Large-scale Rapid Evaluation for the Collision Risk of Mega Constellations

In recent years, low Earth orbit (LEO) mega constellations, composed of hundreds to thousands of satellites, have been proposed by commercial aerospace companies, such as OneWeb and SpaceX. To ensure the safe operation of constellations, it is essential to rapidly monitor and foresee collision risks in real time. Hence, a new method of calculating the satellite density is proposed based on the continuity equation (CE) to assess space collision risks over a large area quickly. The proposed method can eliminate the individual differences between space objects and provide an overall perspective of multiple satellites and orbits. Compared with a determined satellite orbit model, this method significantly reduces calculation time.The contributions of this paper mainly focus on two aspects. The proposed method constructs a density calculation model in the solution space of latitude and time. Different from existing methods which often express density as a function of other variables, such as true anomaly and time, distance and time, the satellite number density is more sensitive to the latitude which can describe the congestion more clearly. On the other hand, the proposed method considers J2 perturbation and atmospheric drag perturbation, which ascends the accuracy of the evolutionary analysis model. A high-precision and efficient long-term space object density evolution analysis model is constructed using differential algebra (DA) and semi-analytical mean orbital dynamics (SAMOD). The simulation results validate the effectiveness of the algorithm.