###### Abstract
While it has been utilized to assess the LEO environment, the analysis has thus far been limited to the period spanning from mid-2008 to mid-2020, lacking a more extensive exploration of subsequent evolutionary trends. [PERSON] et al. [20] formulated a statistical model that integrates the precision of colli-sion probability algorithms with the efficacy of statistical methodologies to assess the in-fluence of satellite swarms on the environment. Nonetheless, the model is built upon sev-eral assumptions, and it lacks a comprehensive long-term evolutionary analysis. Megaconstellation satellites may disintegrate and generate hundreds or thousands of space debris objects if a collision occurs due to their small mass and fast running speed. The debris generated by the collision can stay in space for a long time and may cause secondary damage to the constellations [21]. \begin{table}
\begin{tabular}{c c c} \hline
**Constellation** & **Orbit Altitude/km** & **Number of Satellites** \\ \hline OneWeb & 1200 & 7020 \\ Starlink & 328–614 & 41,926 \\ Kuiper & 590–630 & 3236 \\ Telesat & 1015–1325 & 1671 \\ Boeing/LEO & 1200 & 2956 \\ \hline \end{tabular}
\end{table} 
Table 1: Some plans for megaconstellations in LEO [4; 5; 6; 7; 8]. [PERSON] [22] introduced a large constellation to analyze the influence of low-orbit megacons constellation deployment on the collision probability of space debris. Under the condition that the postmission disposal criteria are met, the amount of space debris will continue to grow. [PERSON] used the MASTER-2009 debris evolution model to simulate the OneWeb and SpaceX constellations, and further analyzed the influence of constellation parameters and the long-term influence of satellites that failed to perform deorbit operations [23]. [PERSON] utilized different tools developed by IFAC-CNR to analyze the short-term to long-term constellation influences for determining the effects associated with constellation deployment and execution [24]. For the long-term sustainable use of the space environment, many scholars have proposed debris mitigation plans for megaconstellations [25; 26]. Scholars have conducted pertinent research on the safety analysis of large constellations in low Earth orbit environments. [PERSON]. [27] recently introduced a spatial-occupancy-based filter for satellite collision screening, employing short-term space occupancy and common orbit screening methods to address space collision challenges. Nonetheless, further enhancements and optimizations of this filter are imperative, necessitating the inclusion of additional factors and constraints to augment its reliability and effectiveness. Additionally, [PERSON] et al. [28] utilized orbital perturbation theory to analyze the long-term orbital evolution characteristics of Starlink satellites. The analysis included studying rendezvous scenarios between faulty and operational satellites within the same or different orbital planes, along with providing collision probabilities stemming from faulty satellites. While that study offers valuable insights for future space traffic management, its primary focus lies on the collision risks associated with satellite malfunctions, with limited consideration given to the potential impact of other factors, such as space debris, on collision risks. However, spacecraft and space debris are mainly concentrated in the low Earth orbit region, and if the traditional two-pair analysis method is used to solve the intersection collision of the two targets, the calculation will be very large. This paper focuses on how to solve the problem quickly and accurately for rendezvous collisions, and uses a sequence of filters to greatly reduce the computational expense of the algorithm. On this basis, to evaluate the collision risk of megaconstellations (especially the Starlink constellation), a short-term collision probability calculation model and a long-term collision probability calculation model are established. These models are used to calculate the collision risks of the Starlink constellation.