# Laser Inter-Satellite Link Visibility and Topology Optimization for Mega Constellation
## 4 Results and Discussion
### Visibility Analysis  
Due to the fact that LEO satellites orbit the Earth at a high rate of speed, the latitude and longitude of the heterodyne satellites change in lockstep with them, affecting the network topology constructed by LISLs. As a result, the visibility analysis among the satellites is performed first in the simulation scenario. Since the geometric configuration of the Starlink constellation is symmetric, any satellite's geometric characteristics can be applied to represent the geometric characteristics of the remaining satellites that are  
Figure 8: Comparison of coverage performance of Starlink and OneWeb constellation under different F. (**a**) OneWeb constellation, F = 1; (**b**) OneWeb constellation, F = 9; (**c**) Starlink constellation, F = 1; (**d**) Starlink constellation, F = 11.  
symmetric with it. We selected a satellite \(S(2,1)\) as the research object in this paper to examine the visibility of LISLs between satellites in the same and different orbits within a 24 h period.  
1. \(S(2,1)\) and the satellites in the same orbit \(P_{2}\)  
From Figure 9, it can be seen that there are sixteen satellites in the same orbit as \(S(2,1)\) that are always visible during 24 h. The remaining satellites are not in the visual range due to the blockage of the Earth's sphere during the whole time, and no interplanetary link can be established. Therefore, it can be concluded that for any satellite \(S(P_{i},M_{j})\), when, \(1\leq i\leq 242\leq j\leq 9\) is its forward eight satellites in the same orbit and \(59\leq j\leq 66\) is its backward eight satellites in the same orbit, these sixteen satellites can form permanent LISLs with a symmetric structure.  
2. \(S(2,1)\) and the satellites in the adjacent orbit \(P_{1}\)  
As can be seen from Figure 10, due to the symmetrical structure of the constellation, there are 17 satellites in each of the two orbits adjacent to \(S(2,1)\), \(P_{1}\) and \(P_{3}\) that can form permanent LISLs with them within 24 h. Therefore, there are 34 satellites that can render LISLs visible throughout the day, and their satellites are not visible throughout the day due to occlusion.  
Figure 10: Visibility analysis of adjacent orbiting satellites.  
Figure 9: Visibility analysis of Co-orbiting satellites.  
3. visibility between \(S(2,1)\) and the satellites in the neighboring non-adjacent orbit \(P_{5}\)  
As shown in Figure 11, it can be seen that on \(P_{5}\), there are ten satellites that are permanently visible 24 h, allowing for uninterrupted LISL establishment throughout the day; there are eight satellites which are intermittently visible on \(S(2,1)\), and the established LISLs may be interrupted. The number of such interruptions is represented in the figure as the number of intervals between the lines, e.g., 29 interruptions occur between \(S(2,1)\) and \(S(5,1)\) in a day; the rest of the satellites in this orbit, not shown in the figure, are unable to establish LISLs with \(S(2,1)\).  
4. \(S(2,1)\) and the satellites in more than three orbits apart \(P_{6}\)  
The hetero-orbit is divided into adjacent orbits and neighboring non-adjacent orbits. From Figure 12, it can be seen that there are no satellites permanently visible to the selected satellite as long as they are separated by more than three orbits, either clockwise or counterclockwise. For the subject of this experiment, \(S(2,1)\), there are permanent LISLs with two adjacent orbits and four neighboring non-adjacent orbits,\(P_{4}\), \(P_{5}\), \(P_{23}\) and \(P_{24}\).  
Figure 11: Visibility analysis of neighboring non-adjacent orbiting satellites.  
Figure 12: Satellite visibility analysis with more than 3 orbits apart.