Old perturbative methods for a new problem in Celestial Mechanics: the space debris dynamics

Abstract

Perturbative methods have been developed and widely used in the XVIII and XIX century to study the behavior of N-body problems in Celestial Mechanics. Such methods apply to nearly-integrable Hamiltonian systems and they have the remarkable property to be constructive. A well-known application of perturbative techniques is represented by the construction of the so-called proper elements, which are quasi-invariants of the dynamics, obtained by removing the perturbing function to higher orders. They have been used to identify families of asteroids; more recently, they have been used in the context of space debris, which is the main core of this work. We describe the dynamics of space debris, considering a model including the Earth’s gravitational attraction, the influence of Sun and Moon, and the Solar radiation pressure. We construct a Lie series normalization procedure and we compute the proper elements associated to the orbital elements. To provide a concrete example, we analyze three different break-up events with nearby initial orbital elements. We use the information coming from proper elements to successfully group the fragments; the clusterization is supported by statistical data analysis and by machine learning methods. These results show that perturbative methods still play an important role in the study of the dynamics of space objects.

A Single-Averaged Model for the Solar Radiation Pressure Applied to Space Debris Mitigation Using a Solar Sail

“…Several authors have taken into account the solar radiation pressure models to explore the dynamics of artificial satellites, asteroids, and space debris; for example, see references [9][10][11][27][28][29][30][31][32][33][34][35][36] (and references therein). For the equation of the perturbing potential due to a third body, we use a single-averaged model [37] including the perturbations coming from the Sun and Moon and assuming that these perturbing bodies are moving in elliptical and inclined orbits.…”

“…Finally, as an analysis tool of the proposed model, averaged dynamical maps will be used, which have already been used in studies considering SRP [22,38] along with plots of the temporal behavior of some orbital elements of the space debris, such as its orbital eccentricity, to show that the solar sail contributes considerably to the orbital excitation of space debris in the GEO regime, promoting its relocation and disposal in a graveyard orbit or pushing the debris back into the atmosphere of the Earth. Finally, according to [36], the application of proper elements has been used to identify families of asteroids and more recently, they have been used in the context of space debris. The authors describe the dynamics of space debris considering the proper elements, taking into account a model that includes the gravitational attraction of the Earth, the influence of the Sun and Moon, and the solar radiation pressure.…”