Dynamics of highly eccentric and highly inclined space debris

A common condition of many artificial satellites around the Earth is that they orbit on highly eccentric and/or highly inclined orbits. In this work, we study the secular dynamics of these bodies and we present some of their dynamical aspects. Highly eccentric satellites experience different forces along their trajectories, as their orbit tends to cross multiple regions in the space around the Earth, making relevant the effects of atmospheric drag, when the orbit enters the atmosphere, or the solar radiation pressure, when it is further away from the Earth. This means that one needs to take into account different forces, whose magnitude drastically depends on the orbital elements of the satellite. Besides, highly inclined orbits are important in the study of satellite dynamics, as large values of the inclination might provoke an increase of the eccentricity when the satellite is close to a lunisolar resonance. An accurate force model is developed for treating highly eccentric and highly inclined orbits, which includes the geopotential (limited to the most important harmonic coefficients), the effects of Moon and Sun (which are treated as third body perturbations), the secular effects of the atmospheric drag and the solar radiation pressure, using simple models for the density of the Earth's atmosphere and the Sun's radiation, respectively. Using canonical transformations we calculate three sets of elements, obtained averaging over different angle variables; we refer to them as mean, averaged mean and proper elements, the latter being quasi integrals of the motion. Using statistical tools, we show that the proper elements of a group of fragments are strongly correlated over time, in contrast to the mean and averaged mean elements, and can be used as an indicator of the group. Finally, we implement machine learning algorithms to efficiently cluster satellite fragments, using their proper elements, and we compare the results to the clusterisation using the averaged mean elements, for highly eccentric orbits, including cases where the dissipation, caused by the atmospheric drag, is relevant for the dynamics.