An analytic method of space debris cloud evolution and its collision evaluation for constellation satellites

• An analytic evolution model is built to propagate the distribution of the space debris cloud.
• The distribution of the debris cloud is evolved and analyzed over a long time scale.
• The long-term collision probability between a space debris cloud and the Globalstar satellites is evaluated.

When a debris cloud is formed in the neighborhood of a constellation, the constellation satellites will face a serious threat of collision. In order to evaluate the collision probability in a long time scale, first we build an analytic model to describe the evolution process of the debris cloud. Under the perturbations of atmospheric drag, nonspherical gravity field, etc., results of numerical simulation indicate that after the breakup of an object, the distribution of debris cloud will evolve into a relatively stable band. Based on the stable distribution characteristic of the debris cloud, fragments are divided into several groups according their orbital heights and area-mass ratios. For each debris group, the dynamics of the distribution process under the perturbation of atmosphere drag is described by a partial differential equation (PDE). Solutions of those PDEs are obtained. And the distribution of the debris cloud can be easily propagated over long time scales. Applying this analytic model, the collision probability between a debris cloud and the Globalstar satellites is analyzed and computed. Results show that the collision probability is nearly 10,000 times of the average collision probability in the near Earth environment. Moreover, as the band distribution of the space debris cloud is stable, the collisional risk on constellation satellites will last for quite a long time.