## 2 System Model  
### LEO Satellite Networks  
Currently, most LEO satellites adopt the Walker constellation configuration [14], which is primarily categorized into inclined-orbit constellations (Walker-Delta) and polar-orbit constellations (Walker-Star) [15].  
(1) Inclined-orbit constellations  
Inclined-orbit constellations feature orbital inclinations ranging from 0\({}^{\circ}\) to 90\({}^{\circ}\), providing uniform satellite coverage with an equal number of satellites in each orbital plane and identical orbital periods for all satellites. The main advantage of inclined-orbit constellations lies in their relatively small satellite population, resulting in lower deployment costs. However, the dynamic nature of inclined-orbit satellites makes inter-satellite link (ISL) connections difficult to predict, posing significant challenges in establishing and maintaining reliable ISLs.  
(2) Polar-orbit constellations  
Polar-orbit constellations, with inclinations approaching 90\({}^{\circ}\), can cover both the Arctic and Antarctic regions, enabling global communication coverage including high-latitude areas. These constellations offer advantages such as lower signal transmission latency and higher data transfer rates. As illustrated in Figure 3, in a polar-orbit configuration, each satellite can establish ISLs with four neighboring satellites (two in the same orbital plane and two in adjacent planes) [16], except for satellites in the first and last orbital planes, which can only connect with three neighbors due to the orbital seam [17]. Satellites maintain stable cross-plane ISLs by precisely adjusting the position and orientation of their inter-plane laser terminals [2].  
Figure 3: Polar-orbit constellation configuration.  
The development of satellite networks has drawn increasing attention in recent years. SpaceX is currently deploying a large-scale constellation comprising thousands of LEO satellites, which includes both inclined- and polar-orbit satellites [18]. Similarly, OneWeb [19] aims to construct a constellation predominantly composed of inclined- and polar-orbit satellites, operating at an altitude of 1200 km. Furthermore, the next-generation Iridium constellation represents a global satellite network that integrates both inclined and polar orbits [20]. As a result, commercial LEO satellite constellations commonly employ a hybrid configuration of inclined and polar orbits, with polar orbits being the predominant choice due to their extensive coverage capabilities. This study adopts a polar orbit model as the basis for routing algorithm research, providing a representative framework for analyzing and optimizing satellite network performance.  
The polar-orbit constellation consists of multiple uniformly distributed satellite orbits with an inclination angle close to 90\({}^{\circ}\), as illustrated in Figure 3.  
Owing to the continuous variation in satellite positions, the connectivity among satellites is highly dynamic. Links connecting adjacent satellites within the same orbital plane are referred to as intra-orbit links, whereas links between the adjacent satellites in the adjacent orbital planes are termed inter-orbit links [21]. In the Iridium system, each satellite is capable of establishing the following four connections: two intra-orbit links (forward and backward) within the same orbital plane and two inter-orbit links (left and right) with satellites in the adjacent orbital planes. This configuration ensures robust and flexible communication within the constellation, enabling efficient data routing and network resilience.