## 6 Monte Carlo Simulation
### Inertial Alignment Hold  
According to the relative orbit control scenario, after the first mission mode (commissioning-IAH) with the occulter stowed, the deputy must orient toward the Sun for five orbital periods to ensure a sufficient power budget. Subsequently, the rendezvous and DADC are executed sequentially with the occulter deployed. Table 10 lists the structural properties based on deployment. After deployment, the maximum cross-sectional area increased by approximately sevenfold, whereas the differential air drag increased by approximately fourteenfold. To compensate for this, the deputy should deploy the occulter and enter mission mode in the along-track direction to maintain the minimum cross-sectional area (Table 11(1)). The staging duration is the same as that in Table 7.  
As a result of the Monte Carlo simulation, the final drift rate of rendezvous was 0.06 m/s or less, even after C-IAH and Sun-pointing mode. The number and duration of mission chances in the DADC for two months are shown in Figure 14. At least one mission chance is guaranteed, but because it enters the mission mode only in the positive direction it has a much smaller number of mission chances compared to Figure 11. However, the duration of the mission chance did not decrease significantly because the range of the along-track distance increased from 10 to 80 m. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Area-to-Mass Ratio** & **Minimum** & **Maximum (Stowed)** & **Maximum (Deployed)** \\ \hline
2U & 0.9578 \(\times 10^{-2}\) & 3.2574 \(\times 10^{-2}\) & 23.7342 \(\times 10^{-2}\) \\
1U & & 1.6719 \(\times 10^{-2}\) & \\ \hline
**Differential** & & & \\
**area-to-mass ratio** & **Minimum** & **Maximum (Stowed)** & **Maximum (Deployed)** \\ \hline
2U-1U & \(-0.7141\)\(\times 10^{-2}\) & +1.5855 \(\times 10^{-2}\) & +22.0623 \(\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Structural properties of 1U and 2U [35]. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & **Fine Req.** & **Coarse Req. (1)** & **Coarse Req. (2)** \\ \hline Mission success & & 75\% & 92\% & 99\% \\ Aligned time (min) & min. & 0.08 & 0.12 & 2.15 \\ Max. & 12.87 & 16.65 & 16.68 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Percentage of the mission succeeded cases and the minimum and maximum aligned time for fine requirement, coarse requirement (1), and coarse requirement (2) during C-IAH. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & **Staging Mode** & **Alignment Mode** & **Total** \\ \hline Impulse (Ns) & \begin{tabular}{c} Avg. \(\pm 3\sigma\) \\ Max. \\ \end{tabular} & \begin{tabular}{c} 2.38 \(\pm\) 2.68 \\ 4.79 \\ \end{tabular} & \
\begin{tabular}{c} 1.02 \(\pm\) 0.50 \\ 1.73 \\ \end{tabular} &
\begin{tabular}{c} 3.41 \(\pm\) 2.74 \\ 5.68 \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Impulse consumption for the staging and alignment mode and total impulse during C-IAH. Compared to C-IAH, IAH shows larger control errors in the staging mode, and some control errors even diverge in the alignment mode (Figure 15). Similar to Figure 12c, the six samples of the deviated alignment angle in Figure 15c are the failure cases of coarse requirement (2) in Table 12. Consequently, it has a lower probability of success for all the fine requirement and coarse requirements (1) and (2) (Figure 16, Table 12). As the effective cross-sectional area increases, the air drag applied to the satellite increases; thus, both the orbital perturbation and the attitude disturbance increase. The orbital perturbation by air drag only has a velocity direction and is controllable by thrust. However, the air drag disturbance torque continuously accumulates and is difficult to compensate for with the MTQ, which degrades the attitude control performance of the staging and alignment modes, resulting in a low probability of success. Because attitude control is necessary for thrust firing, thrust consumption also increases (Table 13).