A trans-lunar injection (TLI) is a propulsive maneuver used to set a spacecraft on a trajectory that will cause it to arrive at the Moon. 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. The burn however didn't go exactly as planned and the spacecraft missed the Moon by more than three times its radius and was sent into a heliocentric orbit. Luna 2 performed the same maneuver more accurately on September 12, 1959 and crashed into the Moon two days later. The Soviets repeated this success with 22 more Luna missions and 5 Zond missions travelling to the Moon between 1959 and 1976. The United States launched its first lunar impactor attempt, Ranger 3, on January 26, 1962, which failed to reach the Moon. This was followed by the first US success, Ranger 4, on April 23, 1962. Another 27 US missions to the Moon were launched from 1962 to 1973, including five successful Surveyor soft landers, five Lunar Orbiter surveillance probes, and nine Apollo missions, which landed the first humans on the Moon. The first human-crewed mission to perform TLI was Apollo 8 on December 21, 1968, making its crew the first humans to leave low earth orbit. For the Apollo lunar missions, TLI was performed by the restartable J-2 engine in the S-IVB third stage of the Saturn V rocket. This particular TLI burn lasted approximately 350 seconds, providing 3.05 to 3.25 km/s (10,000 to 10,600 ft/s) of change in velocity, at which point the spacecraft was traveling at approximately 10.4 km/s (34150 ft/s) relative to the Earth. 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. In 1969, the Apollo 10 pre-dawn TLI was visible from Cloncurry, Australia. 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. In 1990 Japan launched its first lunar mission, using the Hiten satellite to fly by the Moon and place the Hagoromo microsatellite in a lunar orbit.

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Related concepts (13)
NASA
The National Aeronautics and Space Administration (NASA ˈnæsə) is an independent agency of the U.S. federal government responsible for the civil space program, aeronautics research, and space research. Established in 1958, NASA succeeded the National Advisory Committee for Aeronautics (NACA) to give the U.S. space development effort a distinctly civilian orientation, emphasizing peaceful applications in space science.
Apollo Lunar Module
The Apollo Lunar Module (LM ˈlɛm), originally designated the Lunar Excursion Module (LEM), was the lunar lander spacecraft that was flown between lunar orbit and the Moon's surface during the United States' Apollo program. It was the first crewed spacecraft to operate exclusively in the airless vacuum of space, and remains the only crewed vehicle to land anywhere beyond Earth. Structurally and aerodynamically incapable of flight through Earth's atmosphere, the two-stage lunar module was ferried to lunar orbit attached to the Apollo command and service module (CSM), about twice its mass.
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Saturn V is a retired American super heavy-lift launch vehicle developed by NASA under the Apollo program for human exploration of the Moon. The rocket was human-rated, had three stages, and was powered with liquid fuel. It was flown from 1967 to 1973. It was used for nine crewed flights to the Moon, and to launch Skylab, the first American space station. As of 2023, the Saturn V remains the only launch vehicle to carry humans beyond low Earth orbit (LEO).
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