# Laser Inter-Satellite Link Visibility and Topology Optimization for Mega Constellation
## 4 Results and Discussion
### Link Connection Policy  
According to the analysis above, inter-satellite links can be classified in three categories as permanently visible, intermittently visible, or invisible. Satellites in the same orbit as well as those in adjacent orbits have only two permanent states of visibility and invisibility. If the inter-satellite distance is moderate and does not exceed the maximum visible distance, it is within the visible range, allowing for the establishment of a permanent link. Satellites in non-adjacent orbits have three states of visibility, and when the interplanetary link is disrupted several times, it is referred to as a dynamic link, since it is frequently disconnected and reconnected [26]. The AER characteristics of co-orbital links indicate that, for any satellite, the satellite nodes located in the same orbital plane are relatively stationary, suggesting the presence of a permanent link of fixed length with visible satellites in the same orbital plane that is always connected, i.e., the co-orbital links have equal survival time. Consequently, two of each satellite's four intersatellite links are assigned to connect two adjacent satellites in the same orbit, while the forward and backward connections within the same orbit are kept in a constant direction, allowing for hop-by-hop data transmission along the same orbit or in the opposite direction. According to the AER characteristics of the heterodyne link, it is understood that the visible satellites in two adjacent orbits are permanently visible and linked, while the remaining satellites in non-adjacent orbits exist in two scenarios: (1) a permanently visible link can be established between satellites, but the distance between is too great, resulting in an excessive time delay; (2) the distance between satellites is closest at a certain moment, but the visible time is too short, and as the satellites continue to operate, there will be frequent disruptions in the cycle, frequent disconnection and reconnection of the link, resulting in an excessive number of link-switching times. Combining the two scenarios above, it is evident that the best option is to establish a link with an adjacent orbiting visible satellite. The adjacent inter-orbit link is shorter in distance than the non-adjacent orbit permanent link; unlike the non-adjacent orbit closest satellite, the adjacent inter-orbit satellite does not need to switch the link during the cycle, making the link more stable. Meanwhile, the adjacent inter-orbit link can transmit data hop-by-hop along the east-west direction, and the phasing factor selection will slightly deviate the orbit from the positive east-west direction, generating a larger transmission path. In summary, as shown in Figure 17, a static topology of 1584 satellites in the first phase of the Starlink constellation can be constructed, with the arrow indicating the direction of the satellite. As the inter-satellite distance range increases, satellites are able to establish more stable permanent links. If the satellite operation period is divided into equally spaced time slices, then a similar static topology exists within each time slice, and a large number of different temporary links exist within each time slice as time progresses. On the grounds of the periodicity and predictability of the nearest satellites over time, a strategy of dividing the number of time slices based on the number of satellites per orbit can be considered, and the satellite connectivity of all satellites within a time slice can be directly derived from the resulting LISLs law, significantly reducing the computational effort associated with the topology building process. Considering that not all launched satellites approach orbit and that some fail due to electromagnetic storms and other factors, it is also necessary to study the visibility and number law of LISLs in various time slices for link reconfiguration under dynamic topology.