Inclined asymmetric librations in exterior resonances

TL;DR

This paper investigates inclined asymmetric librations in exterior mean-motion resonances within the Sun-Neptune-TNO system, identifying stable periodic orbits and comparing them with observed trans-Neptunian objects to understand their libration behavior.

Contribution

It extends the study of asymmetric librations to three-dimensional space and computes families of stable asymmetric periodic orbits in the CRTBP model.

Findings

Stable asymmetric periodic orbits exist in the 3D model.

Some observed TNOs perform inclined asymmetric librations.

Libration of stable 1:2 TNOs relates to vertically stable planar orbits.

Abstract

Librational motion in celestial mechanics is generally associated with the existence of stable resonant configurations and signified by the existence of stable periodic solutions and oscillation of critical (resonant) angles. When such an oscillation takes place around a value different than 0 or $\pi$, the libration is called asymmetric. In the context of the planar circular restricted three-body problem (CRTBP), asymmetric librations have been identified for the exterior mean-motion resonances (MMRs) 1:2, 1:3 etc. as well as for co-orbital motion (1:1). In exterior MMRs the massless body is the outer one. In this paper, we study asymmetric librations in the 3-dimensional space. We employ the computational approach of Markellos (1978) and compute families of asymmetric periodic orbits and their stability. Stable, asymmetric periodic orbits are surrounded in phase space by domains of initial conditions which correspond to stable evolution and librating resonant angles. Our computations were focused on the spatial circular restricted three-body model of the Sun-Neptune-TNO system (TNO= trans-Neptunian object). We compare our results with numerical integrations of observed TNOs, which reveal that some of them perform 1:2-resonant, inclined asymmetric librations. For the stable 1:2 TNOs librators, we find that their libration seems to be related with the vertically stable planar asymmetric orbits of our model, rather than the 3-dimensional ones found in the present study.