## 4 Design Analysis
### Thermal Analysis  
The objective of the thermal analysis is to ensure that all the electronics and the structure are operating within their allowable temperature ranges throughout the entire mission phase. The thermal analysis for Light-1 was conducted using the CubeSat Wizard, a numerical tool based on MATLAB to estimate the evolution in certain orbital parameters and calculate the heat fluxes [12]. It generates the expected temperature profile for any given date for the CubeSat. The model is based on a single isothermal node approach and considers the orbital parameters as well as the eclipse and the solar illumination cycles on each surface of the CubeSat. In addition, the model includes the effects of the albedo and Earth infrared heat fluxes. For a Nadir pointing attitude and based on the orbital parameters and the CubeSat specifications, we were able to find the critical temperatures by defining the worst hot and cold cases. The worst hot case corresponds to the day in \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Load** & **X axis** & **Y axis** & **Z axis** \\ \hline \multicolumn{5}{c}{Analysis A} \\ \hline Compressive (N) & - & - & 46.6 \\ \hline Static (G) & 9 & - & - \\ \hline \multicolumn{5}{c}{Analysis B} \\ \hline Compressive (N) & - & - & 46.6 \\ \hline Static (G) & - & 9 & - \\ \hline \multicolumn{5}{c}{Analysis C} \\ \hline Compressive (N) & - & - & 46.6 \\ \hline Static (G) & - & - & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Quasi-static analysis loads. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Load Along X**} & \multicolumn{2}{c}{**Load Along Y**} & \multicolumn{2}{c}{**Load Along Z**} \\  & \multicolumn{2}{c}{**Case A**} & \multicolumn{2}{c}{**Case B**} & \multicolumn{2}{c}{**Case C**} \\ \cline{2-5}  & **Max** & **Location** & **Max** & **Location** & **Max** & **Location** \\ \hline Von Misses & 41.16 &
\begin{tabular}{c} reaction wheels \\ board \\ \end{tabular} & 92.02 & Al frame & 97.3 & Al frame \\ \hline Deflection (mm) & 0.027 & reaction wheels & 0.061 & Al frame & 0.061 & Al frame \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Maximum stresses and deformations in each case. which the average total heat flux from the Sun, albedo, and infrared are the maximum, in which case the eclipse ratio is zero. Thus, the entire orbit will be exposed to sunlight. In contrast, the worst cold case condition corresponds to the case in which the satellite is operated on the day that has the lowest incoming average total heat flux in which the orbit, in this case, is experiencing the maximum eclipse ratio. As a result, a large portion of the orbit will be shadowed by the Earth. Table 14 summarizes the parameters used for the thermal analysis, while the results of the two worst-cases are displayed in Table 15. Figure 18 shows the temperature evolution of Light-1 overtime during the worst hot and cold cases. The temperature is estimated to vary between 18 and 27 \({}^{\circ}\)C in the worst hot case and between \(-\)21 and 23 \({}^{\circ}\)C in the cold case. Figure 14: Maximum stress (MPa) in frame: (**a**) Case A; (**b**) Case B; (**c**) Case C.  
Figure 15: Maximum stress (MPa) in frame—zoomed: (**a**) Case A; (**b**) Case B; (**c**) Case C.  
Figure 16: Maximum deformation (mm): (**a**) Case A; (**b**) Case B; (**c**) Case C. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multicolumn{2}{c}{**Parameter**} & \multicolumn{2}{c}{**Value**} \\ \hline Mass & & & & & & \\ \hline Inclination angle & & i & = & & & \\ \hline Inclination angle & & i & = & & & \\ \hline Surface area average emissivity, \(\epsilon\) & & & & & & \\ \hline Surface area average absortivity, \(\alpha\) & & & & & & \\ \hline Specific heat, \(C_{p}\) & & & & & & \\ \hline Albedo constant & & & & & & \\ \hline Generated heat from the electronics & & & & & & \\ \hline Planet temperature & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Light-1 thermal analysis parameters.