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 t rans-Neptunian bodies at the 2 : 3 resonance with Neptune are presented. Th e gravitational influence of die four giant planets was taken into account. For identical initial values of the semimajor axes, eccentricities, and in clinations, but for different initial orbital orientations and initial posi tions in orbits, we obtained different types of variations in the differenc e Delta Omega = Omega - Omega(N) in the ascending-node longitudes of the bo dy and Neptune, and in the perihelion argument omega. When Delta Omega decr eases and omega increases during evolution, then most of the bodies leave t he resonance in 20 Myr. In the case of an increase in Delta Omega and a dec rease in omega, the bodies stay in the resonance for a much longer time. Re gions of eccentricities and inclinations, for which some bodies were in the eta(18) secular resonance (Delta Omega approximate to const) and in the Ko zai resonance (omega approximate to const), were obtained to be larger than those predicted for small variations in the critical angle. Some bodies ca n at the same time be in both these resonances.