The problem of finding optimal trajectories is essential for modern space mission design. When considering multibody
gravitational dynamics and exploiting both low-thrust and high-thrust and alternative forms of propulsion such
as solar sailing, sets of good initial guesses are fundamental for the convergence to local or global optimal solutions,
using both direct or indirect methods available to solve the optimal control problem. This paper deals with obtaining
preliminary trajectories that are designed to be good initial guesses as input to search optimal low-energy short-time
Earth-Moon transfers with ballistic capture. A more realistic modelling is introduced, in which the restricted four-body
system Sun-Earth-Moon-Spacecraft is decoupled in two patched planar Circular Restricted Three-Body Problems,
taking into account the inclination of the orbital plane of the Moon with respect to the ecliptic. We present a heuristic
strategy based on the hyperbolic invariant manifolds of the Lyapunov orbits around the Lagrangian points of the Earth-
Moon system to obtain ballistic capture orbits around the Moon that fulfill specific mission requirements. Moreover,
quasi-periodic orbits of the Sun-Earth system are exploited using a genetic algorithm to find optimal solutions with
respect to total Dv, time of flight and altitude at departure. Finally, the procedure is illustrated and the full transfer
trajectories assessed in view of relevant properties. The proposed methodology provides sets of low-cost and shorttime
initial guesses to serve as inputs to compute fully optimized three-dimensional solutions considering different
propulsion technologies, such as low, high, and hybrid thrust, and/or using more realistic models
