Discrete evolution model based on mean spatial density for space debris environment

Concerning the increasing space debris and its collision threat on operational satellites, a simple and less computation consuming model is built to implement the long-term evolution and prediction of the Low-Earth orbit space debris environment. Space debris is divided into groups according to the orbital height and the area-mass ratio. For each group, the distribution state is described by the mean spatial density, and the dynamics of the evolution process under the effect of mutual collision and the perturbation of atmosphere drag is modeled by a partial differential equation (PDE). A two-dimensional analytical solution is obtained when the collision-associated terms of those PDEs are excluded. Moreover, the analytical results are shown compatible with the results of a numerical simulation code, which means that the mechanical model in the evolution model is reliable. In a hypothetical scenario, i.e. without future launch activities, the collisional chain reaction of the space debris environment will be reached, as shown by the numerically obtained solution of the general evolution model.