Editing Trans-lunar injection

{{short description|Propulsive maneuver used to arrive at the Moon}}
[[File:Tli.svg|thumb|300px|right|Lunar transfer, perspective view. TLI occurs at the red dot near Earth.]]
A '''trans-lunar injection''' ('''TLI''') is a [[Orbital maneuver|propulsive maneuver]], which is used to send a [[spacecraft]] to the [[Moon]]. Typical lunar transfer trajectories approximate [[Hohmann transfer orbit|Hohmann transfer]]s, although [[low-energy transfer]]s have also been used in some cases, as with the [[Hiten (spacecraft)|Hiten]] probe.<ref>{{cite web |title=Hiten |url=https://nssdc.gsfc.nasa.gov/nmc/spacecraft/display.action?id=1990-007A |publisher=[[NASA]]}}</ref>  For short duration missions without significant [[Perturbation theory|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 [[Orbital maneuver|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 [[Elliptical orbit|eccentric orbit]].  As the spacecraft begins coasting on the lunar transfer arc, its trajectory approximates an elliptical orbit about the Earth with an [[apsis|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 (astrodynamics)|sphere of influence]], making a hyperbolic lunar swingby.

== Free return ==
{{main|Free return trajectory}}

[[File:circumlunar-free-return-trajectory.png|thumb|Sketch of a circumlunar free return trajectory (not to scale)]]
In some cases it is possible to design a TLI to target a [[free return trajectory]], so that the spacecraft will [[Loop quantum gravity|loop]] around behind the Moon and return to Earth without need for further propulsive maneuvers.<ref>{{cite book |last=Schwaninger |first=Arthur J. |url=https://ntrs.nasa.gov/api/citations/19630007117/downloads/19630007117.pdf |title=Trajectories in the Earth-Moon Space with Symmetrical Free Return Properties |publisher=[[NASA]] / [[Marshall Space Flight Center]] |year=1963 |series=Technical Note D-1833 |location=Huntsville, Alabama}}</ref>

Such free return trajectories add a margin of safety 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,<ref>{{Cite web |last=Mansfield |first=Cheryl L. |date=May 18, 2017 |title=Apollo 10 |url=http://www.nasa.gov/mission_pages/apollo/missions/apollo10.html |website=NASA}}</ref> while the later missions used a functionally similar hybrid trajectory, in which a midway course correction is required to reach the Moon.<ref>{{Cite web |title=APOLLO 12 |url=https://history.nasa.gov/SP-4029/Apollo_12a_Summary.htm |website=history.nasa.gov}}</ref><ref>{{cite report |url=http://www.esa.int/esapub/bulletin/bullet103/biesbroek103.pdf |title=Ways to the Moon |page=93}}</ref><ref>{{Cite web |title=Launch Windows Essay |url=https://history.nasa.gov/afj/launchwindow/lw1.html |website=history.nasa.gov}}</ref>

== Modeling ==
[[File:Constellation trans-lunar injection.jpg|thumb |Artist's concept of NASA's [[Constellation program|Constellation]] stack performing the trans-lunar injection burn]]

=== Patched conics ===
TLI targeting and lunar transfers are a specific application of the [[N-body problem|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|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 (astrodynamics)|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 calculation|back of the envelope]]" studies.

=== Restricted circular three body (RC3B) ===
More realistically, however, the spacecraft is subject to [[Gravitational force|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 [[Euler's three-body problem|restricted three-body problem]].  This model is a closer approximation but lacks an analytic solution,<ref>[[Henri Poincaré]], ''Les Méthodes Nouvelles de Mécanique Céleste'', Paris, Gauthier-Villars et fils, 1892-99.</ref> requiring numerical calculation.<ref>[[Victor Szebehely]], ''Theory of Orbits, The Restricted Problem of Three Bodies'', Yale University, Academic Press, 1967.</ref>

=== Further accuracy ===
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 [[Gravitational field|gravity]]; including [[Solar wind|solar radiation pressure]]; and so on.  Propagating spacecraft motion in such a model is numerically intensive, but necessary for true mission accuracy.

== History ==
[[File:Animation of GRAIL-A trajectory.gif |thumb |right |Animation of GRAIL-A{{'s}} trajectory<br />{{legend2|magenta|[[GRAIL|GRAIL-A]]}}{{·}}{{legend2|Lime|[[Moon]]}}{{·}}{{legend2|RoyalBlue|[[Earth]]}}]]
[[File:Animation of Chandrayaan-2 around Earth - Geocentric phase.gif|thumb|right|Animation of Chandrayaan-2{{'s}} trajectory<br />{{legend2|RoyalBlue|Earth}}{{·}}{{legend2|Lime|Moon}}{{·}}{{legend2|Magenta|[[Chandrayaan-2]]}}]]
[[File:Animation of Lunar Reconnaissance Orbiter trajectory around Earth.gif|thumb|right|Animation of LRO trajectory<br />{{legend2|magenta|[[Lunar Reconnaissance Orbiter]]}}{{·}}{{legend2|RoyalBlue|Earth}}{{·}}{{legend2|DarkGoldenrod|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.<ref>{{cite web|url=https://solarsystem.nasa.gov/missions/luna-01/in-depth/|title=Luna 01|publisher=[[NASA]]|access-date=2019-06-10|archive-date=2020-09-05|archive-url=https://web.archive.org/web/20200905220216/https://solarsystem.nasa.gov/missions/luna-01/in-depth/|url-status=dead}}</ref> [[Luna 2]] performed the same maneuver more accurately on September 12, 1959 and crashed into the Moon two days later.<ref>{{Cite web|url=https://nssdc.gsfc.nasa.gov/nmc/spacecraft/display.action?id=1959-014A|title=NASA - NSSDCA - Spacecraft - Details|website=nssdc.gsfc.nasa.gov}}</ref> The Soviets repeated this success with 22 more [[Luna programme|Luna]] missions and 5 [[Zond program|Zond]] missions travelling to the Moon between 1959 and 1976.<ref>{{Cite web|url=https://nssdc.gsfc.nasa.gov/planetary/lunar/lunarussr.html|title=Soviet Missions to the Moon|website=nssdc.gsfc.nasa.gov}}</ref>

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.<ref>{{cite web|url=https://solarsystem.nasa.gov/missions/ranger-4/in-depth/|title=Ranger 4|publisher=[[NASA]]}}</ref> Another 27 US missions to the Moon were launched from 1962 to 1973, including five successful [[Surveyor program|Surveyor]] soft landers, five [[Lunar Orbiter program|Lunar Orbiter]] surveillance probes,<ref name=BeyondEarth>{{cite web|url=https://www.nasa.gov/sites/default/files/atoms/files/beyond-earth-tagged.pdf|title=Beyond Earth|publisher=[[NASA]]}}</ref>{{rp|166}} and nine [[Apollo program|Apollo]] missions, which landed the first humans on the Moon.

For the Apollo lunar missions, TLI was performed by the restartable [[J-2 (rocket engine)|J-2]] engine in the [[S-IVB]] third stage of the [[Saturn V]] rocket.  This particular TLI [[combustion|burn]] lasted approximately 350 seconds, providing 3.05 to 3.25&nbsp;km/s (10,000 to 10,600&nbsp;ft/s) of [[Delta-v|change in velocity]], at which point the spacecraft was traveling at approximately 10.4&nbsp;km/s (34150&nbsp;ft/s) relative to the Earth.<ref>{{cite web |url=https://history.nasa.gov/SP-4029/Apollo_18-24_Translunar_Injection.htm |title=Apollo By the Numbers |publisher=[[NASA]]|archive-url=https://web.archive.org/web/20041118103812/https://history.nasa.gov/SP-4029/Apollo_18-24_Translunar_Injection.htm|archive-date=2004-11-18}}</ref> 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.<ref>{{cite web |url=https://newspaperarchive.com/independent-star-news/1968-12-22 |title=Independent Star News, Sunday, December 22, 1968 |date=22 December 1968 }} "The TLI firing was begun at PST while the craft was over Hawaii and it was reported there that the burn was visible from the ground."</ref>  In 1969, the Apollo 10 pre-dawn TLI was visible from [[Cloncurry]], [[Australia]].<ref name=ShadowOfTheMoon372>{{cite book |title=[[In the Shadow of the Moon (book)|In the Shadow of the Moon]] |last=French |first=Francis |author2=Colin Burgess |year=2007 |publisher=[[University of Nebraska Press]] |isbn=978-0-8032-1128-5 |page=[https://archive.org/details/inshadowofmoonch0000fren/page/372 372] }}</ref> 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.<ref name=ShadowOfTheMoon372/>

In 1990 [[Japan]] launched its first lunar mission, using the [[Hiten (spacecraft)|Hiten]] [[satellite]] to fly by the Moon and place the Hagoromo [[Microsatellite (spaceflight)|microsatellite]] in a lunar orbit. Following that, it explored a novel low [[delta-v]] TLI method with a 6-month transfer time (compared to 3 days for Apollo).<ref name="esa">{{cite journal|url=https://www.researchgate.net/publication/245307635|title=Technical Requirements for Lunar Structures |journal=Journal of Aerospace Engineering |author1=Alexander M. Jablonski |author2=Kelly A. Ogden|date=April 2008}}</ref><ref name=BeyondEarth/>{{rp|179}}

The 1994 US ''[[Clementine (spacecraft)|Clementine]]'' spacecraft, designed to showcase lightweight technologies, used a 3 week long TLI with two intermediate Earth flybys before entering a lunar orbit.<ref name="esa"/><ref name=BeyondEarth/>{{rp|185}}

In 1997 [[Asiasat-3]] became the first commercial satellite to reach the Moon's sphere of influence when, after a launch failure, it swung by the Moon twice as a low delta-v way to reach its desired geostationary orbit. It passed within 6200&nbsp;km of the Moon's surface.<ref name="esa"/><ref name=BeyondEarth/>{{rp|203}}

The 2003 ESA [[SMART-1]] technology demonstrator satellite became the first European satellite to orbit the Moon. After being launched into a [[geostationary transfer orbit]] (GTO), it used solar powered ion engines for propulsion. As a result of its extremely low delta-v TLI maneuver, the spacecraft took over 13 months to reach a lunar orbit and 17 months to reach its desired orbit.<ref name=BeyondEarth/>{{rp|229}}

China launched its first Moon mission in 2007, placing the [[Chang'e 1]] spacecraft in a lunar orbit. It used multiple burns to slowly raise its apogee to reach the vicinity of the Moon.<ref name=BeyondEarth/>{{rp|257}}

India followed in 2008, launching the [[Chandrayaan-1]] into a GTO and, like the Chinese spacecraft, increasing its apogee over a number of burns.<ref name=BeyondEarth/>{{rp|259}}

The soft lander ''[[Beresheet]]'' from the [[Israel Aerospace Industries]], used this maneuver in 2019, but crashed on the Moon.

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.<ref name=BeyondEarth/>{{rp|278}}

== See also ==
* [[Astrodynamics]]
* [[Comparison of super heavy lift launch systems]]
* [[Low energy transfer]]
* [[Trans-Earth injection]]
* [[Trans-Mars injection]]

== References ==
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[[Category:Astrodynamics]]
[[Category:Spacecraft propulsion]]
[[Category:Orbital maneuvers]]
[[Category:Exploration of the Moon]]
[[Category:Apollo program]]

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