## 4 Thermal Analysis of Interstellar Laser Communication Payload
### Analysis of External Heat Flux  
The orbital parameters are set as shown in Table 1, which is a typical medium Earth orbit (MEO) of navigation satellite [26]. Assume that Satellite A is a regular hexahedron with each edge measuring 1 m, and all surfaces of the satellite have identical optical properties, with both absorptivity and emissivity set to 1. The pointing attitude is from Satellite A to Satellite B. For a circular orbit with an inclination of \(55^{\circ}\), the \(\beta\) angle varies between \(-78.5^{\circ}\) and \(+78.5^{\circ}\). The cycle-averaged external heat flux of Satellite A for different \(\beta\) angles is shown in Figure 9. It can be observed from the figure that the variation trends of the average heat flux on all faces are symmetric about the \(\beta\) angle. Physically, the \(\beta\) angle fundamentally governs the symmetry and periodicity of solar illumination relative to the spacecraft body axes. A constant \(\beta\) results in a fixed geometric relationship where the Sun's apparent path relative to the satellite repeats identically each orbital period. This deterministic illumination geometry dictates the range and temporal pattern of incident heat flux, irrespective of which specific faces are exposed due to attitude differences [10]. The transient external heat flux variations for several typical \(\beta\) angles (minimum \(\beta\) angle \(0^{\circ}\), critical \(\beta\) angle \(13.2^{\circ}\), and maximum \(\beta\) angle \(78.5^{\circ}\)) are shown in Figure 10. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Orbital Parameters** & **A Satellite** & **B Satellite** \\ \hline Altitude (km) & 21,586 & 21,586 \\ \hline Eccentricity (\({}^{\circ}\)) & 0 & 0 \\ \hline Inclination (\({}^{\circ}\)) & 55 & 55 \\ \hline Argument of Periapsis (\({}^{\circ}\)) & 0 & 0 \\ \hline Longitude of the Ascending Node (\({}^{\circ}\)) & 180 & 180 \\ \hline True Anomaly (\({}^{\circ}\)) & 0 & \(-90\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Interstellar pointing attitude external heat flux calculation conditions setting. Figure 9: Cycle-averaged external heat flux of Satellite A for different \(\beta\) angles. Figure 10: Transient external heat flux variations on Star A’s surfaces over one orbital period. For this type of orbit, the critical \(\beta\) angle is 13.2\({}^{\circ}\). When the \(\beta\) angle is greater than 13.2\({}^{\circ}\), the orbit is a full sunlight orbit with no shadow zones. In this case, the peak external heat flux on the \(\pm\)X and \(\pm\)Z surfaces is the same and is given by the solar constant \(\times\)cos\(\beta\). The instantaneous values differ only in phase. The cycle-averaged external heat flux is the same for both surfaces and is given by the solar constant \(\times\)cos\(\beta/\pi\). When the \(\beta\) angle is less than 13.2\({}^{\circ}\), the influence of shadow zones causes differences in the illumination conditions of the \(\pm\)X and \(\pm\)Z surfaces, leading to different cycle-averaged external heat flux values. For the \(\pm\)Y surfaces, at the same \(\beta\) angle, only one surface is illuminated while the other has zero external heat flux. For the illuminated surface, the external heat flux remains constant during the illumination period and is given by the solar constant \(\times\)sin(\(\mid\beta\mid\)). During the shadow period, the external heat flux is zero. The orbital parameters in [26] are identical to those in this section, with the difference lying in the attitude configuration. In [26], the satellite adopts a yaw-steering attitude, where the satellite maintains Earth-pointing along the +Z axis while ensuring the \(\pm\)Y and \(-\)X faces remain unexposed to solar radiation. In contrast, this work employs a pointing attitude where any satellite face may be illuminated. Nevertheless, for the illuminated faces, the variation range of the heat flux remains identical and the variation trend is similar under the same \(\beta\) angle.