Phase Space Description of the Debris’ Cloud Dynamics Through a Continuum Approach

This paper proposes a continuity equation-based debris' evolutionary model for the long-term propagation of fragments' clouds under atmospheric drag, J2 perturbation, solar radiation pressure and third-body perturbation. In particular, it focuses on enhancing the computational efficiency of the dynamical model. This purpose is achieved by cutting off some long-term effects of the perturbations, through averaging of the dynamics equations, and by deriving analytical expressions for the Earth's and Moon's ephemerides, through least squares fitting method. A new cost-free computation of the needed trace of the Jacobian for conservative forces is also proposed. The paper includes a validation phase, where the tool is applied to the modelling and propagation of two fragmentation clouds, characterised by a different dynamical regime, which allows to preliminarily identify some boundaries of applicability of the implemented dynamical model.