Lunar Flight Study Series: Volume 5. Trajectories in the Earth-Moon Space with Symmetrical Free Return Properties

An extensive investigation has been made of the characteristics of so-called
"free return" trajectories. For the purposes of the study., these trajectories are
defined as having certain symmetric properties which afford flight to the vicinity of the
moon and return to earth without need for propulsion after the initial boost phase. The
restricted three-body model for the earth-moon-probe system is used throughout.
Two kinds of free return trajectories are shown to -exist and are studied. Of
particular interest is the fact that for one kind of free return path, the largest inclination
which can be achieved between the flight plane at periselenum and the plane of the
moon's orbit about earth is about 10. 8 degrees while for the other kind of path the
largest possible inclination is dependent on ·the radius at periselenum. In this case the
inclination is limited to about 14 degrees or less for periselenum radius of 1938 km,
but may be as great as 90 degrees with periselenum radius of 21150 km.
Trajectories are also demonstrated which pass in front of the moon. These
exhibit inclination behavior very much like that given by trajectories which go behind
the moon. The injection velocity for these trajectories also changes only slightly from
the circumlunar trajectories (less than 2 m/s for periselenum radius of 1938 km).
However, the position of injection is changed considerably and the flight time may be
increased by as much as five times that for circumlunar flight.