Evolution of Debris Clouds to Microscopically Chaotic Motion

Abstract

An evaluation is presented of the effects of orbital perturbations that arise in the early phase of debris cloud evolution. This assessment enables the dee nition of various characteristic timescales associated with the cloud evolution to a mature debris population, characterized by a “ chaotic” distribution, required for the statistical description of debris as provided by the direct simulation Monte Carlo method (DSMC). The ine uences of gravitational harmonic terms J2, J3, and J4 together with that for solar radiation pressure upon both the precession of the argument of perifocus (resulting in the familiar torus ) and regression of the line of nodes (resulting in a band structure) are presented. Dimensionless characteristic timescales indicating the rate at which the evolution in the orbital parameters, subject to each of theperturbations relativeto the orbital lifetime, are dee ned. From this modeling approach to debris studies, it is noted that the dimensionless ratio f perturbation evolutionary timescale g to f orbital lifetime g must be greater than unity. A general conclusion is that it is found that for objects of centimetric size above an altitude of approximately 350 km the DSMC methodology is appropriate. The presented analytic approach highlights the signie cant ine uence during the early phase of J3. The methodology is applied to several scenarios for the fragmentation caused by collisions and explosions. The results show clearly how the evolution to a fully chaotic debris distribution is mass specie c and scenario dependent. Debris particles ejected with forward component velocity vectorsresult with a mass spectrum, which differsfrom thoseejected with rearward velocities. Assumptions of isotropic fragmentation must therefore only be considered as approximations.