# Multiple SSO Space Debris Flyby Trajectory Design Based on Cislunar Orbit
## 3 Target Selection of SSO Space Debris  
### Analysis of SSO Space Debris  
SSO has great and scientific research value. Polar-orbiting meteorological satellites and imaging satellites are often located in SSO. The main characteristics of SSO include the fact that the angle between the normal orbital plane and the projection of the solar  
Figure 3: Illustration of flyby mission.  
\begin{table}
\begin{tabular}{c c c} \hline
**Parameters** & **Meaning** & **Requirement** \\ \hline \(\Delta\tau\) & Days between \(\overline{\tau}\) and \(\tau_{0}\) & \(\Delta\tau\leq\xi_{1}\) \\ \(\Delta t_{0}\) & The transfer time from DRO to the perilune & \(\Delta t_{0}\leq\xi_{1}\) \\ \(\Delta t_{1}\) & The transfer time from the perilune to near the perigee & \(\Delta t_{1}\leq\xi_{1}\) \\ \(||\Delta V_{0}||\) & The modulus of \(\Delta V_{0}\) & \(||\Delta V_{0}||\leq\xi_{2}\) \\ \(||\Delta V_{1}||\) & The modulus of \(\Delta V_{1}\) & \(||\Delta V_{1}||\leq\xi_{3}\) \\ \(||\Delta V||\) & The modulus of impulse applied in HEO & \(||\Delta V||\leq\xi_{4}\) \\ \(\Delta t\) & The period of HEO & HEO is resonant with the Moon \\ \(h_{p-moon}\) & The height of perilune & \(h_{p-moon}\geq\widetilde{h}_{1}\) \\ \(h_{p-earth}\) & The height of perigee & \(h_{p-earth}\geq\widetilde{h}_{2}\) \\ \(||\delta\mathbf{r}||\) & The distance of the flyby & \(\zeta_{5}\leq||\delta\mathbf{r}||\leq\xi_{6}\) \\ \(||\delta\mathbf{v}||\) & The magnitude of the relative flyby velocity & \(||\delta\mathbf{v}||\leq\xi_{7}\) \\ \hline \end{tabular}
\end{table}
Table 3: Requirements of the flyby mission.  
direction on the equatorial plane remains constant. Due to the \(J_{2}\) perturbation, the mean rate of change of the right ascending node is as follows:  
\[\dot{\overline{\Omega}}=-\frac{3 nJ_{2}R_{e}^{2}}{2a^{2}(1-e^{2})^{2}}\cos i \tag{6}\]  
where \(n=\sqrt{\mu_{e}/a^{3}}\), \(a\) is the semi-major axis, \(e\) is the eccentricity, and \(i\) is the inclination. \(J_{2}=0.001082\). The rate of change of the ascending node of SSO is the same as the Earth's mean motion around the Sun, which is as follows:  
\[\dot{\overline{\Omega}}=\frac{360^{\circ}}{365.24\text{days}}=1.991\times 10^{-7} \text{ rad}/\text{s} \tag{7}\]  
Substituting Equation (7) into Equation (6) yields the following:  
\[1.991\times 10^{-7}\text{ rad}/\text{s}+\frac{3 nJ_{2}R_{e}^{2}}{2a^{2}(1-e^{2} )^{2}}\cos i=0 \tag{8}\]  
Because of the computational error, this paper defines the orbit satisfying the following equation as SSO:  
\[|1.991\times 10^{-7}\text{ rad}/\text{s}+\frac{3 nJ_{2}R_{e}^{2}}{2a^{2}(1-e^{2} )^{2}}\cos i|\leq 0.001 \tag{9}\]  
Selecting objects from the Space Track Database according to Equation (9), it can be seen that the region with perigee altitude of [600, 900] km, apogee altitude of [650, 1050] km, and orbital inclination of [96.3, 99.3]\({}^{\circ}\) is the most densely distributed region of Chinese SSO space debris. The space debris in this region have mainly come from the Fengyun satellites and Changzheng rockets.  
Reference [49] proposes that states and international intergovernmental organizations should remove spacecraft and launch vehicle orbital stages at the end of the mission life, and also encourage the development and use of relevant technologies for the measurement, monitoring, and characterization of the orbital and physical properties of space debris. All countries should uphold the concept of building a community of human destiny, share the responsibility of maintaining outer space security, and address threats to all aspects of outer space security.  
For the purpose of maintaining the long-term sustainable peaceful use of outer space, and for better measurement and detection of space debris, this paper offers a solution to obtain detailed information on our space debris so that active removal can be better implemented.