A study of collision orbits with the Moon by the method of surface of section

Non-periodic orbits of a natural satellite of the Moon are studied, for the case of the circular three-body problem with the method of surface of section. According to this method, each orbit is represented by a point, in the plane x0\.x, which corresponds to y = 0 and \.y > 0 and a fixed energy. Conclusions are deduced from the shape of this curve for probable collisions of the satellite on the lunar surface. This method of surface of section can be used for the study of orbits which collide with the Moon's surface after a large number of revolutions around the Moon and their study would be difficult to explore with other methods.