## 4 On-Orbit Thermal Analysis
### Results of On-Orbit Thermal Analysis
Among the five cases, Case 4 is the lowest maximum \(\Delta T\), with values of 22.3 \({}^{\circ}\)C and 28.2 \({}^{\circ}\)C in the worst cold and hot conditions, respectively. Case 4 has a single-yarn Atlas knitting pattern and with the lowest OPI (10 OPI) among all case. Accordingly, the transmittance is the highest at 0.93. Conversely, Case 5 demonstrated the largest maximum \(\Delta T\) of 61.6 \({}^{\circ}\)C. Despite having an OPI (12 OPI) which is the second lowest among the specimens, it consists of three plies and has the lowest transmittance of 0.81. This is because transmissivity decreases as the area increases as it is composed of ply wires. Furthermore, a similar trend is observed for the \(\Delta T\) of 61.6 \({}^{\circ}\)C.  
Figure 8: Temperature profile of the primary reflector with transmissivity. (a) Worst cold case; (b) worst hot case. Figure 7: Temperature profile of the primary reflector without transmissivity. (a) Worst cold case; (b) worst hot case. Figure 12 shows the maximum \(\Delta T\) graph of Case 5 to 5-3 to show the influence of the temperature gradient according to the tensile direction of the mesh. The temperature gradient difference between the reflectors of Cases 5 and 5-3, where the transmissivity difference among the four cases is maximized at 0.05, is found to be relatively low at approximately 12.6 \({}^{\circ}\)C. This indicates that the difference in the 1-2 OPI resulting from tension suggests a low thermal sensitivity. As previously mentioned, the metallic mesh is extremely thin and lightweight, making it particularly susceptible to thermal deformation. Therefore, it is crucial to analyze the factors that contribute to high temperature gradients in the mesh reflector while in orbit. In this study, we further examined the impact of shadows cast by large deployed structures, specifically the satellite's solar panels. To assess the temperature gradients induced on the mesh reflector by these shadows, we conducted on-orbit thermal analysis under five different cases, each assuming a different solar panel configuration. The thermal design for the analysis was based on Case1 under the assumption of a hot case. Table 7 summarizes the thermal analysis results of \(Tmax\), \(Tmin\), and \(\Delta T\) for various configurations of the solar panels. The table indicates that the presence of the solar panels causes a shading effect on the partial area of the primary reflector throughout the sunlight period, which results in an increase in \(\Delta T\) in the primary reflector during the imaging period, as shown in Figure 13. The following results show the influence of the number and length of solar panels on \(\Delta T\). In the case of three and four solar panels with an area of 2.2 m \(\times\) 5.5 m, \(\Delta T\) is approximately 8 \({}^{\circ}\)C and 12.6 \({}^{\circ}\)C higher than in the case without solar panels, respectively. The \(\Delta T\) generated by applying six solar panels with an area of 2.2 m \(\times\) 3.5 m is 20.5 \({}^{\circ}\)C, which is 15.6 \({}^{\circ}\)C higher than the case without solar panels, showing the largest \(\Delta T\). However, the variation in temperature gradient with regard to area change is not significantly sensitive. The analysis shows that the \(\Delta T\) of the antenna reflector tends to increase with the number of solar panels, but the difference in temperature gradient is not significant. This is because of the characteristics of the mesh fabric with high transmittance, indicating that the influence of temperature gradient on the solar panel configuration is low. In summary, while \(\Delta T\) of the antenna reflector tends to increase with the number of solar panels, its impact is not significant. This is owing to the characteristics of the mesh fabric with high transmittance, indicating a low influence of the temperature gradient on the configuration of the solar panels. Figure 12: Temperature gradient (\(\Delta\)T) of the mesh reflector for Cases 5–5-3.