Resonance libration and width at arbitrary inclination

Abstract

We apply the analytical disturbing function for arbitrary inclination derived in our previous work to characterize resonant width and libration of mean motion resonances at arbitrary inclination obtained from direct numerical simulations of the three-body problem. We examine the 2:1 and 3:1 inner Jupiter and 1:2 and 1:3 outer Neptune resonances and their possible asymmetric librations using a new analytical pendulum model of resonance that includes the simultaneous libration of multiple arguments and their second harmonics. The numerically derived resonance separatrices are obtained using the mean exponential growth factor of nearby orbits (MEGNO chaos indicator). We find that the analytical and numerical estimates are in agreement and that resonance width is determined by the first few fundamental resonance modes that librate simultaneously on the resonant time-scale. Our results demonstrate that the new pendulum model may be used to ascertain resonance width analytically, and more generally, that the disturbing function for arbitrary inclination is a powerful analytical tool that describes resonance dynamics of low as well as high inclination asteroids in the Solar system.