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Trans-lunar injection

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Lunar transfer, perspective view. TLI occurs at the red dot near Earth.

Atrans-lunar injection(TLI) is apropulsive maneuver,which is used to send aspacecraftto theMoon.Typical lunar transfer trajectories approximateHohmann transfers,althoughlow-energy transfershave also been used in some cases, as with theHitenprobe.[1]For short duration missions without significantperturbationsfrom 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 circularparking orbitaroundEarth.The large TLIburn,usually performed by a chemicalrocketengine, increases the spacecraft's velocity, changing its orbit from a circularlow Earth orbitto a highlyeccentric orbit.As the spacecraft begins coasting on the lunar transfer arc, its trajectory approximates an elliptical orbit about the Earth with anapogeenear 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'ssphere of influence,making a hyperbolic lunar swingby.

Free return

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Main article:Free return trajectory
Sketch of a circumlunar free return trajectory (not to scale)

In some cases it is possible to design a TLI to target afree return trajectory,so that the spacecraft willlooparound behind the Moon and return to Earth without need for further propulsive maneuvers.[2]

Such free return trajectories add a margin of safety tohuman spaceflightmissions, 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,[3]while the later missions used a functionally similar hybrid trajectory, in which a midway course correction is required to reach the Moon.[4][5][6]

Modeling

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Artist's concept of NASA'sConstellationstack performing the trans-lunar injection burn

Patched conics

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TLI targeting and lunar transfers are a specific application of then body problem,which may be approximated in various ways. The simplest way to explore lunar transfer trajectories is by the method ofpatched conics.The spacecraft is assumed to accelerate only under classical 2 body dynamics, being dominated by the Earth until it reaches the Moon'ssphere 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)

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More realistically, however, the spacecraft is subject togravitational forcesfrom 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 arestricted three-body problem.This model is a closer approximation but lacks an analytic solution,[7]requiring numerical calculation.[8]

Further accuracy

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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'sgravity;includingsolar radiation pressure;and so on. Propagating spacecraft motion in such a model is numerically intensive, but necessary for true mission accuracy.

History

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Animation of GRAIL-A'strajectory
GRAIL-A·Moon·Earth
Animation of Chandrayaan-2'strajectory
Earth·Moon·Chandrayaan-2
Animation of LRO trajectory
Lunar Reconnaissance Orbiter·Earth·Moon

The first space probe to attempt TLI was theSoviet Union'sLuna 1on 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.[9]Luna 2performed the same maneuver more accurately on September 12, 1959 and crashed into the Moon two days later.[10]The Soviets repeated this success with 22 moreLunamissions and 5Zondmissions travelling to the Moon between 1959 and 1976.[11]

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.[12]Another 27 US missions to the Moon were launched from 1962 to 1973, including five successfulSurveyorsoft landers, fiveLunar Orbitersurveillance probes,[13]: 166 and nineApollomissions, which landed the first humans on the Moon.

For the Apollo lunar missions, TLI was performed by the restartableJ-2engine in theS-IVBthird stage of theSaturn Vrocket. This particular TLIburnlasted approximately 350 seconds, providing 3.05 to 3.25 km/s (10,000 to 10,600 ft/s) ofchange in velocity,at which point the spacecraft was traveling at approximately 10.4 km/s (34150 ft/s) relative to the Earth.[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.[15]In 1969, the Apollo 10 pre-dawn TLI was visible fromCloncurry,Australia.[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.[16]

In 1990Japanlaunched its first lunar mission, using theHitensatelliteto fly by the Moon and place the Hagoromomicrosatellitein a lunar orbit. Following that, it explored a novel lowdelta-vTLI method with a 6-month transfer time (compared to 3 days for Apollo).[17][13]: 179 

The 1994 USClementinespacecraft, designed to showcase lightweight technologies, used a 3 week long TLI with two intermediate Earth flybys before entering a lunar orbit.[17][13]: 185 

In 1997Asiasat-3became 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 km of the Moon's surface.[17][13]: 203 

The 2003 ESASMART-1technology demonstrator satellite became the first European satellite to orbit the Moon. After being launched into ageostationary 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.[13]: 229 

China launched its first Moon mission in 2007, placing theChang'e 1spacecraft in a lunar orbit. It used multiple burns to slowly raise its apogee to reach the vicinity of the Moon.[13]: 257 

India followed in 2008, launching theChandrayaan-1into a GTO and, like the Chinese spacecraft, increasing its apogee over a number of burns.[13]: 259 

The soft landerBeresheetfrom theIsrael Aerospace Industries,used this maneuver in 2019, but crashed on the Moon.

In 2011 the NASAGRAILsatellites used a low delta-v route to the Moon, passing by the Sun-Earth L1 point, and taking over 3 months.[13]: 278 

See also

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References

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  1. ^"Hiten".NASA.
  2. ^Schwaninger, Arthur J. (1963).Trajectories in the Earth-Moon Space with Symmetrical Free Return Properties(PDF).Technical Note D-1833. Huntsville, Alabama:NASA/Marshall Space Flight Center.
  3. ^Mansfield, Cheryl L. (May 18, 2017)."Apollo 10".NASA.
  4. ^"APOLLO 12".history.nasa.gov.
  5. ^Ways to the Moon(PDF)(Report). p. 93.
  6. ^"Launch Windows Essay".history.nasa.gov.
  7. ^Henri Poincaré,Les Méthodes Nouvelles de Mécanique Céleste,Paris, Gauthier-Villars et fils, 1892-99.
  8. ^Victor Szebehely,Theory of Orbits, The Restricted Problem of Three Bodies,Yale University, Academic Press, 1967.
  9. ^"Luna 01".NASA.Archived fromthe originalon 2020-09-05.Retrieved2019-06-10.
  10. ^"NASA - NSSDCA - Spacecraft - Details".nssdc.gsfc.nasa.gov.
  11. ^"Soviet Missions to the Moon".nssdc.gsfc.nasa.gov.
  12. ^"Ranger 4".NASA.
  13. ^abcdefgh"Beyond Earth"(PDF).NASA.
  14. ^"Apollo By the Numbers".NASA.Archived fromthe originalon 2004-11-18.
  15. ^"Independent Star News, Sunday, December 22, 1968".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."
  16. ^abFrench, Francis; Colin Burgess (2007).In the Shadow of the Moon.University of Nebraska Press.p.372.ISBN978-0-8032-1128-5.
  17. ^abcAlexander M. Jablonski1a; Kelly A. Ogden (2006)."A Review of Technical Requirements for Lunar Structures – Present Status".Journal of Aerospace Engineering.{{cite journal}}:CS1 maint: numeric names: authors list (link)

Public DomainThis article incorporatespublic domain materialfrom websites or documents of theNational Aeronautics and Space Administration.

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