# Multiple SSO Space Debris Flyby Trajectory Design Based on Cislunar Orbit
## 5 Phase 2: HEO Based SSO Objects Flyby  
Starting with the two-impulse DRO-Earth transfer orbit shown in Table 10, this section investigates the approach needed to fly by all of the SSO targets shown in Table A1. As shown in Figure 10a, the flyby procedure in this section is as follows: the spacecraft applies an impulse \(\Delta\mathbf{V}\) when it arrives at the apogee, and it flies by a piece of target debris near the perigee. Multiple transfer orbits of the spacecraft are designed to fly by the debris until all of the pieces of space debris in the database have been flown by at least once. The transfer orbit from the perilune to the first flyby shown in Table 10 is the highly elliptical orbit (HEO). The apogee of HEO is near the altitude of the Moon, and its perigee is near the altitude of SSO, which allows the spacecraft in HEO to make better use of the lunar gravity assist and to quickly fly by SSO debris. Moreover, it is expected to maximize the use of the limited propellent to fly by debris. Lowering the altitude of the apogee will reduce the flight time but increase the fuel consumption. Thus, in this paper, the orbit of the multiple-object flyby is designated as HEO. Other types of orbits with lower apogees are left for later studies. In order to make better use of the lunar gravity assist, the orbit of the multiple-object flyby is required to be a lunar-resonant orbit. The types of lunar-resonant orbits with their apogee near the lunar orbital altitude and their perigee near the SSO debris orbital altitude are 8:3, 5:2, 7:3, and 9:4, as shown in Figure 10b. Because the range of the apogee of the 8:3 resonant orbit is closer to the orbital radius of the Moon (which means that it is easier to adjust the orbit using the lunar gravity), in designing the flyby orbits, this paper tends to choose the 8:3 resonance HEO. For the debris flyby mission, this section expects that the fuel consumption is small and the time of flight is short. These two optimization objectives cannot be optimal at the same time. This section uses a multi-objective evolutionary optimization algorithm to design the spacecraft's orbit. By coordinating and compromising between each objective, the optimal solution, i.e., the Pareto-optimal solution, can be found among all the compromise solutions. Figure 10: (a) Mission scenario of Phase 2; (b) ranges of the perigee and the apogee of the lunar-resonant orbits. There exist several multi-objective evolutionary optimization algorithms, such as the non-dominated sorting genetic algorithm (NSGA-II), the strength Pareto evolutionary algorithm (SPEA2), and the multi-objective particle swarm optimization algorithm (MOPSO). Among these algorithms, the NSGA-II has lower computational complexity and running time [50]. This paper chooses the NSGA-II algorithm to solve the Pareto-optimal orbit with minimum impulse and minimum transfer time. The calculation procedure of Phase 2 is shown in Figure 11. At first, the debris whose orbital plane is closest to the spacecraft after one orbital period of the spacecraft is selected as the flyby target. Then, the NSGA-II algorithm is used to design the Pareto-optimal flyby orbit of the spacecraft. In the Pareto frontier, the optimal solution with the minimum impulse is chosen as the flyby orbit because of the fact that the differences in the time of flight of all solutions in the Pareto frontier are not significant. Because the multi-objective evolutionary algorithms have limitations on the diversity and convergence of solutions, the NSGA-II algorithm is not guaranteed to find the Pareto frontier when the parameters of the maneuver are not within the ranges for generating the initial population. One may think of trying to compensate for this shortcoming by expanding the number of populations and the ranges of generating the initial populations, but this approach will lead to a tremendous increase in computation time.