# Data Naming Mechanism of LEO Satellite Mega-Constellations for the Internet of Things
## 2 LEO Mega Constellation for the IoT
### Interstellar Link of LEO Mega Constellation
#### 2.2.2. ISL Analysis  
Intersatellite communication links include links between adjacent satellites on the same orbital plane and satellite links between adjacent orbital planes. Therefore, the analysis of intersatellite links considers the following two scenarios:  
Case 1: ISL between adjacent satellites on the same orbital plane  
To facilitate analysis, each satellite in the constellation is marked as \(S_{i-jk}\). For example, \(S_{0-01}\) represents the 01 satellite in the 0# orbital plane, and \(S_{1-11}\) represents the 11 satellite in the 1# orbital plane.  
The geometric relationship between adjacent satellites on the same orbital plane remains unchanged, and the ISL distance can be calculated using a simple triangle relationship. Consider satellites \(S_{0-00}\) and \(S_{0-01}\) shown in Figure 6 as an example.  
In Figure 6, if \(r_{e}\) is the radius of the Earth, \(r_{s}\) is the orbital height, \(\theta\) is the angle between adjacent satellites, and \(\varphi\) is the angle between the line connecting points \(O\) and \(S_{0-00}\) and the line connecting points \(S_{0-00}\) and \(S_{0-01}\), then the distance between \(S_{0-00}\) and \(S_{0-01}\) is:  
\[d_{000-001}\ =\ \frac{\alpha\times\sin\theta}{\sin\varphi} \tag{6}\]  
Substituting the relevant parameters in Table 3, \(\theta\ =\ 32.73^{\circ}\), \(\varphi\ =\ 73.635^{\circ}\), and \(d_{000-001}\ =\ 2016.53\) km.  
Case 2: ISL between adjacent satellites on adjacent orbital planes  
The ISL between adjacent track surfaces includes links with short communication distances and links with long communication distances. Therefore, ISL analysis considers the following two situations:  
Figure 6: ISL between two satellites on the same orbit.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Elements** & **Symbol** & **Value** & **Memo** \\ \hline Semimajor Axis (km) & \(\alpha\) & 7159.14 km & Earth Radius + Orbital Height \\ Eccentricity & \(e\) & 0.002 & Circular Orbit \\ Right Ascension of & \(\Omega\) & 0, 31.80, 63.60, 95.41, 127.21, 159.01 & 6 orbital planes \\ Ascending & \(i\) & 86 & Non \\ Inclination (deg) & \(\omega\) & 0 & Circular Orbit \\ \hline  & & 0, 32.73, 65.45, 98.18, 130.91, 163.64, 196.36, 196.36, 196.36, 229.09, 261.82, 294.55, 327.29 & 11 satellites evenly distributed on the odd \\ \cline{2-4} Rue Anomaly (deg) & \(v\) & 229.09, 261.82, 294.55, 327.29 & orbital plane \\ \cline{2-4}  & & 16.36, 49.09, 81.82, 114.55, 147.27, 180, 212.73, 245.45, 278.18, 310.91, 343.64 & 11 satellites evenly distributed on the even \\ \hline \hline \end{tabular}
\end{table}
Table 3: Keplerian elements of the Iridium constellation.  
(1)  
ISL with the closest communication distance  
When \(S_{1-00}\) is over the North Pole or South Pole, the ISL communication distance is the closest, as shown in Figure 7.  
Similarly, the distance between \(S_{0-00}\) and \(S_{1-00}\) is:  
\[d_{000-100}\ =\ \frac{\alpha\times\sin\frac{\theta}{2}}{\sin\varphi} \tag{7}\]  
Substituting the relevant parameters in Table 3, \(\theta\ =\ 32.73^{\circ}\), \(\varphi\ =\ 81.82^{\circ}\), and \(d_{000-100}\ =\ 1010.53\) km.  
(2)  
ISL with the longest communication distance  
When \(S_{1-00}\) is above the equator, the ISL communication distance is the longest, as shown in Figure 8. The midpoint of the connection between points \(S_{0-00}\) and \(S_{0-01}\) is \(M\). In \(\text{Rt}\Delta OMS_{0-00}\) and \(\text{Rt}\Delta OS_{0-00}S_{1-00}\), the length of \(\overline{OS_{0-00}}\) means \(\alpha\), and the angle between two adjacent tracks is \(\gamma\ =\ 31.80^{\circ}\). Thus, \(\overline{OM}\ =\ 7087.78\) km, \(\overline{MS_{1-00}}\ =\ 3903.68\) km, and \(\overline{S_{0-00}S_{1-00}}\ =\ 4393.76\) km.