Investigation of dynamics of a region with high-order orbital resonances

Abstract

In this paper, the regions of orbital resonances 1:5, 1:7, 1:9, 1:10, and 1:11 at the Earth's rotation speed are considered. The motion of objects is simulated using the improved software package "Numerical Model of the Motion of AES Systems" on the SKIF Cyberia cluster of the National Research Tomsk State University. The modeling is performed with account for the effect of geopotential harmonics up to a degree and order of 10, as well as the attraction of the Moon and Sun. As a result, the maps of the distribution of orbital resonance multiplets and the MEGNO maps have been obtained for each region. All the regions are examined for the presence of real objects. The obtained data show that the chaotization of motion in the regions 1:5, 1:7, and 1:9 occurs due to the superposition of other different resonances on the second component of the orbital resonance. In the regions 1:10 and 1:11, the orbital resonance does not affect the chaotization of motion. All real objects located in the regions under consideration are not exposed to the effect of orbital resonances.