Planar fly-by trajectories to Moon in the restricted three-body problem

Planar fly-by trajectories from Earth to Moon are studied in the framework of restricted three-body problem (R3BP). A number of trajectories with initial conditions (x,y,ẋ,ẏ) of the form (x0,0,0,ẏ0) and (-μ,y0,ẋ0,0) close to Earth are propagated for 1000 days. The distribution of the initial conditions which will generate feasible fly-bys to Moon in the phase space are plotted in Jacobi constant, C verses initial x or y plots with color codes on time of flight. It is observed that the flyby trajectories with similar flight duration appear in clusters and show some distinctive patterns. For example for the initial condition of first type the fly-by trajectories with flight duration of about 14 to 16 days appear as a curve in the phase space. While for the second type of initial conditions the trajectories with flight duration ⩽5 days and 5–15 days appear as a band on the phase space. Poincaré surface of section technique is used to identify the existence of periodic and quasi-periodic orbits in other regions of the phase space.