Phasing Delta-V for transfers from Sun–Earth halo orbits to the Moon

Inspired by successful extended missions such as the ISEE-3, an investigation for the extended mission that involves a lunar encounter following a Sun-Earth halo orbit mission is considered valuable. Most previous studies present the orbit-to-orbit transfers where the lunar phase is not considered. Intended for extended missions, the present work aims to solve for the minimum phasing ∆V for various initial lunar phases. Due to the solution multiplicity of the two-point boundary value problem, the general constrained optimization algorithm that does not identify multiple feasible solutions is shown to miss minima. A two-step differential corrector with a two-body Lambert solver is developed for identifying multiple solutions. The minimum ∆V associated with the short-way and long-way approaches can be recovered. It is acquired that the required ∆V to cover all initial lunar phases is around 45 m/s for the halo orbit with out-of-plane amplitude A_z greater than 3.5×10⁵ km, and 14 m/s for a small halo orbit with A_z=1×10⁵ km. In addition, the paper discusses the phasing planning based on the ∆V result and the shift of lunar phase with halo orbit revolution.