# Multiple SSO Space Debris Flyby Trajectory Design Based on Cislunar Orbit
## 6 Numerical Simulations and Analysis  
The two-impulse DRO-Earth transfer orbit shown in Table 10 is defined as the 0 th revolution orbit of the spacecraft. After the spacecraft first flies by the target debris in the 0 th revolution, the orbit from the position of the first flyby to the next perigee is defined as the 1 st revolution orbit. Similarly, the subsequent orbits are defined as the 2 nd revolution orbit, 3 rd revolution orbit \(\ldots\) and Nth revolution orbit. The spacecraft departs the 3:2 resonant DRO at 2025/10/31/23:58:43. The target debris 25733 is flown by in the 0 th revolution orbit. The subsequent transfers and flybys are shown in Table 13. The total impulse of the flyby mission is 1.39 km/s and the total transfer time is 2.23 years. All of the spacecraft's orbits are shown in Figure 14.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Revolution** & **Target** & \(\mathrm{I\,I\,\Delta V\,I\,1\,\mathrm{/}m\cdot s^{-  
As shown in Table 13, it takes 83 revolutions for the spacecraft to flyby all the debris shown in Table A1. In 62 of the 83 revolutions, the spacecraft cruises around the Earth without flying by any debris. The relative velocity versus distance of the 21 flybys are shown in Figure 15a. It shows that the minimum relative velocity of a flyby is about 3.23 km/s. The statistics of the impulses and the flight times are shown in Figure 15b,c. From Figure 15b, it can be seen that all impulses are less than 70 m/s. The average impulse of 83 revolutions is 11.05 m/s. The smallest impulse is 0.16 m/s (6 th revolution) and the largest impulse is 60.70 m/s (50 th revolution). In the 50 th revolution orbit, the spacecraft applies a 60.70 m/s impulse to avoid the spacecraft entering the Earth's atmosphere due to the lunar gravity. In addition, the time of flight of the 50 th revolution orbit is reduced to about 5 days, as shown in Figure 15c. Figure 15c shows that before the 63 rd revolution, the flight times of the most of HEO transfer orbits are between 10-12 days. This proves that the period of the  
Figure 14: HEO transfer orbits: (**a**) the center of mass rotating frame; (**b**) J2000 ECI frame. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Revolution of Orbits** & **Target Debris** & 11 AV11/m\(\cdot\)s\({}^{-1}\) & **a/rad** & **\#/rad** & **\#/rad** & **\(dt_{1}\)/day** & **\(dt_{2}\)/day** & 11\(\delta\)r11/km & 11\(\delta\)v11/km\(\cdot\)s\({}^{-1}\) \\ \hline
54 & / & 4.39 & 0.99 & 5.22 & 5.29 & 5.23 & / & / \\
55–56 & / & / & / & / & / & 20.97 & / & / \\
57 & / & 6.20 & 2.16 & 4.51 & 11.93 & 0.00 & / & / \\
58 & / & / & / & / & / & 12.04 & / & / \\
59 & / & 4.16 & 4.22 & 2.13 & 5.21 & 5.14 & / & / \\
60 & / & 2.14 & 5.23 & 2.97 & 5.10 & 5.11 & / & / \\
61-62 & / & / & / & / & / & 21.01 & / & / \\
63 & / & 23.31 & 5.32 & 3.56 & 0.00 & 7.62 & / & / \\
64 & 32959 & 25.77 & 3.49 & 0.94 & 2.23 & 5.30 & 100.00 & 4.00 \\
65–66 & / & / & / & / & / & 15.19 & / & / \\
67 & / & 48.23 & 4.22 & 4.80 & 4.57 & 3.39 & / & / \\
68 & 31114 & 9.80 & 3.89 & 4.22 & 4.45 & 3.05 & 99.98 & 3.88 \\
69–73 & / & / & / & / & / & 38.36 & / & / \\
74 & / & 42.51 & 5.21 & 2.23 & 3.91 & 3.92 & / & / \\
75 & / & 1.44 & 4.24 & 3.49 & 3.73 & 3.73 & / & / \\
76 & / & 0.97 & 5.18 & 4.91 & 3.78 & 3.74 & / & / \\
77 & / & / & / & / & / & 7.46 & / & / \\
78 & 39203 & 44.64 & 5.83 & 4.31 & 3.19 & 4.76 & 100.00 & 4.00 \\
79–80 & / & / & / & / & / & 15.77 & / & / \\
81 & / & 31.86 & 5.19 & 2.49 & 3.86 & 4.00 & / & / \\
82 & / & 10.62 & 5.98 & 5.97 & 3.61 & 4.25 & / & / \\
83 & 37215 & / & / & / & / & 7.56 & 99.99 & 3.79 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: _Cont._lunar-resonant orbit is not constant due to the influence of the Moon in the CRTBP system. After the 63 rd revolution, the flight times are all about 8 days. It is because of the fact that in the 63 rd revolution, the spacecraft applies 23.31 m/s impulse near the perigee to reduce the height of the apogee; otherwise, the spacecraft would enter the Earth's atmosphere due to the lunar gravity.