Lunar Laser Ranging experiment

Lunar Laser Ranging (LLR) is the practice of measuring the distance between the surfaces of the Earth and the Moon using laser ranging. The distance can be calculated from the 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 one of five retroreflectors installed on the Moon during the Apollo program (11, 14, and 15) and Lunokhod 1 and 2 missions.[1]

Lunar Laser Ranging Experiment from the Apollo 11 mission

Although it is possible to reflect light or radio waves directly from the Moon's surface (a process known as EME), a much more precise measurement can be made using retroreflectors at known locations.

Laser ranging measurements can also be made with retroreflectors installed on Moon-orbiting satellites.[2]


Apollo 15 LRRR
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.[3] Similar measurements were obtained later the same year by a Soviet team at the Crimean Astrophysical Observatory using a Q-switched ruby laser.[4]

Shortly thereafter, Princeton University graduate student James Faller proposed placing optical reflectors on the Moon to improve the accuracy of the measurements.[5] 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 m telescope at Lick Observatory.[5] Observations from Air Force Cambridge Research Laboratories Lunar Ranging Observatory in Arizona, the Pic du Midi Observatory in France, the Tokyo 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.[6] Lunokhod 2's array continues to return signals to Earth.[7] The Lunokhod arrays suffer from decreased performance in direct sunlight—a factor considered in reflector placement during the Apollo missions.[8]

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 new retroreflectors were planned. The 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.[9][10][11] MX-1E was set to launch in July 2020,[12] however, as of February 2020, the launch of the MX-1E has been canceled.[13]


Annotated image of the near side of the moon showing the location of retroreflectors left on the surface by Apollo and Lunokhod missions[14]

The distance to the Moon is calculated approximately using the equation: distance = (speed of light × duration of delay due to reflection) / 2

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 Earth's atmosphere, the location of the observing station and its motion due to crustal motion and tides, and relativistic effects.[15] The distance continually changes for a number of reasons, but averages 385,000.6 km (239,228.3 mi) between the center of the Earth and the center of the Moon.[16]

At the Moon's surface, the beam is about 6.5 kilometers (4.0 mi) wide[17][i] and scientists liken the task of aiming the beam to using a rifle to hit a moving dime 3 kilometers (1.9 mi) away. The reflected light is too weak to see with the human eye. Out of 1021 photons aimed at the reflector, only one is received back on Earth, even under good conditions.[18] 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.[19] 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 retroreflectorsEdit


Lunar laser ranging measurement data is available from the Paris Observatory Lunar Analysis Center,[20] and the active stations. Some of the findings of this long-term experiment are:

Properties of the MoonEdit

  • The distance to the Moon can be measured with millimeter precision.[19]
  • The Moon is spiraling away from Earth at a rate of 3.8 cm/year.[17] This rate has been described as anomalously high.[21]
  • The Moon probably has a liquid core of about 20% of the Moon's radius.[7] The radius of the lunar core-mantle boundary is determined as 381±12 km.[22]
  • The polar flattening of the lunar core-mantle boundary is determined as (2.2±0.6)×10−4.[22]
  • The free core nutation of the Moon is determined as 367±100 yr.[22]

Gravitational physicsEdit

Photo galleryEdit

See alsoEdit


  1. ^ During the round-trip time, an Earth observer will have moved by around 1 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.
  1. ^ Chapront, J.; Chapront-Touzé, M.; Francou, G. (1999). "Determination of the lunar orbital and rotational parameters and of the ecliptic reference system orientation from LLR measurements and IERS data". Astronomy and Astrophysics. 343: 624–633. Bibcode:1999A&A...343..624C.
  2. ^ Mazarico, Erwan; Sun, Xiaoli; Torre, Jean-Marie; Courde, Clément; Chabé, Julien; Aimar, Mourad; Mariey, Hervé; Maurice, Nicolas; Barker, Michael K.; Mao, Dandan; Cremons, Daniel R. (6 August 2020). "First two-way laser ranging to a lunar orbiter: infrared observations from the Grasse station to LRO's retro-reflector array". Earth, Planets and Space. 72 (1): 113. doi:10.1186/s40623-020-01243-w. ISSN 1880-5981.
  3. ^ Smullin, Louis D.; Fiocco, Giorgio (1962). "Optical Echoes from the Moon". Nature. 194 (4835): 1267. Bibcode:1962Natur.194.1267S. doi:10.1038/1941267a0.
  4. ^ Bender, P. L.; et al. (1973). "The Lunar Laser Ranging Experiment: Accurate ranges have given a large improvement in the lunar orbit and new selenophysical information" (PDF). Science. 182 (4109): 229–238. Bibcode:1973Sci...182..229B. doi:10.1126/science.182.4109.229. PMID 17749298.
  5. ^ a b Newman, Michael E. (26 September 2017). "To the Moon and Back … in 2.5 Seconds". NIST. Retrieved 27 January 2021.
  6. ^ McDonald, K. (26 April 2010). "UC San Diego Physicists Locate Long Lost Soviet Reflector on Moon". University of California, San Diego. Retrieved 27 April 2010.
  7. ^ a b c Williams, James G.; Dickey, Jean O. (2002). Lunar Geophysics, Geodesy, and Dynamics (PDF). 13th International Workshop on Laser Ranging. 7–11 October 2002. Washington, D. C.
  8. ^ "It's Not Just The Astronauts That Are Getting Older". Universe Today. 10 March 2010. Retrieved 24 August 2012.
  9. ^ Currie, Douglas; Dell'Agnello, Simone; Delle Monache, Giovanni (April–May 2011). "A Lunar Laser Ranging Retroreflector Array for the 21st Century". Acta Astronautica. 68 (7–8): 667–680. Bibcode:2011AcAau..68..667C. doi:10.1016/j.actaastro.2010.09.001.
  10. ^ Tune, Lee (10 June 2015). "UMD, Italy & MoonEx Join to Put New Laser-Reflecting Arrays on Moon". UMD Right Now. University of Maryland.
  11. ^ Boyle, Alan (12 July 2017). "Moon Express unveils its roadmap for giant leaps to the lunar surface ... and back again". GeekWire. Retrieved 15 March 2018.
  12. ^ Moon Express Lunar Scout (MX-1E), RocketLaunch.Live, retrieved 27 July 2019
  13. ^ "MX-1E 1, 2, 3". Retrieved 24 May 2020.
  14. ^ Cite journal requires |journal= (help); Missing or empty |title= (help)
  15. ^ Seeber, Günter (2003). Satellite Geodesy (2nd ed.). de Gruyter. p. 439. ISBN 978-3-11-017549-3. OCLC 52258226.
  16. ^ Murphy, T. W. (2013). "Lunar laser ranging: the millimeter challenge" (PDF). Reports on Progress in Physics. 76 (7): 2. arXiv:1309.6294. Bibcode:2013RPPh...76g6901M. doi:10.1088/0034-4885/76/7/076901. PMID 23764926.
  17. ^ a b Espenek, F. (August 1994). "NASA - Accuracy of Eclipse Predictions". NASA/GSFC. Retrieved 4 May 2008.
  18. ^ Merkowitz, Stephen M. (2 November 2010). "Tests of Gravity Using Lunar Laser Ranging". Living Reviews in Relativity. 13 (1): 7. doi:10.12942/lrr-2010-7. ISSN 1433-8351. PMC 5253913. PMID 28163616.
  19. ^ a b Battat, J. B. R.; Murphy, T. W.; Adelberger, E. G.; et al. (January 2009). "The Apache Point Observatory Lunar Laser-ranging Operation (APOLLO): Two Years of Millimeter-Precision Measurements of the Earth-Moon Range1". Publications of the Astronomical Society of the Pacific. 121 (875): 29–40. Bibcode:2009PASP..121...29B. doi:10.1086/596748. JSTOR 10.1086/596748.
  20. ^ "Lunar Laser Ranging Observations from 1969 to May 2013". SYRTE Paris Observatory. Retrieved 3 June 2014.
  21. ^ Bills, B. G.; Ray, R. D. (1999). "Lunar Orbital Evolution: A Synthesis of Recent Results". Geophysical Research Letters. 26 (19): 3045–3048. Bibcode:1999GeoRL..26.3045B. doi:10.1029/1999GL008348.
  22. ^ a b c Viswanathan, V.; Rambaux, N.; Fienga, A.; Laskar, J.; Gastineau, M. (9 July 2019). "Observational Constraint on the Radius and Oblateness of the Lunar Core‐Mantle Boundary". Geophysical Research Letters. 46 (13): 7295–7303. arXiv:1903.07205. doi:10.1029/2019GL082677.
  23. ^ Kopeikin, S.; Xie, Y. (2010). "Celestial reference frames and the gauge freedom in the post-Newtonian mechanics of the Earth–Moon system". Celestial Mechanics and Dynamical Astronomy. 108 (3): 245–263. Bibcode:2010CeMDA.108..245K. doi:10.1007/s10569-010-9303-5.
  24. ^ Adelberger, E. G.; Heckel, B. R.; Smith, G.; Su, Y.; Swanson, H. E. (1990). "Eötvös experiments, lunar ranging and the strong equivalence principle". Nature. 347 (6290): 261–263. Bibcode:1990Natur.347..261A. doi:10.1038/347261a0.
  25. ^ Williams, J. G.; Newhall, X. X.; Dickey, J. O. (1996). "Relativity parameters determined from lunar laser ranging". Physical Review D. 53 (12): 6730–6739. Bibcode:1996PhRvD..53.6730W. doi:10.1103/PhysRevD.53.6730. PMID 10019959.
  26. ^ Viswanathan, V; Fienga, A; Minazzoli, O; Bernus, L; Laskar, J; Gastineau, M (May 2018). "The new lunar ephemeris INPOP17a and its application to fundamental physics". Monthly Notices of the Royal Astronomical Society. 476 (2): 1877–1888. arXiv:1710.09167. doi:10.1093/mnras/sty096.
  27. ^ Müller, J.; Biskupek, L. (2007). "Variations of the gravitational constant from lunar laser ranging data". Classical and Quantum Gravity. 24 (17): 4533. doi:10.1088/0264-9381/24/17/017.

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