Free-return trajectory

[1] Many free-return trajectories are designed to intersect the atmosphere; however, periodic versions exist which pass the moon and Earth at constant periapsis, which have been proposed for cyclers.

[2] He studied cases in which the trajectory at some point crosses at a right angle the line going through the center of the Earth and the center of the Moon, and also cases in which the trajectory crosses at a right angle the plane containing that line and perpendicular to the plane of the Moon's orbit.

After returning to low altitude above the Earth (the perigee radius is a parameter, typically 6555 km) the spacecraft would start over on the same trajectory.

While in a true free-return trajectory no propulsion is applied, in practice there may be small mid-course corrections or other maneuvers.

Since all went well, these Apollo missions did not have to take advantage of the free return and inserted into orbit upon arrival at the Moon.

Due to the lunar landing site restrictions that resulted from constraining the launch to a free return that flew by the Moon, subsequent Apollo missions, starting with Apollo 12 and including the ill-fated Apollo 13, used a hybrid trajectory that launched to a highly elliptical Earth orbit that fell short of the Moon with effectively a free return to the atmospheric entry corridor.

[7] Apollo 13 was the only Apollo mission to actually turn around the Moon in a free-return trajectory (however, two hours after perilune, propulsion was applied to speed the return to Earth by 10 hours and move the landing spot from the Indian Ocean to the Pacific Ocean).

Zubrin advocates a slightly faster transfer, that takes only 180 days to Mars, but 2 years back to Earth in case of an abort.

There also exists the option of two- or three-year free-returns that do not rely on the gravity of Mars, but are simply transfer orbits with periods of 2 or 1.5 years, respectively.

[11] It cites a delta-v requirement of approximately 4 km/s for the trans-Mars injection, but does not mention the duration of a free return to Earth.