Dynamics of resonances and equilibria of Low Earth Objects

TL;DR

This paper investigates the dynamics and stability of resonances and equilibrium points of Low Earth Orbit objects, considering atmospheric drag and celestial influences, to better understand space debris behavior.

Contribution

It provides a qualitative analysis of resonances and equilibria in LEO using a simplified model including geopotential and atmospheric drag, highlighting effects of the solar cycle and celestial bodies.

Findings

Atmospheric drag causes tidal decay and can lead to resonance passage or temporary capture.

Resonance locations and stability are affected by atmospheric density fluctuations.

Solar and lunar influences modulate the dynamics of LEO objects.

Abstract

The nearby space surrounding the Earth is densely populated by artificial satellites and instruments, whose orbits are distributed within the Low-Earth-Orbit region (LEO), ranging between 90 and 2 000 $km$ of altitude. As a consequence of collisions and fragmentations, many space debris of different sizes are left in the LEO region. Given the threat raised by the possible damages which a collision of debris can provoke with operational or manned satellites, the study of their dynamics is nowadays mandatory. This work is focused on the existence of equilibria and the dynamics of resonances in LEO. We base our results on a simplified model which includes the geopotential and the atmospheric drag. Using such model, we make a qualitative study of the resonances and the equilibrium positions, including their location and stability. The dissipative effect due to the atmosphere provokes a tidal decay, but we give examples of different behaviors, precisely a straightforward passage through the resonance or rather a temporary capture. We also investigate the effect of the solar cycle which is responsible of fluctuations of the atmospheric density and we analyze the influence of Sun and Moon on LEO objects.