A free-return trajectory is a path designed so that the spacecraft's own motion and the gravity of the Earth and Moon carry it around the far side of the Moon and back toward Earth with no additional engine burn.
- The outbound leg is the coast established earlier: the spacecraft climbs away from Earth, and Earth's gravity steadily removes speed.
- Near the Moon, the Moon's gravity bends the path sharply around its far side — the same capture geometry, but the bend is not quite tight enough to hold the spacecraft.
- Because the path is a closed loop through the combined gravity field, the spacecraft swings back out and falls toward Earth on a return leg.
- Seen from above, the combined Earth-Moon path resembles a figure eight: out from Earth, around the Moon, and back.
Key point: the return leg is not powered. It is the natural continuation of the same trajectory, so no propellant is spent on the way home.