大规模低轨空间目标碰撞风险快速评估方法

A rapid collision risk assessment method based on an analytical relative distance model is proposed to address the orbital congestion and the sharp rise in collision risk caused by the rapid deployment of large low-Earth-orbit （LEO） constellations represented by Starlink. Considering the influence of the dominant J₂ perturbation in the LEO environment， the method employs Bessel series theory to construct an analytical model of the relative distance between space objects. An analytical minimum-distance computation model is further developed. On this basis， the analytical solution of the relative distance is used to determine distance variation trends for preliminary screening of potential collision candidates， after which the minimum relative distance is efficiently computed using the analytical minimum distance method to enable precise risk determination. Numerical simulation results demonstrate that， while maintaining assessment accuracy， the proposed method significantly improves computational efficiency compared with traditional numerical approaches， making it well suited for the rapid collision risk assessment of large-scale LEO space object populations.