## 4 On-Orbit Thermal Analysis  
### Description of the Thermal Model and On-Orbit Conditions  
Figure 5 shows the antenna thermal mathematical model (TMM)that was constructed using Thermal Desktop [20], a CAD-based geometric interface for commercial on-orbit thermal analysis tools of systems integrated differencing numerical analyzer/fluid integrator (SINDA/FLUINT) [21]. The antenna consists of a mesh-type primary reflector, secondary reflector, solar panels, and spacecraft (S/C). To investigate the thermal behavior and temperature gradient of the antenna surface owing to the transmittance characteristics of the reflector, the rim support structure of the reflector was excluded. For the same reason, the  
Figure 4: Degree of the optical characteristics of the mesh specimen. S/C was covered with multilayer insulation (MLI) to insulate its surface from the external heat exchange. To simplify the thermal analysis model of the solar panels, the optical properties of the solar cells were applied on the front side, and white paint was applied on the rear side. Table 4 summarizes the thermo-physical and optical properties that were used during thermal analysis. To analyze the thermal behavior of the reflector under various transmittance characteristics in orbit, eight thermal design cases, based on the previously measured results of the mesh specimens, are listed in Table 5. These cases shown in Table 5 are based on the previously measured results of the mesh specimens. And, the physical properties were based on the thermal-physical property variation curves of gold-plated molybdenum, as analyzed by [PERSON] et al. (2020). Identical physical properties were applied to all the analysis conditions to exclude the influence of material differences. Additionally, the allowable temperature limits for the antenna components were not defined because the objective was to identify a feasible thermal design by comparing the thermal gradients of the reflector in this study. \begin{table}
\begin{tabular}{c c c c} \hline \multicolumn{4}{c}{**Physical Properties**} \\ \hline \multirow{2}{*}{**Material**} & **Conductivity** & **Density** & **Specific Heat** & **Remarks** \\  & **(W/m/K)** & **(kg/m\({}^{3}\))** & **(J/kg/K)** & **Remarks** \\ \hline \multirow{4}{*}{Molybdenum} & 167.9 & 2700 & 961.2 & S/C, \\  & & & solar panel \\ \hline \multirow{4}{*}{Molybdenum} & 178.38 (@ – 103 \({}^{\circ}\)C) & & 185.12 (@ – 200 \({}^{\circ}\)C) & \\  & 146.4 (@ 97 \({}^{\circ}\)C) & & 238.93 (@ 0 \({}^{\circ}\)C) & \\  & 129.21 (@ 297 \({}^{\circ}\)C) & & 277.72 (@ 200 \({}^{\circ}\)C) & \\  & 127.17 (@ 497 \({}^{\circ}\)C) & & 315.62 (@ 400 \({}^{\circ}\)C) & Primary mesh reflector \\  & 106.29 (@ 697 \({}^{\circ}\)C) & & 338.49 (@ 600 \({}^{\circ}\)C) & \\  & 50.76 (@ 1197 \({}^{\circ}\)C) & & 353.63 (@ 800 \({}^{\circ}\)C) & \\ \hline \multicolumn{4}{c}{Thermo-Optical properties} \\ \hline Material & Solar Absorptivity (\(\alpha\)) & IR Emissivity (\(\epsilon\)) & \(\alpha/\epsilon\) & Remarks \\ \hline Gold-plated Mesh (K  
For the analysis, the orbital parameters and thermal conditions for the worst hot and cold conditions were assumed to evaluate the temperature conditions of the reflector, as listed in Table 6. The orbit assumed in this study is circular, with an altitude of 550 km and an orbital inclination angle of 45\({}^{\circ}\). The worst hot and cold conditions correspond to the cases when the reflector is operated during the winter solstice with the highest incoming heat flux and the summer solstice with the lowest incoming heat flux, respectively. Figure 6a,b shows examples of orbital profiles of the antenna under the worst hot and cold conditions. During periods of non-imaging, the solar panels maintain the sun pointing, and the front radiating side of the antenna is installed on the opposite side of the S/C, oriented toward the anti-sun direction. During the eclipse period, the S/C adjusts the attitude toward the nadir pointing of the antenna to prevent excessive heat loss into deep space.