面向低轨巨型星座构型设计的碰撞风险评估

To address the challenge of collision risk assessment in the configuration design of low Earth orbit mega-constellations, an efficient evaluation framework is proposed, progressing from analytical boundary derivation to stochastic risk quantification. First, based on spherical geometry, the orbital encounter conditions between satellites in different planes are analyzed, and the analytical boundaries for the drift in right ascension of the ascending node and argument of latitude to avoid generalized collisions are derived. On this basis, a Monte Carlo sampling method based on an importance sampling strategy is constructed, generating a statistically effective sample set that covers perturbations in all orbital elements, thus simulating the impacts of practical deviations and perturbations. To tackle the computational bottleneck in mega-constellation collision detection, a fast algorithm innovatively employing quadtree spatial partitioning and physical density criteria is adopted, enabling accurate identification and efficient screening of high-risk regions. Simulation results show that the proposed method significantly improves risk assessment efficiency and effectively captures the risk aggregation effects induced by the coupling of multiple perturbation sources, thereby providing a practical analytical tool and theoretical foundation for the safe and robust design of low Earth orbit mega-constellations.