Seminario di Fisica Matematica: “Analytical study of the secular dynamics of geosynchronous space debris”

Giovedì 20 Ottobre 2016, ore 10:00 - Aula 2BC30 - Christos Efthymiopoulos


Giovedì 20 Ottobre 2016 alle ore 10:00 in Aula 2BC30, Christos Efthymiopoulos (Academy of Athens) terrà un seminario dal titolo “Analytical study of the secular dynamics of geosynchronous space debris”.

Understanding the long-term orbital behavior of the population of space debris is a subject of intense current research, since space debris constitute a potentially major contamination of the Earth's near space environment. The talk will provide a summary of recent results obtained in collaboration with colleagues from an astrodynamical network (A. Celletti, F. Gachet, G. Pucacco), aiming at characterizing the long-term orbital behavior of high area-to-mass ratio in the Earth's Geosynchronous resonance using analytical (normal form) techniques. The problem requires to accurately incorporate perturbations upon space debris caused by the geopotential's multipole harmonics, the Moon's and Sun's gravity, and solar radiation pressure. To this end, we construct an analytical model of secular dynamics based on the computation of a Hamiltonian normal form interpolating the flow of an original system of eight degrees of freedom. One relevant outcome is the computation of a so-called `forced equilibrium' solution. In practice, this represents a safe disposal orbit for space debris. Mathematically, this is a solution lying on a 5-dimensional invariant torus, which, when mapped from phase space to configuration space, represents an orbit of nearly constant “forced eccentricity” and “forced inclination” (the latter is called the inclination of the invariant Laplace plane in satellite dynamics literature). We stress the benefits from the analytical approach based on normal forms, which allows to determine an invariant low-dimensional torus, whose otherwise determination by numerical means would constitute a hardly tractable task. We finally comment on the use of the normal form technique in defining proper elements for space debris, in analogy with the methods used in the study of asteroidal populations in our solar system.