## 5 Conclusions  
This paper addresses the issue of external heat flux analysis for inter-satellite pointing attitudes and proposes an external heat flux analysis method for complex inter-satellite pointing attitudes. Numerical simulations of solar external heat flux for typical lunar relay satellite orbit were conducted to validate the feasibility of the method. Finally, the method was applied to the thermal analysis of inter-satellite laser communication payloads, providing the temperature results of key payload components and comparing them with in-orbit measurement results. The conclusions of this paper are as follows:  
1. A complex external heat flux analysis method for inter-satellite pointing attitudes has been proposed. A coordinate system for inter-satellite pointing attitudes was established, based on a three-axis Earth-pointing coordinate system. The +Z axis is rotated from Earth-pointing to the inter-satellite pointing vector direction through yaw and pitch. The calculation methods for yaw and pitch angles during coordinate system transformation were analyzed. Using the satellite orbit parameters and the calculated yaw and pitch angles, the external heat flux on each surface of the inter-satellite pointing attitude can be obtained using space thermal analysis software. 2. The solar heat flux for lunar relay satellites in Halo orbits and large elliptical frozen orbits was analyzed. For inclined elliptical orbits, the transient heat flux on each surface at different \(\beta\) angles was calculated, and the variations of solar heat flux were analyzed. This provides data references for thermal control design of relay satellites in inclined large elliptical orbits. 3. The temperature comparison results of key components of the laser communication payload show that the operational mode based on inter-satellite pointing attitudes aligns with its in-orbit operational conditions. The temperature calculation results obtained using the external heat flux analysis method for inter-satellite pointing attitudes matched the in-orbit temperatures. Therefore, the proposed analysis method is reasonable and feasible, and can provide references and bases for thermal control design of spacecraft/payloads in inter-satellite pointing attitudes. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Thermistor**} & \multicolumn{2}{c}{**Calculation Result**} & \multicolumn{2}{c}{**In-Orbit Data**} \\ \cline{2-5}  & **Minimum Value** & **Maximum Value** & **Minimum Value** & **Maximum Value** \\ \hline TZT102 & 18.5 & 20.5 & 18.7 & 19.2 \\ \hline TZT103 & 18.5 & 20.6 & 18.5 & 19.1 \\ \hline TZT104 & 18.4 & 20.9 & 18.5 & 23.2 \\ \hline TZT105 & 18.8 & 19.5 & 18.6 & 22.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of calculation results and in-orbit data (\({}^{\circ}\)C). The comprehensive analytical method for direct solar heat flux calculation proposed in Chapter 2 of this study, while specifically applicable to first-incidence heat flux computation on convex surfaces, can be extended to more complex scenarios. For concave surfaces or surfaces with complex optical properties, as well as for absorbed heat flux calculations, radiation exchange factors between surfaces can be obtained through many methods, such as ray-tracing or the Monte Carlo method. Subsequently, based on the known first-incidence heat flux, both the actual incident heat flux and absorbed heat flux can be determined. Therefore, for future research, the methodology presented in this paper can serve as a foundation to develop more generalized absorbed external heat flux calculation approaches suitable for complex surface characteristics. Such advancement would enhance the method's universality and provide more accurate computational techniques for spacecraft thermal analysis. Conceptualization, X.H. and T.L. ; methodology, X.H. and H.Y. ; validation, X.H. and H.Y. ; formal analysis, X.H. and H.Y. ; resources, Y.Z. and Y.R. ; writing--original draft preparation, X.H. and T.L. ; writing--review and editing, X.H., Y.Z., F.X.