## 7 Conclusions  
In this study, relative orbit control algorithms and demonstration scenarios for a VT with CubeSats in low-Earth orbit are established and validated. A solar coronagraph is a VT that photographs the solar corona by aligning two satellites with respect to the inertial coordinate frame. When a satellite is operated in a sun-synchronous orbit, the position of the Sun relative to the satellite orbit is constant. Consequently, the reference trajectory was defined as a circular trajectory with a constant cross-track offset on a sphere of radius equal to the focal length. CANYVAL-C is a CubeSat mission that demonstrates the use of an IAH to implement a solar coronagraph. To accomplish this mission, relative orbit  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Staging Mode**} & \multicolumn{2}{c}{**Alignment Mode**} & \multicolumn{1}{c}{**Total**} \\ \hline Impulse (Ns) & Avg. \(\pm\) 3\(\sigma\) & 2.83 \(\pm\) 3.59 & 1.07 \(\pm\) 0.63 & 3.90 \(\pm\) 3.87 \\ Max. & 7.08 & 1.82 & 8.90 \\ \hline \hline \end{tabular}
\end{table}
Table 13: Impulse consumption for the staging and alignment mode and total impulse during IAH.  
Figure 16: Aligned time and total impulse for the fine requirement, coarse requirement (1), and coarse requirement (2) during IAH.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Fine Req.**} & \multicolumn{2}{c}{**Coarse Req. (1)**} & \multicolumn{2}{c}{**Coarse Req. (2)**} \\ \hline Mission success & & 64\% & 87\% & 94\% \\ Aligned time (min) & min. & 0.03 & 0.07 & 0.85 \\ Max. & 10.77 & 16.57 & 16.78 \\ \hline \hline \end{tabular}
\end{table}
Table 12: Percentage of the mission succeeded cases and the minimum and maximum aligned time for fine requirement, coarse requirement (1), and coarse requirement (2) during IAH.  
control algorithms such as rendezvous, differential air drag control, and inertial alignment hold have been developed, as well as supplementary strategies to compensate for the limited performance of cube satellites and the relative orbit control scenarios. To validate this research, the subsystem errors and operational constraints of the cube satellite were considered in Monte Carlo simulations. Consequently, it was verified that the mission had a 3-sigma probability of success.  
Conceptualization, G.-N.K.; data curation, S.J.; formal analysis, S.J.; investigation, S.J.; methodology, S.J.; supervision, S.-Y.P.; validation, S.J.; visualization, S.J.; writing--original draft, S.J. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Challengeable Future Defense Technology Research and Development Program (No. 915027201) of the Agency for Defense Development in 2023.  
The data presented in this study are available on request from the corresponding author.  
I would like to show my appreciation for [PERSON] (NASA/Goddard Space Flight Center, United States) for his technical support with the source code of the inertial alignment hold. I trust that this brief note of appreciation will portray that his assistance has been sincerely appreciated.  
Author [PERSON] was employed by the company NARA Space. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.