A trans-Earth injection (TEI) is a propulsion maneuver used to set a spacecraft on a trajectory which will intersect the Earth.
The maneuver is performed by a rocket engine. The spacecraft is usually in a parking orbit around the Moon at the time of TEI, in which case the burn is timed so that its midpoint is opposite the Earth's location upon arrival. Unmanned space probes have also performed this maneuver from the Moon starting with Luna 16's direct ascent traverse from the lunar surface in 1970. In 2004, from outside the Earth-Moon system, the Stardust probe comet dust return mission performed TEI after visiting Comet Wild 2.
On the Apollo missions, it was performed by the restartable Service Propulsion System (SPS) engine on the Service Module. An Apollo TEI burn lasted approximately 203.7 seconds, providing a posigrade velocity increase of 1,076 m/s (3,531 ft/s). It was first performed by the Apollo 8 mission on December 25, 1968.