Collision risk analysis of mega constellations in low Earth orbit

Abstract The LEO megaconstellations have thousands of satellites, which operate on similar orbital heights. Because of increasing space debris, the satellites accelerate the growth of the number of space objects, increase the threat to their own safety and sustainable utilization of the space environment. This paper focuses on short-term collision probability and long-term collision probability calculation model for collision risk of mega constellations. On the one hand, aiming at how to solve the problem quickly and accurately for rendezvous collisions, a short-term collision risk evolution calculation model of LEO mega-constellation is established. By investigating the space collision target screening methods of large-scale satellites against large-scale space debris, including apogee–perigee filtering, time window filtering, space discrete volume element filtering and relative position filtering, the filtered target trajectory is fitted by Lagrange interpolation method to obtain the motion state at the closest time. Then, the collision probability calculation method of Laplace transform is used to calculate the collision probability of the target at the closest time. On the other hand, the long-term collision risk evolution model of LEO Mega constellation is established. By simplifying the model of debris and collision, we explore the calculation method of space object density, space debris attenuation model, space target disintegration model and the distribution of disintegration targets are studied. According to the way of space debris’ generation and extinction to calculate the change of space density. The collision probability between the satellite and space debris and space debris are calculated by using the calculation method of collision probability of particle-in-a-box (PIB). Finally, through the simulation of Starlink phase I constellation, results show that after the deployment of the Starlink constellation, the probability of a short-term collision in the constellation shell increases by 30–40%, the probability of at least one collision in the constellation lifetime is 70.2%, and the probability of a secondary collision increases by 25.3% after a collision. This study provides a theoretical reference for analyzing the orbital safety of the LEO mega-constellation, and provides a reference for the safe operation of spacecraft on-orbit and the sustainable development and utilization of space resources.