Trans-lunar injection

[1] For short duration missions without significant perturbations from sources outside the Earth-Moon system, a fast Hohmann transfer is typically more practical.

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.

The first space probe to attempt TLI was the Soviet Union's Luna 1 on January 2, 1959 which was designed to impact the Moon.

[11] The United States launched its first lunar impactor attempt, Ranger 3, on January 26, 1962, which failed to reach the Moon.

[14] The Apollo 8 TLI was spectacularly observed from the Hawaiian Islands in the pre-dawn sky south of Waikiki, photographed and reported in the papers the next day.

[16] It was described as resembling car headlights coming over a hill in fog, with the spacecraft appearing as a bright comet with a greenish tinge.

[17][13]: 179 The 1994 US Clementine spacecraft, designed to showcase lightweight technologies, used a 3 week long TLI with two intermediate Earth flybys before entering a lunar orbit.

In 2011 the NASA GRAIL satellites used a low delta-v route to the Moon, passing by the Sun-Earth L1 point, and taking over 3 months.