Free-return trajectory

In orbital mechanics, a free-return trajectory is a trajectory of a spacecraft traveling away from a primary body (for example, the Earth) where gravity due to a secondary body (for example, the Moon) causes the spacecraft to return to the primary body without propulsion (hence the term free). 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. The first spacecraft to use a free-return trajectory was the Soviet Luna 3 mission in October 1959. It used the Moon's gravity to send it back towards the Earth so that the photographs it had taken of the far side of the Moon could be downloaded by radio. Symmetrical free-return trajectories were studied by Arthur Schwaniger of NASA in 1963 with reference to the Earth–Moon system. 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. In both scenarios we can distinguish between: A circumlunar free-return trajectory around the Moon. The spacecraft passes behind the Moon. It moves there in a direction opposite to that of the Moon, or at least slower than the Moon in the same direction. If the craft's orbit begins in a normal (west to east) direction near Earth, then it makes a figure 8 around the Earth and Moon when plotted in a coordinate system that rotates as the Moon goes around the Earth. A cislunar free-return trajectory. The spacecraft goes beyond the orbit of the Moon, returns to inside the Moon's orbit, moves in front of the Moon while being diverted by the Moon's gravity to a path away from the Earth to beyond the orbit of the Moon again, and is drawn back to Earth by Earth's gravity.