## 4 On-Orbit Thermal Analysis of S-STEP  
### Overview of Thermal Analysis  
To verify the effectiveness of the proposed thermal design strategy in meeting the design objectives of the S-STEP system described in Section 3, a system-level transient on-orbit thermal analysis was performed. Table 4 lists the orbital conditions used for the thermal analysis. The hot and cold conditions are defined in the table to implement critical thermal environments on the satellite. The hot and cold cases corresponded to when the satellite was exposed to the highest and lowest environmental heat fluxes, respectively. The thermal analysis cases are defined in Table 5. Cases 1 and 2, respectively, correspond to the SAR imaging operation in the left-and right-looking modes for the hot environment. Cases 3 and 4, respectively, correspond to the SAR imaging operation in the left-and right-looking modes for the cold environment. Case 5 corresponds to the safe-hold mode for the cold environment. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Item** & **Cold Case** & **Hot Case** \\ \hline Altitude (km) & 523.87 & 524.96 \\ \hline RAAN (deg) & 352.34 & 186.03 \\ \hline Eccentricity & 0.00075515 & 0.00075515 \\ \hline Orbit inclination (deg) & 44.2 & 44.2 \\ \hline Date (yyyy.mm.dd hh:mm:ss) & 2024.03.08 07:19:07 & 2025.12.25 00:25:12 \\ \hline Beta angle (deg) & \(-\)0.94 & \(-\)67.49 \\ \hline Solar constant (W/m\({}^{2}\)) & 1287 & 1420 \\ \hline Albedo & 0.30 & 0.35 \\ \hline Planetary flux (W/m\({}^{2}\)) & 227 & 249 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Orbital conditions used for on-orbit thermal analysis. Figure 8a,b, respectively, show the external and internal configurations of a thermal mathematical model (TMM) of the S-STEP system for on-orbit thermal analysis. A total of 13,718 nodes were used for modeling the TMM. The TMM was constructed using Thermal Desktop [26], a CAD-based geometric interface of the commercial on-orbit thermal analysis tool of Systems Improved Numerical Differencing Analyzer/Fluid Integrator (SINDA/FLUINT) [27]. A RadCAD was used to calculate the radiation exchange factors and orbital heating rates based on the geometrical mathematical model (GMM) created by Thermal Desktop. The GMM and output data of RadCAD were used as inputs for on-orbit thermal analysis using SINDA/FLUINT. The representative orbital profiles of S-STEP created based on the information specified in Table 4 are shown in Figure 9a-c. In the SAR imaging operation, the satellite sequentially performed TM/TC communication (60 s), SAR imaging (60 s), and ground station (G/S) pointing for image data downlink (180 s). In the safe-hold mode, the satellite maintained the Sun-pointing of the solar panel (Figure 9c). Tables 6 and 7, respectively, list the thermo-physical and -optical properties used for the thermal analysis. The thermal network was implemented using a node-to-node conductor or a surface-to-surface contactor in the thermal desktop. Figure 8: Thermal mathematical model (TMM) of S-STEP satellite: (**a**) view from +\(z\) side and (**b**) internal configuration. Figure 9: _Cont._  
Figure 9: Representative orbital temperature profiles of S-STEP in left-looking SAR imaging operation: (**a**) hot environment, (**b**) cold environment, and (**c**) safe-hold mode.