## 3 Simulation Results and Analysis
### Simulation and Analysis of Short-Term Collision Probability  
#### 3.1.1 Numerical Experimental Setup  
The short-term collision probability orbit prediction model used the SGP4 model to simulate the first phase of the Starlink constellation and to facilitate the prediction of the orbit of the space cataloging target [35]. The constellation parameters of the first phase of Starlink were Walker \(-\)\(\delta\) 1584/72/33 (1584 is the number of satellites, 72 is the number of orbit planes, and 33 is the relative spacing between satellites in adjacent planes), the orbit inclination was 53\({}^{\circ}\), and the orbit height was 550 km. The shell height was 40 km, the constellation shell interval was the orbit height 530-570 km area, and the simulation time was 7 days.  
All targets cataloged on 12 March 2022 were downloaded through the Spacetrack website [20], and the apogee screening method was used to preliminarily screen the space targets. The targets with perigee greater than 570 km and the selected position less than 530 km were excluded. A total of 4829 space targets were combined with the intersection of the height intervals of the constellation shells. Taking the space debris as the statistical interval of 100 km, the orbital semi-major axis distribution of 4829 space targets was counted. Figure 11 shows the distribution of the number of space targets in accordance with the orbit semi-major axis after screening.  
The remaining space targets were processed, and the TLE data of all satellites and space debris were converted by using STK after the invalid data were eliminated by the apogee screening method. The space targets within the shell were examined, and 653 space targets were likely to be close to space debris for a long time. The SGP4 model was used to predict the orbits of these targets and the low-orbit giant constellation satellites and long-term space targets in the shell, and the simulation step size was set to 1 s. The simulation step size was set to 5 s for the remaining 4176 space targets, and the time interval closest to the shell was solved in accordance with the orbit height, and the simulation step size of this interval was set to 1 s to perform the orbit evolution.  
A total of 4176 space target orbits were screened in terms of height by using the evolved orbit data. The arcs with the height of the space target orbits in the interval of 530-570 km and their latitudes were examined. Given that the actual orbital inclination of the Starlink satellite has shifted by approximately 0.054\({}^{\circ}\) relative to the nominal inclination, and the random deviation between the collision target and the collision position of the satellite was considered, the latitude screening value was set to 54\({}^{\circ}\).  
The space discrete volume element was used to perform a preliminary approach analysis after obtaining the arcs where the space target may collide with the low-orbit giant constellation. The included angle between the adjacent orbital planes of the Starlink constellation was 5\({}^{\circ}\), and the included angle between adjacent satellites in the orbital plane was about 16.3\({}^{\circ}\). Therefore, the trajectory of the space target in the space volume element needed to be increased as much as possible to minimize the number of satellite targets in the space. The values of space volume elements \(\Delta h\), \(\Delta\lambda\), \(\Delta\varphi\) were set to 40 km, 4.8\({}^{\circ}\), and 9\({}^{\circ}\), respectively. In accordance with the space targets that appeared in the same space volume element at the same time, the relative distances were calculated pairwise by using the orbit data, and the distance to the closest trajectory point and the \"3\(\sigma\)\" distance were judged to remove possible collision targets.