oscillations of the perihelion distance and/or libration of the argument of perihelion around a fixed centre. Moreover, the high perihelion distance of the object 2015 FJ345 is plainly explained by long-term resonant dynamics, allowing us to also deduce its orbital elements at the time of capture in resonance (at least 15 million years ago). The same type of past evolution is expected for 2014 FZ71.

Mean plane of the Kuiper belt beyond 50 AU in the presence of Planet 9

“…resonant KBOs have been identified in the a > 100 AU region, i.e., 2004 PB 112 in the 5:27 resonance (Saillenfest & Lari 2017), 2015 KE 172 , and 2007 TC 433 in the 1:9 resonance (Volk et al 2018); these KBOs are in our sample.…”

“…The agreement between our numerical and theoretical approaches suggests that the weak highorder resonances in the distant Kuiper belt could have little impact on the mean plane determination. As a matter of fact, Saillenfest & Lari (2017) found that, for the majority of resonant KBOs with a > 50 AU, their secular behaviors can hardly be affected by mean motion resonances. Up to now, only three 1 http://www.minorplanetcenter.net/iau/lists/TNOs.html Fig.…”

Proper elements for resonant planet-crossing asteroids

“…( 3.3) has one degree of freedom, and the solutions follow its level curves in the (U, u)-plane. This secular model has been successfully used by Saillenfest et al (2016Saillenfest et al ( , 2017; Saillenfest and Lari (2017) to study the long-term evolution of distant resonant trans-Neptunian objects (TNOs), for which the ratio ξ is of the order of 10 −4 . However, NEOs evolve on a much shorter timescale than TNOs, and the condition in Eq.…”

“…Starting from the theory of Gronchi and Milani (2001), we need to keep resonant harmonics in the Hamiltonian by semi-averaging techniques, and the method must remain valid for arbitrary eccentricities and inclinations. Semi-averaged theories have been widely used in the past for describing the long-term orbital dynamics of resonant small bodies (see e.g Wisdom, 1985;Moons and Morbidelli, 1995;Milani and Baccili, 1998;Saillenfest et al, 2016Saillenfest et al, , 2017Sidorenko, 2006Sidorenko, , 2018Sidorenko, , 2020. Our aim is to combine such a method with the model of Gronchi and Milani (2001) to compute proper elements of resonant NEOs.…”

Long-term orbital dynamics of trans-Neptunian objects

“…In this case, the orbital elements have a very smooth, quasi-integrable, long-term evolution that can be studied by analytical (or semi-analytical) means. We will recall here the method proposed by Henrard (1990Henrard ( , 1993 and applied to the trans-Neptunian region by Saillenfest et al (2016Saillenfest et al ( , 2017b and Saillenfest and Lari (2017). We will also discuss its variant introduced independently by Wisdom (1985) and used for instance by Sidorenko (2006Sidorenko ( , 2018.…”