Trajectories in the Earth-Moon System

The Moon is the closest celestial body and the easiest to reach. Traveling to the Moon is relatively easy even with present technology, as it is evidenced by the very fact that half a century ago the Apollo Missions carried 12 people on our satellite. Taking into account the advances in technology in general (non only space technology), today reaching the Moon is much easier and above all much less costly. However, the analysis of the missions in the Earth-Moon system is much more difficult than that of interplanetary missions, since the errors introduced by the restricted two-body problem are much larger and to obtain a good precision the restricted three body problem must be solved. To this a consideration must be added: low thrust propulsion, such as NEP or SEP (and even solar sails) may be expedient to decrease the cost of lunar missions, but imply an increase of the travel time except if very advanced power generators are used. With technologies predictable for the near or medium term future, low-thrust may be used only for slow cargo spacecraft but not to carry human beings to the Moon and back.