Editing Lunar Laser Ranging experiments (section)

==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.