Small Debris Fragment Contribution to Collision Probability for Spacecraft in Low Earth Orbits

Around the Earth there are more than ten million objects larger than 1 mm that can interfere with other orbiting spacecraft. In particular, objects larger than 1 cm are considered massive enough to seriously damage or even destroy a satellite in case of collision. The traditional piece-by-piece approach to study the evolution of debris objects cannot be applied to small fragments their number is so large that the computational time would be prohibitive. This work proposes an alternative method based on the computation of the fragment density, whose evolution in time under the effect of atmospheric drag can be obtained with the continuity equation. The fragment density can then be used to evaluate the resulting collision probability. In particular, the proposed method is here applied to evaluate the consequence of some reference breakups on a list of target objects. In addition, the low computational time allows simulating many collision scenarios with different collision conditions to understand which parameters have the largest effect on the risk for other spacecraft.