Collision risk assessment for constellation satellites based on a space debris environment topological network model

In recent years, the rapid development of mega-constellations has significantly exacerbated the deterioration of the space debris environment, posing substantial and escalating threats to the safety of spacecraft. This study aims to explore the complex evolution of the space debris environment and assess the collision risks associated with spacecraft. First, a space debris environment topological network model is proposed, which incorporates interdisciplinary methods from topological networks, fluid mechanics, and spacecraft dynamics. This model enables a structured representation of the relationships among space objects and provides rapid predictions of the space debris environment. Then, a collision probability algorithm based on the topological network model is introduced. This algorithm inherits the efficiency advantages of the topological network model and has been validated for reliability through comparison with the classical ESA's DRAMA software. Finally, based on the above models, the collision risks of constellation satellites in Low Earth Orbit (LEO) are analyzed, including both operational and deorbit processes. The study reveals that constellation satellites face a much higher risk of internal collisions with satellites from the same constellation during operations than that with other space objects. Additionally, during the satellite deorbit process, the collision risk peaks when satellites traverse the operational region of Starlink satellites.