## 4 On-Orbit Thermal Analysis
### Results of On-Orbit Thermal Analysis  
As the first step in analyzing the thermal properties of the reflector, the temperature of the primary reflector was compared with and without transmissivity properties owing to the characteristics of the mesh fabric. For this purpose, the optical properties of the reflector were analyzed for Case 5, which resulted in minimum transmittance among the analyzed conditions shown in Figure 4, and for the experimentally measured optical properties of [PERSON] et al. [23], which are listed in Table 5, without considering transmittance. The analysis results confirmed the maximum (\(T_{max}\)), minimum (\(T_{min}\)), and average (\(T_{avg}\)) temperatures under the worst hot and cold conditions. The temperature gradient of the reflector was evaluated by estimating the temperature deviation between the maximum and minimum temperature values. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Worst Cold Case** & **Worst Hot Case** \\ \hline Altitude (km) & 550 & 550 \\ \hline Inclination (\({}^{\circ}\)) & 45 & 45 \\ \hline Solar flux (W/m\({}^{2}\)) & 1287 & 1420 \\ \hline Albedo & 0.30 & 0.35 \\ \hline Planetary IR flux (W/m\({}^{2}\)) & 227 & 249 \\ \hline Beta angle (\({}^{\circ}\)) & \(-\)21.2 & \(-\)68.1 \\ \hline RAN (\({}^{\circ}\)) & 7.8 & 190 \\ \hline Date (MM/DD) & 06/21 & 12/22 \\ \hline \end{tabular}
\end{table} 
Table 6: On-orbit parameter. \begin{table}
\begin{tabular}{c c c c} \hline
**Case** & **Absorptivity (\(\alpha\))** & **Reflectivity (\(\rho\))** & **Transmissivity (\(\tau\))** \\ \hline
1 & 0.03 & 0.08 & 0.89 \\ \hline
2 & 0.05 & 0.11 & 0.84 \\ \hline
3 & 0.04 & 0.11 & 0.85 \\ \hline
4 & 0.05 & 0.02 & 0.93 \\ \hline
5 & 0.07 & 0.13 & 0.81 \\ \hline
5-1 & 0.07 & 0.12 & 0.81 \\ \hline
5-2 & 0.05 & 0.11 & 0.84 \\ \hline
5-3 & 0.05 & 0.10 & 0.86 \\ \hline \end{tabular}
\end{table} 
Table 5: Definition of optical properties of mesh reflectors for on-orbit analysis. Figures 7 and 8 show the temperature profiles with and without the transmittance, respectively. Moreover, representative temperature contours of the reflector during imaging, sunlight, and eclipse periods are shown in Figures 9 and 10 to explain the temperature gradient (\(\Delta T=T_{max}-T_{min}\)) of the reflector. In the worst hot condition, the largest \(\Delta T\) during the orbital period was observed for the reflector during imaging period. This is because the partial area of the reflector is shaded by the S/C body, whereas the remaining area is exposed to the illumination of the sun. In the worst cold condition, the largest \(\Delta T\) occurs after the antenna exits the eclipse period. Since the eclipse period is 30.8 minutes longer under worst cold case compared to worst hot condition, the antenna's temperature remains lower. Consequently, when the antenna is exposed to the sunlight period, a significant temperature difference occurs. This trend in the temperature profile is similar to that of the other analysis conditions, which will be described later. Figure 7 shows that the \(T_{max}\) of the reflector without transmittance is 278.29 \({}^{\circ}\)C and \(T_{min}\) is \(-\)59.09 \({}^{\circ}\)C, whereas Figure 8 shows that the \(T_{max}\) of the reflector with transmittance is 90.46 \({}^{\circ}\)C and \(T_{min}\) is \(-\)54.04 \({}^{\circ}\)C, which is relatively low. Additionally, the comparison of the maximum \(\Delta T\) shows that the temperature deviation is up to 176.07 \({}^{\circ}\)C without transmittance and 57.29 \({}^{\circ}\)C with transmittance, which is approximately 118.78 \({}^{\circ}\)C lower, indicating that the consideration of transmittance is essential to determine the reliable thermal behavior of the reflector. Figure 6: On-orbit profile for thermal analysis ((**a**) cold and (**b**) hot case). Figure 11 shows a graph comparing the maximum \(\Delta T\) within a single orbit under various optical characteristic (Cases 1 to 5) under the worst cold and hot conditions.