A trans-lunar injection (TLI) is a propulsive maneuver used to send a spacecraft toward the Moon. 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. The mission phase following TLI – while the spacecraft is flying passively towards the moon under its own momentum and influenced by terrestrial and lunar gravity – is called translunar coast. 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.
Free return
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 and cost-effectiveness 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. Artemis I and II were both also free return missions.
Modeling
Patched conics TLI targeting and lunar transfers are a specific application of the n body problem, which may be approximated in various ways. The simplest way to explore lunar transfer trajectories is by the method of patched conics. The spacecraft is assumed to accelerate only under classical 2 body dynamics, being dominated by the Earth until it reaches the Moon's sphere of influence. Motion in a patched-conic system is deterministic and simple to calculate, lending itself for rough mission design and "back of the envelope" studies.
Restricted circular three body (RC3B) More realistically, however, the spacecraft is subject to gravitational forces from many bodies. Gravitation from Earth and Moon dominate the spacecraft's acceleration, and since the spacecraft's own mass is negligible in comparison, the spacecraft's trajectory may be better approximated as a restricted three-body problem. This model is a closer approximation but lacks an analytic solution, requiring numerical integration.
High fidelity numerical propagation and perturbation models More detailed simulation involves modeling the Moon's true orbital motion; gravitation from other astronomical bodies; the non-uniformity of the Earth's and Moon's gravity; including solar radiation pressure; and so on. Propagating spacecraft motion in such a model is numerically intensive, but necessary for true mission accuracy.
See Also Runge–Kutta–Fehlberg method Dormand–Prince method
History
… excerpt ends here. Continue reading the full article.
