Lunar Laser Ranging experiments

Last updated

Lunar Laser Ranging Experiment from the Apollo 11 mission Apollo 11 Lunar Laser Ranging Experiment.jpg
Lunar Laser Ranging Experiment from the Apollo 11 mission

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 several retroreflectors installed on the Moon. Three were placed by the United States' Apollo program (11, 14, and 15), two by the Soviet Lunokhod 1 and 2 missions, [1] and one by India's Chandrayaan-3 mission. [2] [3]

Contents

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 range measurement can be made using retroreflectors, since because of their small size, the temporal spread in the reflected signal is much smaller [4] and because the return will be more evenly reflected with less diffusion.

Laser ranging measurements can also be made with retroreflectors installed on Moon-orbiting satellites such as the LRO. [5] [6]

History

Apollo 15 LRRR ALSEP AS15-85-11468.jpg
Apollo 15 LRRR
Apollo 15 LRRR schematic Laser Ranging Retroreflector Apollo 15.svg
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. [7] Similar measurements were obtained later the same year by a Soviet team at the Crimean Astrophysical Observatory using a Q-switched ruby laser. [8]

Shortly thereafter, Princeton University graduate student James Faller proposed placing optical reflectors on the Moon to improve the accuracy of the measurements. [9] 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. [9] 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. [10] Lunokhod 2's array continues to return signals to Earth. [11] The Lunokhod arrays suffer from decreased performance in direct sunlight—a factor considered in reflector placement during the Apollo missions. [12]

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. [13] [14] [15] MX-1E was set to launch in July 2020, [16] however, as of February 2020, the launch of the MX-1E has been canceled. [17] India's Chandrayaan-3 lunar lander successfully placed a sixth reflector on the Moon in August 2023. [3] MoonLIGHT will be launched in early 2024 with a Commercial Lunar Payload Services (CLPS) mission. [18]

Principle

Annotated image of the near side of the Moon showing the location of retroreflectors left on the surface by Apollo and Lunokhod missions Lunar retroreflector locations.jpg
Annotated image of the near side of the Moon showing the location of retroreflectors left on the surface by Apollo and Lunokhod missions

The distance to the Moon is calculated approximately using the equation: distance = (speed of light × duration of delay due to reflection) / 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 Earth's atmosphere, the location of the observing station and its motion due to crustal motion and tides, and relativistic effects. [20] [21] 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. [22] The orbits of the Moon and planets are integrated numerically along with the orientation of the Moon called physical libration. [23]

At the Moon's surface, the beam is about 6.5 kilometers (4.0 mi) wide [24] [lower-roman 1] 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 a pulse of 3×1017 photons [25] aimed at the reflector, only about 1–5 are received back on Earth, even under good conditions. [26] 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. [27] 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

List of observatories

The table below presents a list of active and inactive Lunar Laser Ranging stations on Earth. [22] [28]

Lunar Laser Ranging stations
ObservatoryProjectOperating timespanTelescopeLaserRange accuracyRef.
McDonald Observatory, Texas, USMLRS1969–1985

1985–2013

2.7 m694 nm, 7 J

532 nm, 200 ps, 150 mJ

 [29]

[22]

Crimean Astrophysical Observatory (CrAO), USSR1974, 1982–1984694 nm3.0–0.6 m [30]
Côte d'Azur Observatory (OCA), Grasse, FranceMeO1984–1986

1986–2010

2010–present (2021)

694 nm

532 nm, 70 ps, 75 mJ

532/1064 nm

 [22] [31]
Haleakala Observatory, Hawaii, USLURE1984–1990532 nm, 200 ps, 140 mJ2.0 cm [22] [32]
Matera Laser Ranging Observatory (MLRO), Italy2003–present (2021)532 nm
Apache Point Observatory, New Mexico, US APOLLO 2006–2021

2021–present (2023)

532 nm, 100 ps, 115 mJ1.1 mm [22]

[33]

Geodetic Observatory Wettzell, GermanyWLRS2018–present (2021)1064 nm, 10 ps, 75 mJ [34]
Yunnan Astronomical Observatory, Kunming, China20181.2 m532 nm, 10 ns, 3 Jmeter level [35]

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 cm weighted rms residual.

The range model includes [36] [37]

For the terrestrial model, the IERS Conventions (2010) is a source of detailed information. [38]

Results

Lunar laser ranging measurement data is available from the Paris Observatory Lunar Analysis Center, [39] the International Laser Ranging Service archives, [40] [41] and the active stations. Some of the findings of this long-term experiment are: [22]

Properties of the Moon

Gravitational physics

See also

Related Research Articles

<span class="mw-page-title-main">Moon</span> Natural satellite orbiting Earth

The Moon is Earth's only natural satellite. It orbits at an average distance of 384,400 km (238,900 mi), about 30 times the diameter of Earth. Tidal forces between Earth and the Moon have over time synchronized the Moon's orbital period with its rotation period at 29.5 Earth days, causing the same side of the Moon to always face Earth. The Moon's gravitational pull – and to a lesser extent, the Sun's – are the main drivers of Earth's tides.

<span class="mw-page-title-main">Tidal acceleration</span> Natural phenomenon due to which tidal locking occurs

Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite and the primary planet that it orbits. The acceleration causes a gradual recession of a satellite in a prograde orbit, and a corresponding slowdown of the primary's rotation. The process eventually leads to tidal locking, usually of the smaller body first, and later the larger body. The Earth–Moon system is the best-studied case.

<span class="mw-page-title-main">Corner reflector</span> Retroreflector with three orthogonal, intersecting flat surfaces

A corner reflector is a retroreflector consisting of three mutually perpendicular, intersecting flat surfaces, which reflects waves directly towards the source, but translated. The three intersecting surfaces often have square shapes. Radar corner reflectors made of metal are used to reflect radio waves from radar sets. Optical corner reflectors, called corner cubes or cube corners, made of three-sided glass prisms, are used in surveying and laser ranging.

<span class="mw-page-title-main">Lunokhod programme</span> Soviet Moon rover program

Lunokhod was a series of Soviet robotic lunar rovers designed to land on the Moon between 1969 and 1977. Lunokhod 1 was the first roving remote-controlled robot to land on an extraterrestrial body.

<i>Lunokhod 1</i> Soviet lunar rover; first rover to operate on the Moon)

Lunokhod 1, also known as Аппарат 8ЕЛ № 203 was the first robotic rover on the Moon and the first to freely move across the surface of an astronomical object beyond the Earth. Sent by the Soviet Union it was part of the robotic rovers Lunokhod program. The Luna 17 spacecraft carried Lunokhod 1 to the Moon in 1970. Lunokhod 0 (No.201), the previous and first attempt to land a rover, launched in February 1969 but failed to reach Earth orbit.

<i>Lunokhod 2</i> Second robotic Moon rover (1973)

Lunokhod 2 was the second of two uncrewed lunar rovers that landed on the Moon by the Soviet Union as part of the Lunokhod programme.

<span class="mw-page-title-main">Retroreflector</span> Device to reflect radiation back to its source

A retroreflector is a device or surface that reflects radiation back to its source with minimum scattering. This works at a wide range of angle of incidence, unlike a planar mirror, which does this only if the mirror is exactly perpendicular to the wave front, having a zero angle of incidence. Being directed, the retroflector's reflection is brighter than that of a diffuse reflector. Corner reflectors and cat's eye reflectors are the most used kinds.

<i>Luna 17</i> 1970 Soviet uncrewed lunar mission

Luna 17 was an uncrewed space mission of the Luna program, also called Lunik 17. It deployed the first robotic rover onto the surface of the Moon.

<span class="mw-page-title-main">Libration</span> Apparent oscillation of a minor body seen from the major body it orbits

In lunar astronomy, libration is the cyclic variation in the apparent position of the Moon perceived by Earth-bound observers and caused by changes between the orbital and rotational planes of the moon. It causes an observer to see slightly different hemispheres of the surface at different times. It is similar in both cause and effect to the changes in the Moon's apparent size due to changes in distance. It is caused by three mechanisms detailed below, two of which cause a relatively tiny physical libration via tidal forces exerted by the Earth. Such true librations are known as well for other moons with locked rotation.

<span class="mw-page-title-main">Satellite laser ranging</span>

In satellite laser ranging (SLR) a global network of observation stations measures the round trip time of flight of ultrashort pulses of light to satellites equipped with retroreflectors. This provides instantaneous range measurements of millimeter level precision which can be accumulated to provide accurate measurement of orbits and a host of important scientific data. The laser pulse can also be reflected by the surface of a satellite without a retroreflector, which is used for tracking space debris.

<span class="mw-page-title-main">Apache Point Observatory Lunar Laser-ranging Operation</span>

The Apache Point Observatory Lunar Laser-ranging Operation, or APOLLO, is a project at the Apache Point Observatory in New Mexico. It is an extension and advancement of previous Lunar Laser Ranging experiments, which use retroreflectors on the Moon to track changes in lunar orbital distance and motion.

<span class="mw-page-title-main">Lunar distance</span> Distance from center of Earth to center of Moon

The instantaneous Earth–Moon distance, or distance to the Moon, is the distance from the center of Earth to the center of the Moon. Lunar distance, or Earth–Moon characteristic distance, is a unit of measure in astronomy. More technically, it is the semi-major axis of the geocentric lunar orbit. The lunar distance is on average approximately 385,000 km (239,000 mi), or 1.28 light-seconds; this is roughly 30 times Earth's diameter or 9.5 times Earth's circumference. Around 389 lunar distances make up an AU astronomical unit.

Lunar theory attempts to account for the motions of the Moon. There are many small variations in the Moon's motion, and many attempts have been made to account for them. After centuries of being problematic, lunar motion can now be modeled to a very high degree of accuracy.

<span class="mw-page-title-main">Third-party evidence for Apollo Moon landings</span> Independent confirmations of Apollo Moon landings

Third-party evidence for Apollo Moon landings is evidence, or analysis of evidence, about the Moon landings that does not come from either NASA or the U.S. government, or the Apollo Moon landing hoax theorists. This evidence provides independent confirmation of NASA's account of the six Apollo program Moon missions flown between 1969 and 1972.

The Hollow Moon and the closely related Spaceship Moon are pseudoscientific hypotheses that propose that Earth's Moon is either wholly hollow or otherwise contains a substantial interior space. No scientific evidence exists to support the idea; seismic observations and other data collected since spacecraft began to orbit or land on the Moon indicate that it has a solid, differentiated interior, with a thin crust, extensive mantle, and a dense core which is significantly smaller than Earth's.

Jet Propulsion Laboratory Development Ephemeris designates one of a series of mathematical models of the Solar System produced at the Jet Propulsion Laboratory in Pasadena, California, for use in spacecraft navigation and astronomy. The models consist of numeric representations of positions, velocities and accelerations of major Solar System bodies, tabulated at equally spaced intervals of time, covering a specified span of years. Barycentric rectangular coordinates of the Sun, eight major planets and Pluto, and geocentric coordinates of the Moon are tabulated.

MoonLIGHT is a laser retroreflector developed as a collaboration primarily between the University of Maryland in the United States, and the Italian National Institute for Nuclear Physics - National Laboratories of Frascati (INFN-LNF) to complement and expand on the Lunar Laser Ranging experiment started with the Apollo Program in 1969. MoonLIGHT was planned to be launched in July 2020 as a secondary payload on the MX-1E lunar lander built by the private company Moon Express. However, as of February 2020, the launch of the MX-1E has been canceled. In 2018 INFN proposed to the European Space Agency (ESA) the MoonLIGHT Pointing Actuators (MPAc) project and was contracted by ESA to deliver it. MPAc is an INFN development for ESA, with auxiliary support by the Italian Space Agency (ASI) for prototyping work. In 2021, ESA agreed with NASA to launch MPAc with a Commercial Lunar Payload Services (CLPS) mission. Nova-C, the lander on which MPAc will be integrated, is designed by Intuitive Machines and the landing site is Reiner Gamma. The expected launch date of the Nova-C mission carrying the instrument, IM-3, is in 2025.

<span class="mw-page-title-main">Queqiao-1</span> Chinese lunar communications satellite

Queqiao relay satellite (Chinese: 鹊桥号中继卫星; pinyin: Quèqiáo hào zhōngjì wèixīng; lit. 'Magpie Bridge relay satellite'), is the first of the pair of communications relay and radio astronomy satellites for the Chinese Lunar Exploration Program. The China National Space Administration (CNSA) launched the Queqiao relay satellite on 20 May 2018 to a halo orbit around the Earth–Moon L2 Lagrangian point Queqiao is the first ever communication relay and radio astronomy satellite at this location.

<span class="mw-page-title-main">Laser Ranging Retroreflector</span> 1969 American experiment on the Moon

The Laser Ranging Retroreflector (LRRR) is the first ever deployable lunar laser ranging experiment. It was carried on Apollo 11 as part of the Early Apollo Scientific Experiments Package, and on Apollo 14 and Apollo 15 as part of the Apollo Lunar Surface Experiments Package (ALSEP). The LRRR consists of a series of corner reflectors set within a panel. Laser beams sent from Earth are bounced off the retroreflector and the timing of the return signal can be used to measure the distance from the signal source to the reflector. The reflector was conceived by James E. Faller in 1961. The experiment's principal investigator was initially Carroll Alley of the University of Maryland who was eventually succeeded by Faller.

References

  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. ↑ "Chandrayaan-3". ISRO. Retrieved 15 August 2023.
  3. 1 2 Dhillon, Amrit (23 August 2023). "India lands spacecraft near south pole of moon in historic first". The Guardian . Retrieved 23 August 2023.
  4. ↑ Müller, Jürgen; Murphy, Thomas W.; Schreiber, Ulrich; Shelus, Peter J.; Torre, Jean-Marie; Williams, James G.; Boggs, Dale H.; Bouquillon, Sebastien; Bourgoin, Adrien; Hofmann, Franz (2019). "Lunar Laser Ranging: a tool for general relativity, lunar geophysics and Earth science". Journal of Geodesy. 93 (11): 2195–2210. Bibcode:2019JGeod..93.2195M. doi:10.1007/s00190-019-01296-0. ISSN   1432-1394. S2CID   202641440.
  5. ↑ 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.; Bouquillon, Sébastien; Carlucci, Teddy; Viswanathan, Vishnu; Lemoine, Frank; Bourgoin, Adrien; Exertier, Pierre; Neumann, Gregory; Zuber, Maria; Smith, David (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. Bibcode:2020EP&S...72..113M. doi: 10.1186/s40623-020-01243-w . hdl: 11603/19523 . ISSN   1880-5981.
  6. ↑ Kornei, Katherine (15 August 2020). "How Do You Solve a Moon Mystery? Fire a Laser at It". The New York Times. ISSN   0362-4331 . Retrieved 1 June 2021.
  7. ↑ Smullin, Louis D.; Fiocco, Giorgio (1962). "Optical Echoes from the Moon". Nature . 194 (4835): 1267. Bibcode:1962Natur.194.1267S. doi: 10.1038/1941267a0 . S2CID   4145783.
  8. ↑ 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. S2CID   32027563.
  9. 1 2 Newman, Michael E. (26 September 2017). "To the Moon and Back … in 2.5 Seconds". NIST. Retrieved 27 January 2021.
  10. ↑ McDonald, K. (26 April 2010). "UC San Diego Physicists Locate Long Lost Soviet Reflector on Moon". University of California, San Diego. Archived from the original on 30 April 2010. Retrieved 27 April 2010.
  11. 1 2 3 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.
  12. ↑ "It's Not Just The Astronauts That Are Getting Older". Universe Today . 10 March 2010. Retrieved 24 August 2012.
  13. ↑ 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.
  14. ↑ Tune, Lee (10 June 2015). "UMD, Italy & MoonEx Join to Put New Laser-Reflecting Arrays on Moon". UMD Right Now. University of Maryland. Archived from the original on 22 March 2018. Retrieved 21 March 2018.
  15. ↑ 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.
  16. ↑ Moon Express Lunar Scout (MX-1E), RocketLaunch.Live, archived from the original on 27 July 2019, retrieved 27 July 2019
  17. ↑ "MX-1E 1, 2, 3" . Retrieved 24 May 2020.
  18. ↑ "NASA Payloads for (CLPS PRISM) CP-11".
  19. ↑ "Was Galileo Wrong?". NASA. 6 May 2004. Archived from the original on 30 April 2022.
  20. ↑ Seeber, Günter (2003). Satellite Geodesy (2nd ed.). de Gruyter. p.  439. ISBN   978-3-11-017549-3. OCLC   52258226.
  21. ↑ Williams, James G.; Boggs, Dale H. (2020). "The JPL Lunar Laser range model 2020". ssd.jpl.nasa.gov. Retrieved 24 May 2021.
  22. 1 2 3 4 5 6 7 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. S2CID   15744316.
  23. 1 2 Park, Ryan S.; Folkner, William M.; Williams, James G.; Boggs, Dale H. (2021). "The JPL Planetary and Lunar Ephemerides DE440 and DE441". The Astronomical Journal. 161 (3): 105. Bibcode:2021AJ....161..105P. doi: 10.3847/1538-3881/abd414 . ISSN   1538-3881. S2CID   233943954.
  24. 1 2 Espenek, F. (August 1994). "NASA – Accuracy of Eclipse Predictions". NASA/GSFC. Retrieved 4 May 2008.
  25. ↑ "The Basics of Lunar Ranging" . Retrieved 21 July 2023.
  26. ↑ Merkowitz, Stephen M. (2 November 2010). "Tests of Gravity Using Lunar Laser Ranging". Living Reviews in Relativity. 13 (1): 7. Bibcode:2010LRR....13....7M. doi: 10.12942/lrr-2010-7 . ISSN   1433-8351. PMC   5253913 . PMID   28163616.
  27. 1 2 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.
  28. ↑ Biskupek, Liliane; Müller, Jürgen; Torre, Jean-Marie (3 February 2021). "Benefit of New High-Precision LLR Data for the Determination of Relativistic Parameters". Universe. 7 (2): 34. arXiv: 2012.12032 . Bibcode:2021Univ....7...34B. doi: 10.3390/universe7020034 .
  29. ↑ Bender, P. L.; Currie, D. G.; Dickey, R. H.; Eckhardt, D. H.; Faller, J. E.; Kaula, W. M.; Mulholland, J. D.; Plotkin, H. H.; Poultney, S. K.; et al. (1973). "The Lunar Laser Ranging Experiment". Science. 182 (4109): 229–238. Bibcode:1973Sci...182..229B. doi:10.1126/science.182.4109.229. ISSN   0036-8075. PMID   17749298. S2CID   32027563.
  30. ↑ Yagudina (2018). "Processing and analysis of lunar laser ranging observations in Crimea in 1974-1984". Institute of Applied Astronomy of the Russian Academy of Sciences. Retrieved 1 June 2021.
  31. ↑ Chabé, Julien; Courde, Clément; Torre, Jean-Marie; Bouquillon, Sébastien; Bourgoin, Adrien; Aimar, Mourad; Albanèse, Dominique; Chauvineau, Bertrand; Mariey, Hervé; Martinot-Lagarde, Grégoire; Maurice, Nicolas (2020). "Recent Progress in Lunar Laser Ranging at Grasse Laser Ranging Station". Earth and Space Science. 7 (3): e2019EA000785. Bibcode:2020E&SS....700785C. doi: 10.1029/2019EA000785 . ISSN   2333-5084. S2CID   212785296.
  32. ↑ "Lure Observatory". Institute for Astronomy, University of Hawaii. 29 January 2002. Retrieved 3 June 2021.
  33. ↑ "APOL - Apache Point Observatory".
  34. ↑ Eckl, Johann J.; Schreiber, K. Ulrich; Schüler, Torben (30 April 2019). "Lunar laser ranging utilizing a highly efficient solid-state detector in the near-IR". In Domokos, Peter; James, Ralph B; Prochazka, Ivan; Sobolewski, Roman; Gali, Adam (eds.). Quantum Optics and Photon Counting 2019. Vol. 11027. International Society for Optics and Photonics. p. 1102708. Bibcode:2019SPIE11027E..08E. doi:10.1117/12.2521133. ISBN   9781510627208. S2CID   155720383.
  35. ↑ Li Yuqiang, 李语强; Fu Honglin, 伏红林; Li Rongwang, 李荣旺; Tang Rufeng, 汤儒峰; Li Zhulian, 李祝莲; Zhai Dongsheng, 翟东升; Zhang Haitao, 张海涛; Pi Xiaoyu, 皮晓宇; Ye Xianji, 叶贤基; Xiong Yaoheng, 熊耀恒 (27 January 2019). "Research and Experiment of Lunar Laser Ranging in Yunnan Observatories". Chinese Journal of Lasers. 46 (1): 0104004. doi:10.3788/CJL201946.0104004. S2CID   239211201.
  36. 1 2 Pavlov, Dmitry A.; Williams, James G.; Suvorkin, Vladimir V. (2016). "Determining parameters of Moon's orbital and rotational motion from LLR observations using GRAIL and IERS-recommended models". Celestial Mechanics and Dynamical Astronomy. 126 (1): 61–88. arXiv: 1606.08376 . Bibcode:2016CeMDA.126...61P. doi:10.1007/s10569-016-9712-1. ISSN   0923-2958. S2CID   119116627.
  37. ↑ Williams, James G.; Boggs, Dale H. (2020). "The JPL Lunar Laser range model 2020". ssd.jpl.nasa.gov. Retrieved 1 June 2021.
  38. ↑ "IERS - IERS Technical Notes - IERS Conventions (2010)". www.iers.org. Retrieved 1 June 2021.
  39. ↑ "Lunar Laser Ranging Observations from 1969 to May 2013". SYRTE Paris Observatory. Retrieved 3 June 2014.
  40. ↑ "International Laser Ranging Service".
  41. ↑ "International Laser Ranging Service".
  42. 1 2 Williams, James G.; Boggs, Dale H. (2016). "Secular tidal changes in lunar orbit and Earth rotation". Celestial Mechanics and Dynamical Astronomy. 126 (1): 89–129. Bibcode:2016CeMDA.126...89W. doi:10.1007/s10569-016-9702-3. ISSN   0923-2958. S2CID   124256137.
  43. ↑ 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 .
  44. ↑ Williams, James G.; Boggs, Dale H.; Yoder, Charles F.; Ratcliff, J. Todd; Dickey, Jean O. (2001). "Lunar rotational dissipation in solid body and molten core". Journal of Geophysical Research: Planets. 106 (E11): 27933–27968. Bibcode:2001JGR...10627933W. doi: 10.1029/2000JE001396 .
  45. ↑ Rambaux, N.; Williams, J. G. (2011). "The Moon's physical librations and determination of their free modes" (PDF). Celestial Mechanics and Dynamical Astronomy. 109 (1): 85–100. Bibcode:2011CeMDA.109...85R. doi:10.1007/s10569-010-9314-2. S2CID   45209988.
  46. 1 2 3 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 . Bibcode:2019GeoRL..46.7295V. doi:10.1029/2019GL082677. S2CID   119508748.
  47. ↑ Wagner, R. V.; Nelson, D. M.; Plescia, J. B.; Robinson, M. S.; Speyerer, E. J.; Mazarico, E. (2017). "Coordinates of anthropogenic features on the Moon". Icarus. 283: 92–103. Bibcode:2017Icar..283...92W. doi: 10.1016/j.icarus.2016.05.011 . ISSN   0019-1035.
  48. 1 2 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.
  49. ↑ 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. S2CID   122789819.
  50. ↑ 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. S2CID   4286881.
  51. ↑ 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 . Bibcode:2018MNRAS.476.1877V. doi: 10.1093/mnras/sty096 .
  52. ↑ 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. S2CID   120195732.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.