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 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]

History
Apollo 15 LRRR
Apollo 15 LRRR schematic

The first successful lunar ranging tests were carried out in 1962 when a team from the Massachusetts Institute of Technology succeeded in observing laser pulses reflected from the Moon's surface using a laser with a 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, but no return signals were detected after 1971 until a team from University of California rediscovered the array in April 2010 using images from NASA's Lunar Reconnaissance Orbiter.[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]

Principle

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.[14] 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.[15]

At the Moon's surface, the beam is about 6.5 kilometers (4.0 mi) wide[16][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 1021 photons aimed at the reflector, only one is received back on Earth, even under good conditions.[17] They can be identified as originating from the laser because the laser is highly monochromatic.

The distance to the Moon can now be measured with millimeter precision.[18] 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.

Results

Lunar laser ranging measurement data is available from the Paris Observatory Lunar Analysis Center,[19] and the active stations. Some of the findings of this long-term experiment are:

Properties of the Moon
  • The distance to the Moon can be measured with millimeter precision.[18]
  • The Moon is spiraling away from Earth at a rate of 3.8 cm/year.[16] This rate has been described as anomalously high.[20]
  • 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.[21]
  • The polar flattening of the lunar core-mantle boundary is determined as (2.2±0.6)×10−4.[21]
  • The free core nutation of the Moon is determined as 367±100 yr.[21]

Gravitational physics

See also

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. 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.
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  21. 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.
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