Low-Cost Rendezvous and Phasing With the Lunar Gateway Leveraging Quasi-Periodic Tori

In recent years, the cislunar environment has emerged as a vital base for space research and a stepping stone to destinations like Mars. The development of the Lunar Gateway is a result of this trend. In fact, it will support experiments, serve as a refueling hub, and facilitate the construction of a human outpost on the Moon. For these reasons, cost-effective transport to and from the station’s orbit will be pivotal in maximizing its potential. Additionally, constraints on launch dates are currently a driving factor during the mission design, leading to suboptimal solutions during spacecraft development. The current state of the art exploits periodic orbits to identify efficient Earth-to-Moon transfer trajectories. This work leverages the manifold theory to extend that concept to quasi-periodic orbits in the Three-Body Problem and exploits their properties to retrieve a more efficient path to the station. In fact, manifolds are natural trajectories that do not require active propellant consumption from the spacecraft. The objective is to optimize the approach to the Lunar Gateway by balancing fuel consumption and operational flexibility. This solution reduces dependency on fixed launch dates and expands the range of feasible mission profiles while minimizing overall transfer propellant costs. Numerical methods are used to generate quasi-periodic tori around the initial and target orbits, and interpolating functions are retrieved for each torus. These analytical curves can be later exploited to identify the intersections between tori and produce feasible transfer trajectories to the Lunar Gateway, reducing propellant needs. These transfers also serve as starting conditions for an optimization algorithm that models the finite-burn maneuvers. The outcome of this study is the identification of optimized trajectories that outperform current baseline solutions, offering advantages in terms of reduced fuel consumption and enhanced scheduling flexibility. This investigation contributes to the sustainability and cost-effectiveness of lunar exploration, paving the way for human presence on the Moon and future missions to Mars and beyond.