# Laser Inter-Satellite Link Visibility and Topology Optimization for Mega Constellation
## 4 Results and Discussion
### AER Analysis  
The AER characteristics of the Starlink constellation LISLs are analyzed, where A denotes the azimuth of the link, E denotes the elevation angle, and R denotes the interstellar distance, and it is discovered that LISLs in the same and different orbits exhibit distinct characteristics, which are correlated with the permanent LISLs calculated in the visibility analysis.  
1. AER characteristics of the satellite \(S(2,1)\) and the co-orbital link  
From Figure 13, it can be seen that \(S(2,1)\) has constant elevation and proximity angles and periodic azimuthal variation when \(S(2,2)\) establishes co-orbital forward link; \(S(2,1)\) has constant A, E, and R indicators when \(S(2,66)\) establishes co-orbital backward link, which is due to the equal velocity vectors of satellite node motion within the same orbit and the their relative stationary relationship. This observation also indicates the permanent LISLs between visible satellites in the orbital plane.  
Figure 13: This is the schematic diagram of co-orbit link AER characteristic analysis. **(a)** Co-orbit forward link; **(b)** Co-orbit backward link.  
AER characteristics of the satellite \(S(2,1)\) and the heterodyne link  
As shown in Figures 14-16, it can be seen that the LISLs established between \(S(2,1)\) and \(S(3,66)\) on adjacent orbits, whose link AER characteristics are all periodic and have similar trends, are still permanent LISLs; the temporary LISLs established between \(S(2,1)\) and \(S(5,1)\) on non-adjacent orbits can be seen to take non-continuous values, and when the visual distance is exceeded, the LISLs are disconnected, and no azimuth and elevation angles exist at this time; There are also a large number of temporary LISLs on \(S(2,1)\) and \(S(14,21)\) established on the intersecting orbit plane, with a longer interval between link disconnections. While the LISLs between the crossing orbit planes may provide a backup option for link reconstruction in the event of a network node failure by increasing the topology structure's redundancy, there are also numerous challenges to resolve in developing hardware functions.  
The link length is a critical parameter in the geometric characterization of intersatellite links, as it affects the link's transmission efficiency, time delay, throughput, and other indexes, and the AER characterization reveals the relevant laws to a certain extent. After analyzing the AER characteristics of LISLs established between co-orbital and heterodyne orbits, it is concluded in this paper that when LISLs are established with permanently visible satellites, the link AER characteristics exhibit periodic changes and take continuous values, whereas LISLs established with intermittently visible satellites break the link when out of the visible range. The change in azimuth affects the on/off state of LISLs, and the time delay introduced by the link communication varies with distance. is similar for both co-orbital and heterodyne LISLs, which reflects the geometric characteristic of the Starlink constellation, which is a uniformly distributed LEO layer, in accordance with the Delta constellation characteristics at an orbital altitude of 550 km.  
Figure 14: Characterization of the adjacent orbital link AER.