Strength, stability and three dimensional structure of mean motion resonances in the Solar System

TL;DR

This paper investigates the strength and structure of mean-motion resonances in the Solar System using numerical methods within the circular restricted three-body problem, revealing how resonance strength varies with orbital parameters.

Contribution

It introduces a numerical indicator for resonance strength and maps its dependence on orbital elements, providing new insights into resonance behavior in the Solar System.

Findings

Resonance strength depends on eccentricity, inclination, and argument of perihelion.

Exterior 1:k resonances are strong even for retrograde orbits.

Resonance structures in (a,i) space resemble those in (a,e) space.

Abstract

In the framework of the circular restricted three body problem we show that the numerically computed strength SR(e,i,w) is a good indicator of the strength and width of the mean-motion resonances in the full space (e,i,w). We present a survey of strengths in the space (e,i) for typical interior and exterior resonances. The resonance strength is highly dependent on (e,i,w) except for exterior resonances of the type 1:k for which the dependence with (i,w) is softer. Such resonances are thus strong even for retrograde orbits. All other resonances are weaker at very-high eccentricities for w ~ 90 or 270 and 60 < i < 120. We explore the resonance structure in the space (a,i) by means of dynamical maps and we find structures similar to those of space (a,e).