Five-impulse low-energy earth-moon transfer using manifolds

The libration points in the Earth-Moon and Sun-Earth systems are widely regarded as cost-effective gateways into interstellar space. The associated manifold tubes have been utilized by numerous researchers in the development of transfers between distinct systems. In this paper, a five-impulse transfer method, based on the manifold, has been proposed for designing the low-energy transfer trajectory for the Earth-Moon system. The Sun-Earth-Moon-Spacecraft four-body problem is decomposed into two circular restricted three-body problems: Sun-Earth-Spacecraft and Earth-Moon-Spacecraft. Moreover, a time parameter is employed to describe the positional relationship between the Sun-Earth and Earth-Moon systems, thereby facilitating their conversion. A phase angle is utilized to characterize the position of the Poincare section, and multiple orbital elements, such as orbital altitude and inclination, are considered in the constraints. To solve the design of multi-constrained transfer trajectories, sequential differential correction algorithms are proposed. The results demonstrate that this method can be used to create compliant low-energy transfer trajectories for various combinations of time parameters and phase angles. Additionally, excellent velocity increments and time-of-flight metrics can be found within a single Sun-Earth-Moon conjunction cycle. In parallel, the method is validated by reconstructing transfer trajectories in a bicircular restricted four-body problem model (BCR4BP) of the Sun-Earth/Moon system.