Modeling early medium-term evolution of debris clouds using the reachable domain method

The early medium-term evolution of a debris cloud refers to the phase when the debris cloud has evolved into a toroid after several revolutions since the breakup event and when effects of natural perturbations are negligible. A debris cloud is described by two essential factors: geometry of the cloud, and spatial debris density within the cloud. In this study, a new approach, the reachable domain method, is introduced for modeling the toroid-shaped medium-term debris cloud. The conventional reachable domain algorithm is first modified to simplify the computations and, more importantly, enable a further volume calculation. Then, the geometry of the medium-term debris cloud, a toroid, is defined by the envelope of the reachable domain, and the volume of the debris cloud is obtained based on the reachable domain volume computation. Thus, a mean uniform spatial debris density is evaluated by dividing the total number of fragments by the volume. Moreover, a nonuniform spatial density is determined by dividing the debris cloud into several subclouds corresponding to different ejecting velocity bins. The utility of the proposed method is demonstrated by simulating a typical breakup event on a medium Earth orbit.