A Sun–Earth Stable Manifold-Based Method for Planar Two-Impulse Earth–Moon Transfer Design

A Sun–Earth stable manifold-based method for designing planar two-impulse Earth–Moon transfer trajectories is proposed in this paper. In this method, stable manifolds associated with Sun–Earth L₁/L₂ Lyapunov orbits provide initial guess trajectories for the planar two-impulse Earth–Moon trajectories. The perilune map of the initial guess trajectories is then applied to estimate the Moon’s initial phase angle for the two-impulse Earth–Moon trajectory in the Sun–Earth rotating frame. Then the accurate value of the Moon’s initial phase angle can be calculated to achieve a two-impulse Earth–Moon transfer trajectory. Furthermore, a global set of solutions for two-impulse Earth–Moon transfers are calculated by exploring the Jacobi constant of Lyapunov orbits around the Sun–Earth L₁/L₂. Numerical results indicate that stable manifolds of Sun–Earth L₁/L₂ Lyapunov orbits with larger Jacobi constants can be more easily applied to achieve two-impulse Earth–Moon transfers with lower energy.