Credit: NASA — Like a whirling dervish, the path of Apollo 8 about the Earth and Moon spanned seven days and well over half a million miles. Ten lunar revolutions, at distances as close as 60 miles, were made. Translunar trip takes about 20 percent longer than the return trip because going out one has to overcome the stronger gravity of the Earth but can capitalize on it coming back. Not shown is the solar orbit trajectory taken by the burned S-IVB stage.
A trans-lunar injection (TLI) is a propulsive maneuver used to set a spacecraft on a trajectory that will cause it to arrive at the Moon. Technically, a TLI is not one of the orbit types, rather a maneuver.
Typical lunar transfer trajectories approximate Hohmann transfers, although low-energy transfers have also been used in some cases, as with the Hiten probe. For short duration missions without significant perturbations from sources outside the Earth-Moon system, a fast Hohmann transfer is typically more practical.
A spacecraft performs TLI to begin a lunar transfer from a low circular parking orbit around Earth. The large TLI burn, usually performed by a chemical rocket engine, increases the spacecraft’s velocity, changing its orbit from a circular low Earth orbit to a highly eccentric orbit. As the spacecraft begins coasting on the lunar transfer arc, its trajectory approximates an elliptical orbit about the Earth with an apogee near to the radius of the Moon’s orbit. The TLI burn is sized and timed to precisely target the Moon as it revolves around the Earth. The burn is timed so that the spacecraft nears apogee as the Moon approaches. Finally, the spacecraft enters the Moon’s sphere of influence, making a hyperbolic lunar swingby.
In some cases it is possible to design a TLI to target a free return trajectory, so that the spacecraft will loop around behind the Moon and return to Earth without need for further propulsive maneuvers.
Such free return trajectories add a margin of safety to human spaceflight missions, since the spacecraft will return to Earth “for free” after the initial TLI burn. The Apollos 8, 10 and 11 began on a free return trajectory, while the later missions used a functionally similar hybrid trajectory, in which a midway course correction is required to reach the moon.
