## 2 System Modeling
### Individual-Satellite-Oriented Multi-Directional FoV
This seasonal variation is modeled using inclination angles of \(0^{\circ}\) for fall, \(23.5^{\circ}\) for summer, and \(-23.5^{\circ}\) for winter (considering the northern hemisphere). The location of the sun is determined using azimuth and elevation angles, represented as follows:  
\[\psi_{sun}=-v_{e}\cdot t \tag{13}\]  
\[x_{sun}=d_{sun}\cdot cos(\theta_{sun})\cdot sin(\psi_{sun})y_{sun}=d_{sun}\cdot cos (\theta_{sun})z_{sun}=d_{sun}\cdot sin(\theta_{sun})\,, \tag{14}\]  
where \(\theta_{sun}\) is adjusted for the season, and \(\psi_{sun}\) is determined by the rotational velocity of the Earth (\(v_{e}\)) and the elapsed time (\(t\)). These parameters establish the Cartesian coordinates of the sun, (\(x_{sun}\), \(y_{sun}\), \(z_{sun}\)). Satellites with a distance to the sun of less than the maximum \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Feature** & **Ref. [12]** & **Ref. [16]** & **Our Work** \\ \hline Dedicated solar irradiance modeling & O & O & O \\ Distinguishment of unaffected solar exposure & \(\Delta\) & X & O \\ Analysis of seasonal influence & X & X & O \\ Fully adaptive & X & \(\Delta\) & O \\ multi-directional FoV & & \(\Delta\) & O \\ Robustness against varying orbital & & \(\Delta\) & O \\ inclinations & & \(\Delta\) & O \\ Large-scale multi-shell & & & \\ scenarios & & & \\ \hline \hline \end{tabular} \({}^{a}\)O\({}^{a}\) = fully supported, \({}^{a}\)A\({}^{a}\) = partial/limited, and \({}^{a}\)X\({}^{a}\) = not covered.  
\end{table} 
Table 1: Investigation coverage comparison. Figure 3: Impact of solar irradiance on multi-directional receivers in a satellite with an incident angle of solar irradiance on the satellite \(\theta_{\rm s}\) with \(0^{\circ}\) in (**a**), \(45^{\circ}\) in (**b**), and \(135^{\circ}\) in (**c**). threshold (\(d_{max}\), defined earlier) are investigated for further analysis of the impact of the solar irradiance. Practical constraints are incorporated to simulate a realistic operational environment. These constraints include alignment requirements for transmitter and receiver modules, equipment specifications, the maximum laser propagation distance, and link altitude limitations. The position of each satellite is defined by its elevation angle (\(\theta\)) and an azimuth angle (\(\psi\)), which vary according to the orbital characteristics and elapsed time. Using these parameters, the simulator identifies linkable satellites while considering environmental constraints and solar irradiance interference. The optimal path is then constructed by selecting the shortest possible communication path. The workflow of the solar irradiance model is illustrated conceptually in Figure 6. Satellites in the FoV of a reference satellite (\(S_{ego}\)) are evaluated for usability based on their exposure to solar interference. For instance, satellite (a) is within the FoV of \(S_{ego}\) and unaffected by solar light, making it a possible communication link. Similarly, satellite (c) is  
Figure 4: Illustrations showing (**a**) the solar-irradiance-influenced case and (**b**) the non-influenced case, despite the entities being at the exact same locations. Figure 5: Differences in satellite classification based on seasons (within the northern hemisphere). in the FoV, but its receiver module on \(S_{ego}\) is illuminated by solar light, possibly making it blind. Satellite (b), on the other hand, is outside the FoV of \(S_{ego}\), even though it is not directly affected by solar interference, and, thus, is also unsuitable for communications. By simulating these conditions and constraints, the proposed analysis method effectively models the impacts of solar irradiance on satellite communications and support to find the optimal mitigation strategies and path configurations for O-ISLs.