Minimal Delta-V-Based Orbital Rendezvous for Approaching a Non-cooperative Target on GEO

This paper addresses multi-impulse optimal trajectory design for approaching Geostationary Earth Orbit (GEO) targets. The study focuses on a servicing spacecraft initiating its mission at a predefined distance along the geostationary orbit, aiming to establish a 2:1 elliptical relative orbit for close inspection. The optimization problem includes dynamic constraints during trajectory transfer, terminal constraints ensuring circling orbit attainment, and mission duration constraints. Key variables are transfer duration, impulse count, timing, and entry point. The objective is minimizing total velocity increment. Uncertain terminal states, constrained by the circling orbit, add complexity. Linear state transition matrices from orbital dynamics construct an optimization model and solution approach. The study explores optimization criteria variations with different variables for GEO missions. Optimal entry points for various impulses are identified. This work offers guidance for GEO orbit approaching missions and inspires space maneuver tasks in diverse domains.