Satellite Initial Positioning Optimization for Passive Multi-Debris Approaches

The increasing population of space debris poses significant risks to space operations. A major challenge in debris removal is the high propellant cost associated with reaching the debris. This paper presents a methodology to select a satellite's initial orbital conditions, enabling passive approaches to multiple debris objects by leveraging Earth's J2-induced orbital precession. The methodology begins with an evaluation of active debris removal techniques, analyzing their requirements for relative velocity, distance, and timing for successful debris removal. These parameters are then integrated into the optimization framework. Statistical clustering analysis of tracked debris data identifies high-density regions, guiding the algorithm's initialization and focusing on a specific orbital regime. The approach combines analytical methods for efficient relative distance calculations with numerical orbit propagation considering J2 perturbations. A genetic algorithm explores the solution space thoroughly, converging after 150 generations to find an optimal debris approach sequence. The methodology has been demonstrated using an in-space laser system; results show that by optimizing the satellite's initial conditions, it can passively approach 18 debris objects within a 30-day period from a catalog of 115 objects. This represents 30% of the maximum possible debris approaches achievable within the time horizon, considering a 12-hour interval between approach opportunities because of power constraints. Monte Carlo simulations incor-porating positional uncertainties demonstrate the robustness of the solution, with average distances of close approach ranging from approximately 127 km to 275 km, and a mean standard deviation of 30.4 km. This methodology offers a cost-effective strategy for debris removal, as demonstrated in our case study.