Achievable halo phasing with short-range trajectories

Short-range halo phasing orbits, which are a type of phasing orbit remaining around the halo orbit, are investigated in the Earth-moon system. The influence of the start and end points on the halo phasing problem is investigated by numerical computation. Under the limitation of the thrust engine, an optimization problem for two-impulse phasing orbits is proposed to achieve the maximum phase change. Numerical computations show that, for the given maximum possible impulsive burn, there exist four types of locally optimal preceding phasing orbits and four types of locally optimal receding phasing orbits. The results of the eight types of optimal phasing orbits are discussed in detail. The “leapfrogging” strategy, composed of several two-impulse phasing arcs, is proposed for phasing missions requiring a large phase difference. Furthermore, halo phasing orbits with continuous thrusts are constructed and investigated. By first using the backstepping method to transform impulsive maneuvers into continuous thrusts and then using the backstepping results as initial guesses, optimal continuous phasing orbits are further constructed.