## 4 Investigation on Orbital Decent
### Evaluation of SDOM De-Orbiting Capability  
The results of the overall analysis are shown in Figure 8 together with the orbit altitude information of ALE-1 based on the TLE. In 2020, the orbit of ALE-1 with \(C_{\rm D}A=3.0\) m\({}^{2}\) was in good agreement with the TLE. However, in 2021, the descent began to accelerate, causing the orbit to significantly change from \(C_{\rm D}A=1.5\) m\({}^{2}\) to \(A=4.0\) m\({}^{2}\) over the course of the year until the SDOM was finally separated. It is worth noting that the \(C_{\rm D}A\) of the drag flag increased as the orbital altitude decreased. This result is a very important finding on the de-orbiting performance of a drag flag attached to a satellite in low Earth orbit (LEO). The value of \(C_{\rm D}A=4.0\) m\({}^{2}\) is corresponding to a mean cross-sectional area of \(A=1.8\) m\({}^{2}\) if the drag coefficient \(C_{\rm D}\) is approximated as 2.2.  
As discussed in Section 3.2, the SDOM was observed to be freely moving around a single axis, fluttering like a flag. Even in this state, the drag flag delivered a de-orbiting effect on the order of \(C_{\rm D}A=3.0\) m\({}^{2}\) to 4.0 m\({}^{2}\), or approximately 22 to 29% of the possible maximum value of the scenario where the drag sail is always set vertical to the velocity  
\begin{table}
\begin{tabular}{c c c} \hline
**Environment** & **Model** & **References** \\ \hline Earth gravity model & EGM-08 (degree, order) = (40,40) & Ref. [22] \\ Sun and Moon model & DE431 & Ref. [22; 23] \\ Atmosphere model & NRLMSISE-00 & Ref. [26] \\ \hline \end{tabular}
\end{table}
Table 2: Environmental models of the orbit analysis.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Items** & **Parameters** & **Value** & **References** \\ \hline \multirow{4}{*}{Atmospheric drag} & \(C_{\rm D}\) & - & Ref. [22] \\  & A [m\({}^{2}\)] & - & - \\  & F\({}_{10.7}\) & Variable & Ref. [26] \\  & F\({}_{10.7}\) 81 days & Variable & Ref. [26] \\ \hline \multirow{4}{*}{Solar radiation} & \(c_{\rm R}\) [-] (reflectivity) & 1.0 & Ref. [22] \\  & P\({}_{\rm srp}\) [N/m\({}^{2}\)] (solar-radiation pressure) & 4.54 E-6 & Ref. [22] \\ \hline Time system & \(\Delta AT\) [s] (delta atomic time) & 37.0 & Ref. [27] \\ \hline \multirow{2}{*}{Satellite properties} & Mass of satellite [kg] (after SDOM separation) & 65.29 & - \\  & \(C_{\rm D}A\) [m\({}^{2}\)] & 0.80 to 7.43 & - \\ \hline \end{tabular}
\end{table}
Table 3: Parameters of the orbit analysis.  
vector, and approximately 41 to 54% of the mean value of the scenario where the satellite is freely tumbling.  
This result indicates that the shape of the de-orbiting film does not necessarily need to be fixed as a flat surface, as was regarded as the requirement so far worldwide; instead, a trailing drag flag can be about up to half as effective as a flat drag sail in LEO in the case of ALE-1 implementation. This new finding can open up breakthrough opportunities for more effective ways of implementing PMD (Post-Mission Disposal) devices in terms of their simplicity, size, mass, and reliability.  
The trailing drag flag is expected to move backwards with the increase in atmospheric density and is expected to stabilize in a cloak-like manner, resulting in a smaller effective cross-sectional area; in other words, \(\rho\) and \(A\) may be inversely related. The above-mentioned increasing effective cross-sectional area along the descent of the orbit can suggest that the complex behavior of the drag flag in the rarefied atmosphere may have resulted in a three-dimensional shape, which in turn resulted in the increasing mean atmospheric perturbation. It was also reported in the past study that even a flat surface that is parallel to the velocity vector delivers a non-zero atmospheric drag coefficient due to the thermochemical properties of the upper atmosphere [28]. It can be that this effect also helped the drag flag to achieve the above-mentioned de-orbiting performance. Details on this topic needs to be investigated further in the future.