2D continuity equation method for space debris cloud collision analysis

Small fragments are rarely included in the evolution of the debris population as their number is so large that the computational time would become prohibitive. However, they also can be dangerous to operational satellites, so it is important to study their contribution to the collision probability. This work proposes an analytical method to propagate fragment clouds, whose evolution under the effect of drag is studied on the space defined by the semi-major axis and the eccentricity. This approach provides an analytical expression of the cloud density that can be translated into a quick estimation of the collision probability.