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