Resonant and near-resonant dynamics of narrow rings around minor bodies: Symmetric and asymmetric solutions

¹ Observatorio Astronómico, Universidad Nacional de Córdoba, Laprida 854, (X5000BGR) Córdoba, Argentina
² Instituto de Astronomía Teórica y Experimental (IATE), UNC-CONICET, Laprida 854, (X5000BGR) Córdoba, Argentina

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 12 December 2025
Accepted: 9 March 2026

Abstract

Context. Narrow, dense rings have been detected around several Centaurs and trans-Neptunian objects, and they appear located in the immediate vicinity of spin-orbit resonances (SORs) with the central body. Although resonant motion has not been confirmed, the associated eccentricity excitation may explain several of their dynamical characteristics, including the existence of rings outside of the Roche radius. Adequate models for these commensurabilities are thus necessary.

Aims. While asymmetric librations are known to occur in the circular restricted three-body problem with a Keplerian perturber, it is not clear if the same behavior should be expected in asteroid rings, where the perturber (i.e., nonspherical component) moves in a sub-Keplerian orbit. The aim of this work is thus to extend those classical studies to the case of narrow rings. In particular, our objectives are to study the 1/2 and 1/3 SORs, understand in which cases asymmetric solutions may appear, how they can be adequately modeled, and to analyze their effects on ring dynamics.

Methods. The topology of the SORs was studied using a semi-analytical model for the averaged Hamiltonian extended to the case of a sub-Keplerian perturber. The minor planet was modeled by a spherical body plus a mass anomaly on its surface. Varying both the sign and magnitude of the mass anomaly, we can reproduce a variety of irregular shapes, such as prolate ellipsoids and cratered bodies.

Results. For the 1/2 and 1/3 SORs, we confirm the existence of asymmetric librations for a wide range of rotational frequencies of the mass anomaly. These solutions were found for eccentricities beyond a certain limit, usually on the order of ~0.01–0.1. For more circular orbits, the phase space does not contain a separatrix, and motion is nonresonant. However, its dynamical behavior shows kinematic librations of the critical angle, and capture is possible under the effect of an exterior nonconservative force. We thus denote these solutions as near-resonance motion. Other SORs, such as the 5/7, are expected to exhibit only symmetric librations.