Earth escape from a sun-earth halo orbit using unstable manifold and lunar swingbys

This paper investigates the Earth escape for spacecraft in a Sun-Earth halo orbit. The escape trajectory consists of first ejecting to the unstable manifold associated with the halo orbit, then coasting along the manifold until encountering the Moon, and finally performing lunar-gravity-assisted escape. The first intersection of the manifold tube and Moon's orbit results in four intersection points. These four manifold-guided encounters have different relative velocities (v∞) to the Moon; therefore, the corresponding lunar swingbys can result in different levels of characteristic energy (C₃) with respect to the Earth. To further exploit these manifold-guided lunar encounters, subsequent swingbys utilizing solar perturbation are considered. A graphical method is introduced to reveal the theoretical upper limits of the C₃ achieved by double and multiple swingbys. The numerically solved Sun-perturbed Moon-to-Moon transfers indicate that a second lunar swingby can efficiently increase C₃. Compared to the direct low-energy escape along the manifold, applying a portion of the lunar swingbys before escape is shown to be more advantageous for deep-space mission design.