Abstract: The presence of the debris in the Earth’s orbit poses a significant risk to human activity in outer space. This debris population continues to grow due to ground launches, the loss of external parts from space ships, and uncontrollable collisions between objects. A computationally feasible continuum model for the growth of the debris population and its spatial distribution is therefore critical. Here we propose a diffusion-collision model for the evolution of the debris density in the low-Earth orbit and its dependence on the ground-launch policy. We parametrize this model and test it against data from publicly available object catalogs to examine timescales for the uncontrolled growth. Finally, we consider sensible launch policies and cleanup strategies and how they reduce the future risk of collisions with active satellites or space ships.

Key words: Population dynamics, Space debris, Kessler syndrome, Diffusion, Low-Earth orbit