## 4 Analysis
### Simulation Experiments for the Optimal Satellite Orbit in the Common-View Mode between Two Stations
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**SLR Station** & **Coordinates X, Y, Z (km)** & **Latitude** & **Longitude** & **Height** \\ \hline
7237 Changchun & \(-2674.387\), \(3757.189\), \(4391.508\) & \(43.7905^{\circ}\)N & \(125.4434^{\circ}\)E & \(274.900\) \\
7396 Wuhan & \(-2279.756\), \(5004.737\), \(3219.791\) & \(30.515667^{\circ}\)N & \(114.490167^{\circ}\)E & \(76.7\) \\
7821 Shanghai & \(-2830.744\), \(4676.580\), \(3275.072\) & \(31.0961^{\circ}\)N & \(121.1866^{\circ}\)E & \(99.961\) \\
7249 Beijing & \(-2148.760\), \(4426.759\), \(4044.509\) & \(39.6069^{\circ}\)N & \(115.8920^{\circ}\)E & \(82.300\) \\
7819 Kunming & \(-1281.301\), \(5640.724\), \(2682.905\) & \(25.0298^{\circ}\)N & \(102.7977^{\circ}\)E & \(1987.05\) \\
7306 Tsukuba & \(-3961.641\), \(3308.774\), \(3308.774\) & \(36.0675^{\circ}\)N & \(140.1313^{\circ}\)E & \(68.21\) \\
7838 Simosato & \(-3822.388\), \(3699.363\), \(3507.573\) & \(33.5777^{\circ}\)N & \(135.9370^{\circ}\)E & \(62.44\) \\
7394 Sejong & \(-3110.108\), \(4082.170\), \(3774.911\) & \(36.520991^{\circ}\)N & \(127.302913^{\circ}\)E & \(176.415\) \\
7090 Yarragadee & \(-2389.008\), \(5043.332\), \(-3078.526\) & \(29.0464^{\circ}\)S & \(115.3467^{\circ}\)E & \(244\) \\
7825 Mt. Stromlo & \(-4467.064\), \(2683.034\), \(-3667.007\) & \(35.3161^{\circ}\)S & \(149.0099^{\circ}\)E & \(805.0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Selected Stations within the Asia-Pacific SLR Station Network. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Altitude (km)** & **Satellite** & **Inclination** & **10 Days** & **Optimized (\(i_{com}\Omega_{com}\))** & **10 Days** & **Multiplier** \\ \hline
1336 & Jason-3 & 66 & 3.05 & 48.101305, \(27.578522\) & \(27.313\) & \(8.955\) \\
1488 & Ajisai & 50 & 8.792 & 48.043023, \(27.651744\) & \(29.339\) & \(3.337\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of common-view duration results between some existing satellite orbits and optimized satellite orbits. During the optimization process, it was a requirement that any pair of the selected ten SLR stations could establish common-view, ensuring a minimum common-view duration of no less than 2 min for each pair. Additionally, the objective was to maximize the total common-view duration across all possible pairs of stations. The resulting common-view durations between pairs of SLR station networks within the Asia-Pacific region and those across Europe to Asia SLR station networks are presented in Figure 10, respectively. From Figure 10, it is evident that the minimum common-view duration between any two stations within the Asia-Pacific region is 6.183 min, and is especially longer for closer sites, reaching a maximum of 60.633 min. Between any two stations spanning Europe to Asia, the minimum common-view duration is 5.583 min, extending up to a maximum of 61.75 min. Figure 11 portrays the optimized satellite trajectories: Figure 11a displays the optimal orbits for the ten SLR stations within the Asia-Pacific region, while Figure 11b delineates the optimal orbits for the ten SLR stations spanning the Europe to Asia region. From Figure 11, it is evident that the optimized optimal satellite orbits, refined using an improved simulated annealing algorithm, traverse across various stations within the Asia-Pacific region and between Europe and Asia. This achieved the precise optimization of satellite orbits for the multi-region common-view SLR station network employed in Laser Time Transfer. Figure 11: Graphs illustrating satellite trajectories derived from optimization results obtained using the improved simulated annealing (SA) algorithm. These graphs represent the most optimal trajectories for common-view satellite orbits across two scenarios: (**a**) the ten SLR stations within the Asia-Pacific region and (**b**) ten SLR stations spanning the Eurasian intercontinental region.