Analysis of a dynamic structure of secular resonances in circumlunar orbital space

N. A. Popandopulo   ; A. G. Aleksandrova   ; T. V. Bordovitsyna

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 77 (2022), pp. 110-124

Résumé

When developing new circumlunar satellite systems for various purposes, it is necessary to know the dynamic features of various regions of circumlunar space. It is noted that one of the main features of the dynamics of artificial Moon satellites (AMS) is the increase in the eccentricity of their orbits. It is known that such orbital evolution of objects can be caused by resonant perturbations. In this regard, the purpose of this paper is to study the influence of secular and half-secular resonances occurring on the AMS. The results are obtained by means of the processing of data from an extensive numerical experiment to study the orbital evolution of the uniformly distributed circumlunar objects moving in the range of large semi-axes from 1911.8 to 26070 km and with inclinations from 0 to 180$^{\circ}$. The study of the influence of secular and half-secular resonances on the orbital evolution of the AMS is carried out using numerical and analytical techniques. Both techniques have advantages and disadvantages and are used in the study. Maps of secular and half-secular resonances are of great practical importance. They clearly demonstrate the areas of influence of secular resonances on the orbital evolution of circumlunar objects depending on the initial values of the semimajor axis and inclination of the orbits of objects. The analysis of each particular resonance consists in the revealing of a resonant characteristic type, which is determined by the nature of the change in a critical argument: libration - stable resonance, libration/circulation - unstable resonance, and circulation - no resonance. To estimate the whole range of the influence of resonances on the AMS dynamics, maps of their overlaps are built. The maps allow one to determine areas with significant influence of the resonances on the orbital evolution of circumlunar objects. The obtained results show that the reason for a large increase in the eccentricity in a vast area of circumlunar orbital space is the presence of the stable apsidal resonance of the Kozai-Lidov type.

Détail

Keywords: circumlunar space, artificial satellites of the Moon, dynamic structure, secular and half-secular resonances, resonance maps.

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