Evolution of orbits of trans-Neptunian bodies at the 2:3 resonance with Neptune
The results of the numerical investigations of the evolution of orbits of trans-Neptunian bodies at the 2 : 3 resonance with Neptune are presented. The gravitational influence of the four giant planets was taken into account. For identical initial values of the semimajor axes, eccentricities, and inclinations, but for different initial orbital orientations and initial positions in orbits, we obtained different types of variations in the difference ΔΩ=Ω-Ω_N in the ascending-node longitudes of the body and Neptune, and in the perihelion argument ω. When ΔΩ decreases and ω increases during evolution, then most of the bodies leave the resonance in 20 Myr. In the case of an increase in ΔΩ and a decrease in ω, the bodies stay in the resonance for a much longer time. Regions of eccentricities and inclinations, for which some bodies were in the η_18 secular resonance (ΔΩ is almost constant) and in the Kozai resonance (ω is almost constant), were obtained to be larger than those predicted for small variations in the critical angle. Some bodies can at the same time be in both these resonances.