# Multiple SSO Space Debris Flyby Trajectory Design Based on Cislunar Orbit
###### Abstract  
This paper investigates the trajectory design problem in the scenario of a multiple Sun-synchronous Orbit (SSO) space debris flyby mission from a DRO space station. At first, the characteristics of non-planar transfer from DRO to SSO in the Earth-Moon system are analyzed. The methods of large-scale ergodicity and pruning are utilized to investigate single-impulse and two-impulse DRO-Earth transfers. Using a powered lunar flyby, the two-impulse DRO-Earth transfer is able to fly by SSO debris while satisfying the requirements of the mission. After the local optimization, the optimal result of two-impulse DRO-Earth transfer and flyby is obtained. A multi-objective evolutionary algorithm is used to design the Pareto-optimal trajectories of multiple flybys. The semi-analytical optimization method is developed to provide the estimations of the transfer parameters in order to reduce the computations caused by the evolutionary algorithm. Simulations show that transferring from the 3:2 resonant DRO to a near-coplanar flyby of a SSO target debris using a powered lunar gravity assist needs a 0.47 km/s velocity increment. The mission's total velocity increment is 1.39 km/s, and the total transfer time is 2.23 years. distant retrograde orbit (DRO); circular restricted three-body problem; Sun-synchronous orbit (SSO) space debris; lunar gravity assist +
Footnote †: journal: _Journal of the Royal Society Interface_  
Space debris has seriously affected the safety of space missions. Between the years 2000 and 2013, only 12% of spacecraft performed reentry or deorbit maneuvers at their end-of-life, and only 10% of spacecraft successfully performed 25-year deorbit maneuvers [18]. NASA research shows that even if 90% of constellations successfully perform 25-year deorbit maneuvers, there will still be 290% more space debris in the next 200 years than if there were no giant constellations [19]. Even if no new man-made objects were put in space, the space debris in the LEO region would still grow exponentially [20]. Active removal is a direct approach to reduce the amount of space debris. Space robotic arm capture [21] and flying net capture [22] have been the subjects of long-term research in various space agencies. The above \"one-to-one\" methods need complex techniques for grappling an uncooperative object, which is costly and inefficient. Apart from the deorbit removal methods for spacecraft at the end of mission life, i.e., drag sail [23], inflate-sail [24], and electrodynamic tether [25], contactless active removal methods such as Coulomb thrusting [26], laser beam [27], artificial atmosphere [28], and expanding foam [29] have been proposed in the application of space debris mitigation. Coulomb thrusting removal is applicable only when the Debye shielding is weak [30; 31]. Laser beam removal can only remove very small debris [32; 33]. The method of artificial atmosphere is a technique in which the spacecraft releases an artificial atmosphere in a region near the path of the space debris to decelerate the debris and accelerate natural orbital decay [28; 34; 35]. The approach of expanding foam is similar to the artificial atmosphere method, except that the material released by the spacecraft is expanding foam. The artificial atmosphere and expanding foam removal methods are suitable for removing LEO debris. Moreover, the expanding foam removal method can deorbit large LEO debris (1.4-3.5 tons per year) [29; 36]. Both of these two methods require a spacecraft to arrive in the vicinity of the debris and release the deorbit material. Regarding the analysis of space debris removal mission, one author [37] designs a space mission in which, when the spacecraft rendezvous with a piece of debris, a deorbit device is attached to the object by a robotic arm and the device is activated, and then the spacecraft travels to the next piece of debris. However, the results show that this removal mission would take more than 30 km/s of total impulse to deorbit 35 large objects in 7 years.