###### Abstract  
The deployment of megaconstellations in low Earth orbit (LEO) poses significant collision risks with space debris. This paper focuses on analyzing the short-term and long-term collision probabilities of megaconstellations to assess their collision risk. Firstly, a short-term collision risk evolution model is developed to accurately address rendezvous collisions. Secondly, a long-term collision risk evolution model is established by considering space object density, space debris attenuation, space target disintegration, and the distribution of disintegration targets. Through simulations conducted on the Starlink Phase I constellation, the results demonstrate a 30-40% increase in short-term collision probability within the constellation shell, a 70.2% probability of at least one collision during the constellation's lifetime, and a 25.3% increase in secondary collisions following a collision event. This study provides a reference and application for analyzing the orbital safety of LEO megaconstellations and for promoting the sustainable development and utilization of space resources. low Earth orbit; megaconstellation; space debris; collision probability; short/long-term collision risk +
Footnote †: journal: Medical  
the deployments are completed in accordance with the plans, then the number of satellites in orbit will be several times the sum of the number of past launches. Table 1 gives some plans for megaconstellations in LEO. Therefore, whether from the perspective of the safety of the LEO megaconstellation itself or the sustainability of the space environment, research on the orbital safety of low-orbit megaconstellations, especially collision safety, is necessary and urgent. The megaconstellations in LEO represented by the Starlink constellation have begun to be deployed. From 2019 to April 2023, Starlink showed frequent close proximity during the first phase of deployment. Starlink-44 had a close approach with Euro-Aeolus satellites in 2019 [9]. About 1600 close proximity events occurred in 2021, accounting for half of all the space proximity events of the year [10; 11]. With the deployment of the constellation programs, the environment in LEO space is becoming increasingly problematic. Taking the OneWeb constellation as an example, [PERSON] et al. studied the interaction between the space debris environment and the megaconstellations [12], where the influence of LEO megaconstellations on the space environment was investigated [13; 14]. [PERSON] designed a simple risk assessment statistical tool for megaconstellations in the LEO space debris environment to analyze the influence of the main parameters of the constellation on their vulnerability [15]. In addition, [PERSON] proposed an uncertainty-aware Cube mid-term collision risk assessment algorithm, which is capable of evaluating the target mid-term collision frequency in low orbit [16]. [PERSON] et al. estimated the expected annual cost of a satellite's collision with orbital debris based on orbital debris economics [17]. Due to the limited accuracy of the tracking data used to assess the risk of collisions, the maneuvers currently being performed far exceed the necessary level, which leads to overestimates. [PERSON] proposes a solution for equipping satellites with sensors that will enable them to autonomously track dangerous objects when at risk of collision and refine their location knowledge before making maneuvering decisions, enabling data collection and estimating collision risk, thereby improving the accuracy of final predictions and reducing false alarms [18]. [PERSON] [19] introduced a dimensionless index, termed the \"volumetric collision rate index\", through an analysis of the analytical equation that delineates collision rates. This index, developed based on rational simplifications and assumptions, is distinctly contingent upon the spatial density of both intact objects and cataloged fragments.