View source for Lunar Laser Ranging experiments

{{Short description|Measuring the distance between the Earth and the Moon with laser light}}
{{Use dmy dates|date=March 2018}}
[[Image:Apollo 11 Lunar Laser Ranging Experiment.jpg|thumb|Lunar Laser Ranging Experiment from the Apollo 11 mission]]

'''Lunar Laser Ranging''' (LLR) is the practice of measuring [[Lunar distance (astronomy)|the distance]] between the surfaces of the [[Earth]] and the [[Moon]] using [[Lidar|laser ranging]]. The distance can be calculated from the [[Round-trip delay|round-trip time]] of [[laser]] light pulses travelling at the [[speed of light]], which are reflected back to Earth by the Moon's surface or by [[List of retroreflectors on the Moon|one of several]] [[retroreflector]]s installed on the Moon. Three were placed by the United States' [[Apollo program]] ([[Apollo 11|11]], [[Apollo 14|14]], and [[Apollo 15|15]]), two by the Soviet [[Lunokhod programme|Lunokhod 1 and 2 missions]],<ref name="Lunakhod 2">{{cite journal |last1=Chapront |first1=J. |last2=Chapront-Touzé |first2=M. |last3=Francou |first3=G. |date=1999 |title=Determination of the lunar orbital and rotational parameters and of the ecliptic reference system orientation from LLR measurements and IERS data |journal=[[Astronomy and Astrophysics]] |volume=343 |pages=624–633 |bibcode=1999A&A...343..624C }}</ref> and one by India's [[Chandrayaan-3]] mission.<ref>{{Cite web |title=Chandrayaan-3 |url=https://www.isro.gov.in/Chandrayaan3_Details.html |access-date=15 August 2023 |website=ISRO}}</ref><ref name=":5">{{Cite news |title=India lands spacecraft near south pole of moon in historic first |url=https://www.theguardian.com/science/2023/aug/23/india-chandrayaan-3-moon-landing-mission |last=Dhillon |first=Amrit |date=2023-08-23 |access-date=2023-08-23 |work=[[The Guardian]]}}</ref>

Although it is possible to reflect light or radio waves directly from the Moon's surface (a process known as [[Earth–Moon–Earth communication|EME]]), a much more precise range measurement can be made using retroreflectors, since because of their small size, the temporal spread in the reflected signal is much smaller<ref>{{Cite journal|last1=Müller|first1=Jürgen|last2=Murphy|first2=Thomas W.|last3=Schreiber|first3=Ulrich|last4=Shelus|first4=Peter J.|last5=Torre|first5=Jean-Marie|last6=Williams|first6=James G.|last7=Boggs|first7=Dale H.|last8=Bouquillon|first8=Sebastien|last9=Bourgoin|first9=Adrien|last10=Hofmann|first10=Franz|date=2019|title=Lunar Laser Ranging: a tool for general relativity, lunar geophysics and Earth science|url=https://doi.org/10.1007/s00190-019-01296-0|journal=Journal of Geodesy|language=en|volume=93|issue=11|pages=2195–2210|doi=10.1007/s00190-019-01296-0|bibcode=2019JGeod..93.2195M|s2cid=202641440|issn=1432-1394|url-access=subscription}}</ref> and because the return will be more evenly reflected with less diffusion.

Laser ranging measurements can also be made with retroreflectors installed on [[List of missions to the Moon|Moon-orbiting satellites]] such as the [[Lunar Reconnaissance Orbiter|LRO]].<ref>{{Cite journal|last1=Mazarico|first1=Erwan|last2=Sun|first2=Xiaoli|last3=Torre|first3=Jean-Marie|last4=Courde|first4=Clément|last5=Chabé|first5=Julien|last6=Aimar|first6=Mourad|last7=Mariey|first7=Hervé|last8=Maurice|first8=Nicolas|last9=Barker|first9=Michael K.|last10=Mao|first10=Dandan|last11=Cremons|first11=Daniel R.|last12=Bouquillon|first12=Sébastien|last13=Carlucci|first13=Teddy|last14=Viswanathan|first14=Vishnu|last15=Lemoine|first15=Frank|last16=Bourgoin|first16=Adrien|last17=Exertier|first17=Pierre|last18=Neumann|first18=Gregory|last19=Zuber|first19=Maria|last20=Smith|first20=David|date=2020-08-06|title=First two-way laser ranging to a lunar orbiter: infrared observations from the Grasse station to LRO's retro-reflector array|journal=Earth, Planets and Space|volume=72|issue=1|pages=113|doi=10.1186/s40623-020-01243-w|bibcode=2020EP&S...72..113M|issn=1880-5981|doi-access=free|hdl=11603/19523|hdl-access=free}}</ref><ref>{{Cite news|last=Kornei|first=Katherine|date=2020-08-15|title=How Do You Solve a Moon Mystery? Fire a Laser at It|language=en-US|work=The New York Times|url=https://www.nytimes.com/2020/08/15/science/moon-lasers-dust.html|access-date=2021-06-01|issn=0362-4331}}</ref>

==History==
[[Image:ALSEP AS15-85-11468.jpg|thumb|Apollo 15 LRRR]]
[[Image:Laser Ranging Retroreflector Apollo 15.svg|thumb|Apollo 15 LRRR schematic]]

The first successful lunar ranging tests were carried out in 1962 when [[Louis Smullin]] and [[Giorgio Fiocco]] from the [[Massachusetts Institute of Technology]] succeeded in observing laser pulses reflected from the Moon's surface using a laser with a 50J 0.5 millisecond pulse length.<ref>{{cite journal |last1=Smullin |first1=Louis D. |last2=Fiocco |first2=Giorgio |year=1962 |title=Optical Echoes from the Moon |journal=[[Nature (journal)|Nature]] |volume=194 |issue=4835 |pages=1267 |bibcode=1962Natur.194.1267S |doi=10.1038/1941267a0|s2cid=4145783 |doi-access=free }}</ref> Similar measurements were obtained later the same year by a Soviet team at the [[Crimean Astrophysical Observatory]] using a [[Q-switching|Q-switched]] [[ruby laser]].<ref>{{cite journal |last1=Bender |first1=P. L. |display-authors=etal |year=1973 |title=The Lunar Laser Ranging Experiment: Accurate ranges have given a large improvement in the lunar orbit and new selenophysical information |url=http://www.physics.ucsd.edu/~tmurphy/apollo/doc/Bender.pdf |journal=[[Science (journal)|Science]] |volume=182 |issue=4109 |pages=229–238 |bibcode=1973Sci...182..229B |doi=10.1126/science.182.4109.229 |pmid=17749298|s2cid=32027563 }}</ref>

Shortly thereafter, [[Princeton University]] graduate student [[James E. Faller|James Faller]] proposed placing optical reflectors on the Moon to improve the accuracy of the measurements.<ref name=":0">{{Cite journal|last=Newman|first=Michael E.|date=2017-09-26|title=To the Moon and Back … in 2.5 Seconds|url=https://www.nist.gov/nist-time-capsule/any-object-any-need-call-nist/moon-and-back-25-seconds|access-date=2021-01-27|journal=NIST|language=en}}</ref> This was achieved following the installation of a [[retroreflector]] array on July 21, 1969 by the crew of [[Apollo 11]]. Two more retroreflector arrays were left by the [[Apollo 14]] and [[Apollo 15]] missions. Successful lunar laser range measurements to the [[retroreflectors]] were first reported on Aug. 1, 1969 by the 3.1&nbsp;m telescope at [[Lick Observatory]].<ref name=":0" /> Observations from [[Air Force Cambridge Research Laboratories]] Lunar Ranging Observatory in Arizona, the [[Pic du Midi de Bigorre|Pic du Midi Observatory]] in France, the Tokyo [[National Astronomical Observatory of Japan|Astronomical Observatory]], and [[McDonald Observatory]] in Texas soon followed.

The uncrewed Soviet ''[[Lunokhod 1]]'' and ''[[Lunokhod 2]]'' rovers carried smaller arrays. Reflected signals were initially received from ''Lunokhod 1'' by the Soviet Union up to 1974, but not by western observatories that did not have precise information about location. In 2010 [[NASA]]'s [[Lunar Reconnaissance Orbiter]] located the Lunokhod 1 rover on images and in April 2010 a team from University of California ranged the array.<ref>{{cite news |last=McDonald |first=K. |date=26 April 2010 |title=UC San Diego Physicists Locate Long Lost Soviet Reflector on Moon |url=http://ucsdnews.ucsd.edu/newsrel/science/04-26SovietReflector.asp |publisher=University of California, San Diego |access-date=27 April 2010|archive-date=30 April 2010|archive-url=https://web.archive.org/web/20100430164946/http://ucsdnews.ucsd.edu/newsrel/science/04-26SovietReflector.asp|url-status=dead}}</ref> ''Lunokhod 2''{{'s}} array continues to return signals to Earth.<ref name="jwjd1">{{cite conference |url=https://ilrs.cddis.eosdis.nasa.gov/docs/williams_lw13.pdf |title=Lunar Geophysics, Geodesy, and Dynamics |conference=13th International Workshop on Laser Ranging. 7–11 October 2002. Washington, D. C. |first1=James G. |last1=Williams |first2=Jean O. |last2=Dickey |date=2002}}</ref> The Lunokhod arrays suffer from decreased performance in direct sunlight—a factor considered in reflector placement during the Apollo missions.<ref name="UniverseToday">{{cite news |title=It's Not Just The Astronauts That Are Getting Older |date=10 March 2010 |work=[[Universe Today]] |url=http://www.universetoday.com/59310/its-not-just-the-astronauts-that-are-getting-older/ |access-date=24 August 2012}}</ref>

The Apollo 15 array is three times the size of the arrays left by the two earlier Apollo missions. Its size made it the target of three-quarters of the sample measurements taken in the first 25 years of the experiment. Improvements in technology since then have resulted in greater use of the smaller arrays, by sites such as the [[Côte d'Azur Observatory]] in [[Nice]], France; and the [[Apache Point Observatory Lunar Laser-ranging Operation]] (APOLLO) at the [[Apache Point Observatory]] in [[New Mexico]].

In the 2010s several [[List of retroreflectors on the Moon|new retroreflectors]] were planned. The [[MoonLIGHT (experiment)|MoonLIGHT]] reflector, which was to be placed by the private [[MX-1E]] lander, was designed to increase measurement accuracy up to 100 times over existing systems.<ref name="Currie 2011">{{cite journal|last1=Currie|first1=Douglas|last2=Dell'Agnello|first2=Simone|last3=Delle Monache|first3=Giovanni|date=April–May 2011|title=A Lunar Laser Ranging Retroreflector Array for the 21st Century|journal=Acta Astronautica|volume=68|issue=7–8|pages=667–680|bibcode=2011AcAau..68..667C|doi=10.1016/j.actaastro.2010.09.001|url=https://www.openaccessrepository.it/record/137265 |archive-url=https://web.archive.org/web/20231119044553/https://www.openaccessrepository.it/record/137265 |url-status=dead |archive-date=19 November 2023 |url-access=subscription}}</ref><ref name="Tune 2015">{{cite news|last=Tune|first=Lee|date=10 June 2015|title=UMD, Italy & MoonEx Join to Put New Laser-Reflecting Arrays on Moon|work=UMD Right Now|publisher=University of Maryland|url=https://umdrightnow.umd.edu/news/umd-italy-moonex-join-put-new-laser-reflecting-arrays-moon|access-date=21 March 2018|archive-date=22 March 2018|archive-url=https://web.archive.org/web/20180322081731/https://umdrightnow.umd.edu/news/umd-italy-moonex-join-put-new-laser-reflecting-arrays-moon|url-status=dead}}</ref><ref name="MX-1">{{Cite news|last=Boyle|first=Alan|date=12 July 2017|title=Moon Express unveils its roadmap for giant leaps to the lunar surface ... and back again|work=GeekWire|url=https://www.geekwire.com/2017/moon-express-unveils-roadmap-giant-leaps-lunar-surface-back/|access-date=15 March 2018}}</ref> MX-1E was set to launch in July 2020,<ref>{{Citation|title=Moon Express Lunar Scout (MX-1E)|url=https://www.rocketlaunch.live/launch/lunar-scout|publisher=RocketLaunch.Live|access-date=27 July 2019|archive-date=27 July 2019|archive-url=https://web.archive.org/web/20190727095927/https://www.rocketlaunch.live/launch/lunar-scout|url-status=dead}}</ref> however, as of February 2020, the launch of the MX-1E has been canceled.<ref>{{cite web|title=MX-1E 1, 2, 3|url=https://space.skyrocket.de/doc_sdat/mx-1e.htm|access-date=24 May 2020}}</ref> India's [[Chandrayaan-3]] lunar lander successfully placed a sixth reflector on the Moon in August 2023.<ref name=":5" /> MoonLIGHT will be launched in early 2024 with a [[Commercial Lunar Payload Services]] (CLPS) mission.<ref>{{Cite web |title=NASA Payloads for (CLPS PRISM) CP-11 |url=https://science.nasa.gov/lunar-discovery/deliveries/cp-11}}</ref>

==Principle==
{{see also|Apache Point Observatory Lunar Laser-ranging Operation#Principles of operation}}
[[File:Lunar_retroreflector_locations.jpg|thumb|right|250px|Annotated image of the near side of the Moon showing the location of retroreflectors left on the surface by Apollo and Lunokhod missions<ref name="llrnasa">{{cite web |url=http://science.nasa.gov/science-news/science-at-nasa/2004/06may_lunarranging/ |title=Was Galileo Wrong? |publisher=[[NASA]] |date=6 May 2004 |url-status=live |archive-url=https://web.archive.org/web/20220430111349/https://science.nasa.gov/science-news/science-at-nasa/2004/06may_lunarranging/ |archive-date=30 April 2022 }}</ref>]]
The distance to the Moon is calculated {{em|approximately}} using the equation:
{{serif|1=''distance'' {{=}} (''speed of light'' × ''duration of delay due to reflection'')&nbsp;/&nbsp;2}}. Since the [[speed of light]] is a defined constant, conversion between distance and time of flight can be made without ambiguity.

To compute the lunar distance precisely, many factors must be considered in addition to the round-trip time of about 2.5 seconds. These factors include the location of the Moon in the sky, the relative motion of Earth and the Moon, Earth's rotation, [[lunar libration]], [[polar motion]], [[weather]], speed of light in various parts of air, propagation delay through [[Atmosphere of Earth|Earth's atmosphere]], the location of the observing station and its motion due to [[plate tectonics|crustal motion]] and [[tide]]s, and [[Theory of relativity|relativistic effects]].<ref>{{cite book |title=Satellite Geodesy |url=https://archive.org/details/satellitegeodesy00seeb |url-access=limited |publisher=de Gruyter |first=Günter |last=Seeber |edition=2nd |page=[https://archive.org/details/satellitegeodesy00seeb/page/n458 439] |date=2003 |isbn=978-3-11-017549-3 |oclc=52258226}}</ref><ref>{{Cite web|last1=Williams|first1=James G.|last2=Boggs|first2=Dale H.|date=2020|title=The JPL Lunar Laser range model 2020|url=https://ssd.jpl.nasa.gov/ftp/eph/planets/ioms/|access-date=2021-05-24|website=ssd.jpl.nasa.gov}}</ref> The distance continually changes for a number of reasons, but averages {{convert|385000.6|km|mi|abbr=on}} between the center of the Earth and the center of the Moon.<ref name="millimeter challenge">{{cite journal |last1=Murphy |first1=T. W. |date=2013 |title=Lunar laser ranging: the millimeter challenge |url=http://physics.ucsd.edu/~tmurphy/papers/rop-llr.pdf |journal=[[Reports on Progress in Physics]] |volume=76 |issue=7 |page=2 |arxiv=1309.6294 |bibcode=2013RPPh...76g6901M |doi=10.1088/0034-4885/76/7/076901|pmid=23764926 |s2cid=15744316 }}</ref> The orbits of the Moon and planets are integrated numerically along with the orientation of the Moon called physical [[libration]].<ref name=":3">{{Cite journal|last1=Park|first1=Ryan S.|last2=Folkner|first2=William M.|last3=Williams|first3=James G.|last4=Boggs|first4=Dale H.|date=2021|title=The JPL Planetary and Lunar Ephemerides DE440 and DE441|journal=The Astronomical Journal|language=en|volume=161|issue=3|pages=105|doi=10.3847/1538-3881/abd414|bibcode=2021AJ....161..105P|s2cid=233943954|issn=1538-3881|doi-access=free}}</ref>

At the Moon's surface, the beam is about {{convert|6.5|km|mi|sp=us}} wide<ref name=ApolloLaser >{{cite web
  |last=Espenek |first=F. |date=August 1994 |title=NASA – Accuracy of Eclipse Predictions
  |url=http://eclipse.gsfc.nasa.gov/SEhelp/ApolloLaser.html
  |publisher=NASA/GSFC
  |access-date=4 May 2008
}}</ref>{{efn-lr|During the round-trip time, an Earth observer will have moved by around {{val|1|u=km}} (depending on their latitude). This has been presented, incorrectly, as a 'disproof' of the ranging experiment, the claim being that the beam to such a small reflector cannot hit such a moving target. However the size of the beam is far larger than any movement, especially for the returned beam.}} and scientists liken the task of aiming the beam to using a rifle to hit a moving [[Dime (United States coin)|dime]] {{convert|3|km|mi|sp=us}} away. The reflected light is too weak to see with the human eye. Out of a pulse of 3×10<sup>17</sup> photons<ref>{{cite web |title=The Basics of Lunar Ranging |url=https://tmurphy.physics.ucsd.edu/apollo/basics.html |access-date=21 July 2023}}</ref> aimed at the reflector, only about 1{{ndash}}5 are received back on Earth, even under good conditions.<ref>{{Cite journal|last=Merkowitz|first=Stephen M.|date=2010-11-02|title=Tests of Gravity Using Lunar Laser Ranging|url= |journal=Living Reviews in Relativity|language=en|volume=13|issue=1|pages=7|doi=10.12942/lrr-2010-7|doi-access=free |issn=1433-8351|pmc=5253913|pmid=28163616|bibcode=2010LRR....13....7M}}</ref> They can be identified as originating from the laser because the laser is highly [[monochromatic]].

As of 2009, the distance to the Moon can be measured with millimeter precision.<ref name=":1" /> In a relative sense, this is one of the most precise distance measurements ever made, and is equivalent in accuracy to determining the distance between Los Angeles and New York to within the width of a human hair.

==  List of retroreflectors ==
{{main article|List of retroreflectors on the Moon}}

== List of observatories ==
The table below presents a list of active and inactive Lunar Laser Ranging stations on Earth.<ref name="millimeter challenge" /><ref>{{Cite journal|last1=Biskupek|first1=Liliane|last2=Müller|first2=Jürgen|last3=Torre|first3=Jean-Marie|date=2021-02-03|title=Benefit of New High-Precision LLR Data for the Determination of Relativistic Parameters|journal=Universe|language=en|volume=7|issue=2|pages=34|doi=10.3390/universe7020034|arxiv=2012.12032|bibcode=2021Univ....7...34B|doi-access=free}}</ref>   
{| class="wikitable"
|+Lunar Laser Ranging stations
!Observatory
!Project
!Operating timespan
!Telescope
!Laser
!Range accuracy
!Ref.
|-
|[[McDonald Observatory]], Texas, US
|MLRS
|1969–1985 
1985–2013
|2.7 m
|694&nbsp;nm, 7 J
532&nbsp;nm, 200 ps, 150 mJ
|
|<ref>{{Cite journal|last1=Bender|first1=P. L.|last2=Currie|first2=D. G.|last3=Dickey|first3=R. H.|last4=Eckhardt|first4=D. H.|last5=Faller|first5=J. E.|last6=Kaula|first6=W. M.|last7=Mulholland|first7=J. D.|last8=Plotkin|first8=H. H.|last9=Poultney|first9=S. K.|last10=Silverberg|first10=E. C.|last11=Wilkinson|display-authors=9|date=1973|title=The Lunar Laser Ranging Experiment|url=https://www.science.org/doi/10.1126/science.182.4109.229|journal=Science|language=en|volume=182|issue=4109|pages=229–238|doi=10.1126/science.182.4109.229|pmid=17749298|bibcode=1973Sci...182..229B|s2cid=32027563|issn=0036-8075|url-access=subscription}}</ref>
<ref name="millimeter challenge" />
|-
|[[Crimean Astrophysical Observatory]] (CrAO), USSR
|
|1974, 1982–1984
|
|694&nbsp;nm
|3.0–0.6 m
|<ref>{{Cite web|last=Yagudina|date=2018|title=Processing and analysis of lunar laser ranging observations in Crimea in 1974-1984|url=http://iaaras.ru/en/library/paper/1943/|access-date=2021-06-01|website=Institute of Applied Astronomy of the Russian Academy of Sciences}}</ref>
|-
|[[Côte d'Azur Observatory]] (OCA), Grasse, France
|MeO
|1984–1986
1986–2010

2010–present (2021)
|
|694&nbsp;nm
532&nbsp;nm, 70 ps, 75 mJ

532/1064&nbsp;nm
|
|<ref name="millimeter challenge" /><ref>{{Cite journal|last1=Chabé|first1=Julien|last2=Courde|first2=Clément|last3=Torre|first3=Jean-Marie|last4=Bouquillon|first4=Sébastien|last5=Bourgoin|first5=Adrien|last6=Aimar|first6=Mourad|last7=Albanèse|first7=Dominique|last8=Chauvineau|first8=Bertrand|last9=Mariey|first9=Hervé|last10=Martinot-Lagarde|first10=Grégoire|last11=Maurice|first11=Nicolas|date=2020|title=Recent Progress in Lunar Laser Ranging at Grasse Laser Ranging Station|journal=Earth and Space Science|language=en|volume=7|issue=3|pages=e2019EA000785|doi=10.1029/2019EA000785|bibcode=2020E&SS....700785C|s2cid=212785296 |issn=2333-5084|doi-access=free}}</ref>
|-
|[[Haleakalā Observatory|Haleakala Observatory]], Hawaii, US
|LURE
|1984–1990
|
|532&nbsp;nm, 200 ps, 140 mJ
|2.0&nbsp;cm
|<ref name="millimeter challenge" /><ref>{{Cite web|date=2002-01-29|title=Lure Observatory|url=http://koa.ifa.hawaii.edu/Lure/|access-date=2021-06-03|website=Institute for Astronomy, University of Hawaii}}</ref>
|-
|Matera Laser Ranging Observatory (MLRO), Italy
|
|2003–present (2021)
|
|532&nbsp;nm
|
|
|-
|[[Apache Point Observatory]], New Mexico, US
|[[Apache Point Observatory Lunar Laser-ranging Operation|APOLLO]]
|2006–2021
2021–present (2023)
|
|532&nbsp;nm, 100 ps, 115 mJ
|1.1&nbsp;mm
|<ref name="millimeter challenge" />
<ref>{{Cite web |title=APOL - Apache Point Observatory|url=https://space-geodesy.nasa.gov/NSGN/sites/Apache_Point/Apache_Point.html}}</ref>
|-
|[[Geodetic Observatory Wettzell]], Germany
|WLRS
|2018–present (2021)
|
|1064&nbsp;nm, 10 ps, 75 mJ 
|
|<ref>{{Cite book|last1=Eckl|first1=Johann J.|last2=Schreiber|first2=K. Ulrich|last3=Schüler|first3=Torben|title=Quantum Optics and Photon Counting 2019 |chapter=Lunar laser ranging utilizing a highly efficient solid-state detector in the near-IR |editor1-first=Peter|editor1-last=Domokos|editor2-first=Ralph B|editor2-last=James|editor3-first=Ivan|editor3-last=Prochazka|editor4-first=Roman|editor4-last=Sobolewski|editor5-first=Adam|editor5-last=Gali|date=2019-04-30|chapter-url=https://www.spiedigitallibrary.org/conference-proceedings-of-spie/11027/1102708/Lunar-laser-ranging-utilizing-a-highly-efficient-solid-state-detector/10.1117/12.2521133.short|publisher=International Society for Optics and Photonics|volume=11027|pages=1102708|doi=10.1117/12.2521133|bibcode=2019SPIE11027E..08E|isbn=9781510627208|s2cid=155720383}}</ref>
|-
|[[Yunnan Astronomical Observatory]], Kunming, China
|
|2018
|1.2 m
|532&nbsp;nm, 10 ns, 3 J
|meter level
|<ref>{{Cite journal|date=2019-01-27|title=Research and Experiment of Lunar Laser Ranging in Yunnan Observatories|url=http://www.opticsjournal.net/Articles/Abstract/zgjg/46/1/0104004.cshtml|journal=Chinese Journal of Lasers|volume=46|issue=1|doi=10.3788/CJL201946.0104004|last1=Li Yuqiang |first1=李语强 |last2=Fu Honglin |first2=伏红林 |last3=Li Rongwang |first3=李荣旺 |last4=Tang Rufeng |first4=汤儒峰 |last5=Li Zhulian |first5=李祝莲 |last6=Zhai Dongsheng |first6=翟东升 |last7=Zhang Haitao |first7=张海涛 |last8=Pi Xiaoyu |first8=皮晓宇 |last9=Ye Xianji |first9=叶贤基 |last10=Xiong Yaoheng |first10=熊耀恒 |page=0104004 |s2cid=239211201 |url-access=subscription }}</ref>
|}

== Data analysis ==
The Lunar Laser Ranging data is collected in order to extract numerical values for a number of parameters. Analyzing the range data involves dynamics, terrestrial geophysics, and lunar geophysics. The modeling problem involves two aspects: an accurate computation of the lunar orbit and lunar orientation, and an accurate model for the time of flight from an observing station to a retroreflector and back to the station. Modern Lunar Laser Ranging data can be fit with a 1&nbsp;cm weighted rms residual.

* The center of Earth to center of Moon distance is computed by a program that numerically integrates the lunar and planetary orbits accounting for the gravitational attraction of the Sun, planets, and a selection of asteroids.<ref name=":4">{{Cite journal|last1=Pavlov|first1=Dmitry A.|last2=Williams|first2=James G.|last3=Suvorkin|first3=Vladimir V.|date=2016|title=Determining parameters of Moon's orbital and rotational motion from LLR observations using GRAIL and IERS-recommended models|url=http://link.springer.com/10.1007/s10569-016-9712-1|journal=Celestial Mechanics and Dynamical Astronomy|language=en|volume=126|issue=1|pages=61–88|doi=10.1007/s10569-016-9712-1|issn=0923-2958|arxiv=1606.08376|bibcode=2016CeMDA.126...61P|s2cid=119116627}}</ref><ref name=":3" />
* The same program integrates the 3-axis orientation of the Moon called physical [[Libration]].

The range model includes<ref name=":4" /><ref>{{Cite web|last1=Williams|first1=James G.|last2=Boggs|first2=Dale H.|date=2020|title=The JPL Lunar Laser range model 2020|url=https://ssd.jpl.nasa.gov/ftp/eph/planets/ioms/|access-date=2021-06-01|website=ssd.jpl.nasa.gov}}</ref>

* The position of the ranging station accounting for motion due to [[plate tectonics]], [[Earth's rotation|Earth rotation]], [[Axial precession|precession]], [[nutation]], and [[polar motion]].
* Tides in the solid Earth and seasonal motion of the solid Earth with respect to its [[center of mass]].
* Relativistic transformation of time and space coordinates from a frame moving with the station to a frame fixed with respect to the solar system center of mass. Lorentz contraction of the Earth is part of this transformation.
* Delay in the Earth's atmosphere.
* Relativistic delay due to the gravity fields of the Sun, Earth, and Moon.
* The position of the retroreflector accounting for orientation of the Moon and solid-body tides.
* [[Length contraction|Lorentz contraction]] of the Moon.
* [[Thermal expansion]] and contraction of the retroreflector mounts.

For the terrestrial model, the IERS Conventions (2010) is a source of detailed information.<ref>{{Cite web|title=IERS - IERS Technical Notes - IERS Conventions (2010)|url=https://www.iers.org/IERS/EN/Publications/TechnicalNotes/tn36.html|access-date=2021-06-01|website=www.iers.org}}</ref>

==Results==
Lunar laser ranging measurement data is available from the Paris Observatory Lunar Analysis Center,<ref>{{cite web |url=http://polac.obspm.fr/llrdatae.html |title=Lunar Laser Ranging Observations from 1969 to May 2013 |publisher=SYRTE Paris Observatory |access-date=3 June 2014}}</ref> the International Laser Ranging Service archives,<ref>{{Cite FTP |title=International Laser Ranging Service|server=FTP server|url-status=dead|url=ftp://cddis.gsfc.nasa.gov/pub/slr/data/npt_crd/}}</ref><ref>{{Cite web|title=International Laser Ranging Service|url=https://edc.dgfi.tum.de/pub/slr/data/npt_crd/}}</ref> and the active stations. Some of the findings of this [[long-term experiment]] are:<ref name="millimeter challenge" />

=== Properties of the Moon ===
* The distance to the Moon can be measured with millimeter precision.<ref name=":1">{{cite journal|last1=Battat|first1=J. B. R.|last2=Murphy|first2=T. W.|last3=Adelberger|first3=E. G.|last4=Gillespie|first4=B.|last5=Hoyle|first5=C. D.|last6=McMillan|first6=R. J.|last7=Michelsen|first7=E. L.|last8=Nordtvedt|first8=K.|last9=Orin|first9=A. E.|last10=Stubbs|first10=C. W.|last11=Swanson|first11=H. E.|display-authors=3|date=January 2009|title=The Apache Point Observatory Lunar Laser-ranging Operation (APOLLO): Two Years of Millimeter-Precision Measurements of the Earth-Moon Range1|journal=Publications of the Astronomical Society of the Pacific|volume=121|issue=875|pages=29–40|bibcode=2009PASP..121...29B|doi=10.1086/596748|jstor=10.1086/596748|doi-access=free}}</ref>
*The Moon is spiraling away from Earth at a rate of {{val|3.8|u=cm|up=year}}.{{r|ApolloLaser}}<ref name="link.springer.com">{{Cite journal|last1=Williams|first1=James G.|last2=Boggs|first2=Dale H.|date=2016|title=Secular tidal changes in lunar orbit and Earth rotation|url=http://link.springer.com/10.1007/s10569-016-9702-3|journal=Celestial Mechanics and Dynamical Astronomy|language=en|volume=126|issue=1|pages=89–129|doi=10.1007/s10569-016-9702-3|bibcode=2016CeMDA.126...89W|s2cid=124256137|issn=0923-2958|url-access=subscription}}</ref> This rate has been described as anomalously high.<ref>{{Cite journal |last1=Bills |first1=B. G. |last2=Ray |first2=R. D. |year=1999 |title=Lunar Orbital Evolution: A Synthesis of Recent Results |journal=[[Geophysical Research Letters]] |volume=26 |issue=19 |pages=3045–3048 |bibcode=1999GeoRL..26.3045B |doi=10.1029/1999GL008348|doi-access=free }}</ref>
*The fluid core of the Moon was detected from the effects of core/mantle boundary dissipation.<ref>{{Cite journal|last1=Williams|first1=James G.|last2=Boggs|first2=Dale H.|last3=Yoder|first3=Charles F.|last4=Ratcliff|first4=J. Todd|last5=Dickey|first5=Jean O.|date=2001|title=Lunar rotational dissipation in solid body and molten core|journal=Journal of Geophysical Research: Planets|language=en|volume=106|issue=E11|pages=27933–27968|doi=10.1029/2000JE001396|bibcode=2001JGR...10627933W|doi-access=free}}</ref>
*The Moon has free physical [[librations]] that require one or more stimulating mechanisms.<ref>{{Cite journal|last1=Rambaux|first1=N.|last2=Williams|first2=J. G.|date=2011|title=The Moon's physical librations and determination of their free modes|journal=Celestial Mechanics and Dynamical Astronomy|volume=109|issue=1 |pages=85–100|doi=10.1007/s10569-010-9314-2|bibcode=2011CeMDA.109...85R |s2cid=45209988|url=https://hal.archives-ouvertes.fr/hal-00588671/file/PEER_stage2_10.1007%252Fs10569-010-9314-2.pdf}}</ref>  
*Tidal dissipation in the Moon depends on tidal frequency.<ref name="link.springer.com"/>  
* The Moon probably has a liquid core of about 20% of the Moon's radius.{{r|jwjd1}} The radius of the lunar core-mantle boundary is determined as {{val|381|12|u=km}}.{{r|viswanathan2019grl}}
*The polar [[flattening]] of the lunar core-mantle boundary is determined as {{val|2.2|0.6|e=-4}}.{{r|viswanathan2019grl}}
*The free core [[nutation]] of the Moon is determined as {{val|367|100|u=yr}}.<ref name="viswanathan2019grl">{{cite journal|last1=Viswanathan|first1=V.|last2=Rambaux|first2=N.|last3=Fienga|first3=A.|last4=Laskar|first4=J.|last5=Gastineau|first5=M.|date=9 July 2019|title=Observational Constraint on the Radius and Oblateness of the Lunar Core-Mantle Boundary|journal=[[Geophysical Research Letters]]|volume=46|issue=13|pages=7295–7303|arxiv=1903.07205|doi=10.1029/2019GL082677|bibcode=2019GeoRL..46.7295V|s2cid=119508748}}</ref>
*Accurate locations for retroreflectors serve as reference points visible to orbiting spacecraft.<ref>{{Cite journal|last1=Wagner|first1=R. V.|last2=Nelson|first2=D. M.|last3=Plescia|first3=J. B.|last4=Robinson|first4=M. S.|last5=Speyerer|first5=E. J.|last6=Mazarico|first6=E.|date=2017|title=Coordinates of anthropogenic features on the Moon|journal=Icarus|language=en|volume=283|pages=92–103|doi=10.1016/j.icarus.2016.05.011|bibcode=2017Icar..283...92W|issn=0019-1035|doi-access=free}}</ref>

=== Gravitational physics ===
*[[Albert Einstein|Einstein's]] theory of gravity (the [[General relativity|general theory of relativity]]) predicts the [[Orbit of the Moon|Moon's orbit]] to within the accuracy of the laser ranging measurements.{{r|jwjd1}}<ref name=":2" />
* [[Gauge fixing|Gauge freedom]] plays a major role in a correct physical interpretation of the relativistic effects in the Earth-Moon system observed with LLR technique.<ref>{{cite journal |last1=Kopeikin |first1=S. |last2=Xie |first2=Y. |year=2010 |title=Celestial reference frames and the gauge freedom in the post-Newtonian mechanics of the Earth–Moon system |journal=[[Celestial Mechanics and Dynamical Astronomy]] |volume=108 |issue=3 |pages=245–263 |bibcode=2010CeMDA.108..245K |doi=10.1007/s10569-010-9303-5|s2cid=122789819 }}</ref>
* The likelihood of any [[Nordtvedt effect]] (a hypothetical differential acceleration of the Moon and Earth towards the Sun caused by their different degrees of compactness) has been ruled out to high precision,<ref>{{cite journal|last1=Adelberger|first1=E. G.|last2=Heckel|first2=B. R.|last3=Smith|first3=G.|last4=Su|first4=Y.|last5=Swanson|first5=H. E.|year=1990|title=Eötvös experiments, lunar ranging and the strong equivalence principle|journal=[[Nature (journal)|Nature]]|volume=347|issue=6290|pages=261–263|bibcode=1990Natur.347..261A|doi=10.1038/347261a0|s2cid=4286881}}</ref><ref name=":2">{{cite journal|last1=Williams|first1=J. G.|last2=Newhall|first2=X. X.|last3=Dickey|first3=J. O.|year=1996|title=Relativity parameters determined from lunar laser ranging|journal=[[Physical Review D]]|volume=53|issue=12|pages=6730–6739|bibcode=1996PhRvD..53.6730W|doi=10.1103/PhysRevD.53.6730|pmid=10019959}}</ref><ref>{{cite journal|last1=Viswanathan|first1=V|last2=Fienga|first2=A|last3=Minazzoli|first3=O|last4=Bernus|first4=L|last5=Laskar|first5=J|last6=Gastineau|first6=M|date=May 2018|title=The new lunar ephemeris INPOP17a and its application to fundamental physics|journal=Monthly Notices of the Royal Astronomical Society|volume=476|issue=2|pages=1877–1888|arxiv=1710.09167|doi=10.1093/mnras/sty096|doi-access=free|bibcode=2018MNRAS.476.1877V}}</ref> strongly supporting the [[strong equivalence principle]].
* The universal force of [[gravity]] is very stable.  The experiments have constrained the change in [[Isaac Newton|Newton's]] [[gravitational constant]] ''G'' to a factor of {{val|2|7|e=-13}} per year.<ref>{{cite journal|last1=Müller|first1=J.|last2=Biskupek|first2=L.|year=2007|title=Variations of the gravitational constant from lunar laser ranging data|journal=[[Classical and Quantum Gravity]]|volume=24|issue=17|page=4533|doi=10.1088/0264-9381/24/17/017|s2cid=120195732 }}</ref>

==Gallery==
<gallery widths="200" heights="160">
File:ALSEP AS14-67-9386.jpg|Apollo 14 Lunar Ranging Retro Reflector ([[Apollo Lunar Surface Experiments Package|LRRR]])
File:LunarPhotons.png|[[Apache Point Observatory Lunar Laser-ranging Operation|APOLLO]] collaboration photon pulse return times
File:Wettzell Laser Ranging System.jpg|Laser ranging facility at [[Geodetic Observatory Wettzell|Wettzell]] [[fundamental station]], [[Bavaria]], [[Germany]]
File:Goddard Spaceflight Center Laser Ranging Facility.jpg|Laser Ranging at [[Goddard Space Flight Center]] 
</gallery>

==See also==
{{Portal|Solar System}}
* [[Carroll Alley]] (first principal investigator of the Apollo Lunar Laser Ranging team)
* [[Lidar]]
* [[Lunar distance (astronomy)]]
* [[Satellite laser ranging]]
* [[Space geodesy]]
* [[Third-party evidence for Apollo Moon landings]]
* [[List of artificial objects on the Moon]]

==References==
{{Notelist-lr}}

{{reflist}}

==External links==
* [http://www.issibern.ch/teams/lunarlaser/#Team "Theory and Model for the New Generation of the Lunar Laser Ranging Data"] by [[Sergei Kopeikin]]
* [http://www.lpi.usra.edu/lunar/missions/apollo/apollo_15/experiments/lrr/ Apollo 15 Experiments - Laser Ranging Retroreflector] by the [[Lunar and Planetary Institute]]
* [http://www.csr.utexas.edu/mlrs/history.html "History of Laser Ranging and MLRS"] by the [[University of Texas at Austin]], Center for Space Research
* [http://physics.ucsd.edu/~tmurphy/apollo/lrrr.html "Lunar Retroreflectors"] by Tom Murphy
* [https://web.archive.org/web/20061112025133/http://www.obs-azur.fr/cerga/laser/laslune/llr.htm Station de Télémétrie Laser-Lune] in [[Grasse|Grasse, France]]
* [http://ilrs.gsfc.nasa.gov/science/scienceContributions/lunar.html Lunar Laser Ranging] from International Laser Ranging Service
* [http://www.washington.edu/news/2002/01/14/uw-researcher-plans-project-to-pin-down-moons-distance-from-earth/ "UW researcher plans project to pin down moon's distance from Earth"] by Vince Stricherz, [[University of Washington|UW Today]], 14 January 2002
* [https://science.nasa.gov/science-news/science-at-nasa/2004/21jul_llr/ "What Neil & Buzz Left on the Moon"] by Science@NASA, 20 July 2004
* [http://www.cnn.com/TECH/space/9907/21/apollo.experiment/ "Apollo 11 Experiment Still Returning Results"] by Robin Lloyd, [[CNN]], 21 July 1999
* [https://www.youtube.com/watch?v=WbOBbZ6A51k "Shooting Lasers at the Moon: Hal Walker and the Lunar Retroreflector"] by Smithsonian National Air and Space Museum, YouTube, 20 Aug 2019

{{The Moon}}
{{Apollo program hardware}}
{{Authority control}}

[[Category:Apollo program hardware]]
[[Category:Tests of general relativity]]