Lunar Laser Ranging (LLR) is the practice of measuring the distance between the surfaces of the

Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...

and the

Moon The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar ...

using

laser ranging A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word ''laser'' originated as an acronym for light amplification by stimulated emission of radi ...

. The distance can be calculated from the

round-trip time In telecommunications, round-trip delay (RTD) or round-trip time (RTT) is the amount of time it takes for a signal to be sent ''plus'' the amount of time it takes for acknowledgement of that signal having been received. This time delay includes p ...

laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word ''laser'' originated as an acronym for light amplification by stimulated emission of radi ...

light pulses travelling at the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...

, which are reflected back to Earth by the Moon's surface or by one of several

retroreflector A retroreflector (sometimes called a retroflector or cataphote) is a device or surface that reflects light or other radiation back to its source with minimum scattering. This works at a wide range of angle of incidence (optics), angle of incidenc ...

s installed on the Moon. Three were placed by the United States'

Apollo program The Apollo program, also known as Project Apollo, was the United States human spaceflight program led by NASA, which Moon landing, landed the first humans on the Moon in 1969. Apollo followed Project Mercury that put the first Americans in sp ...

( 11, 14, and 15), two by the Soviet Lunokhod 1 and 2 missions, and one by India's

Chandrayaan-3 Chandrayaan-3 ( ) is the third mission in the Chandrayaan programme, a series of Exploration of the Moon, lunar-exploration missions developed by the ISRO, Indian Space Research Organisation (ISRO). The mission consists of a Chandrayaan-2#Vikra ...

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 range measurement can be made using retroreflectors, since because of their small size, the temporal spread in the reflected signal is much smaller 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.

History

The first successful lunar ranging tests were carried out in 1962 when

Louis Smullin Louis Dijour Smullin (February 5, 1916 – June 4, 2009) was an American electrical engineer who spend most of his career at the Massachusetts Institute of Technology (MIT). He is best known for his work with Giorgio Fiocco to measure the dis ...

and

Giorgio Fiocco Giorgio Fiocco (13 June 1931 – 31 July 2012) was an Italian physicist, known for the development of the Lidar for the remote sensing of the atmosphere. In 1962 at MIT, together with Louis Smullin, Fiocco developed the first Lidar system, ...

from the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...

succeeded in observing laser pulses reflected from the Moon's surface using a laser with a 50J 0.5 millisecond pulse length. Similar measurements were obtained later the same year by a Soviet team at the

Crimean Astrophysical Observatory The Crimean Astrophysical Observatory (CrAO, obs. code: 095) is located at Nauchnij research campus, near the Central Crimean city of Bakhchysarai, on the Crimean peninsula. CrAO is often called simply by its location and campus name ...

using a Q-switched

ruby laser A ruby laser is a solid-state laser that uses a synthetic ruby crystal as its gain medium. The first working laser was a ruby laser made by Theodore H. "Ted" Maiman at Hughes Research Laboratories on May 16, 1960. Ruby lasers produce pulses of ...

. Shortly thereafter,

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

graduate student James Faller proposed placing optical reflectors on the Moon to improve the accuracy of the measurements. This was achieved following the installation of a

array on July 21, 1969 by the crew of

Apollo 11 Apollo 11 was a spaceflight conducted from July 16 to 24, 1969, by the United States and launched by NASA. It marked the first time that humans Moon landing, landed on the Moon. Commander Neil Armstrong and Lunar Module pilot Buzz Aldrin l ...

. Two more retroreflector arrays were left by the

Apollo 14 Apollo 14 (January 31February 9, 1971) was the eighth crewed mission in the United States Apollo program, the third to Moon landing, land on the Moon, and the first to land in the Geology of the Moon#Highlands, lunar highlands. It was the las ...

and

Apollo 15 Apollo 15 (July 26August 7, 1971) was the ninth crewed mission in the Apollo program and the fourth Moon landing. It was the first List of Apollo missions#Alphabetical mission types, J mission, with a longer stay on the Moon and a greate ...

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 The Lick Observatory is an astronomical observatory owned and operated by the University of California. It is on the summit of Mount Hamilton (California), Mount Hamilton, in the Diablo Range just east of San Jose, California, United States. The ...

. Observations from

Air Force Cambridge Research Laboratories An atmosphere () is a layer of gases that envelop an astronomical object, held in place by the gravity of the object. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A stellar atmosphere ...

Lunar Ranging Observatory in Arizona, the Pic du Midi Observatory in France, the Tokyo

Astronomical Observatory An observatory is a location used for observing terrestrial, marine, or celestial events. Astronomy, climatology/meteorology, geophysics, oceanography and volcanology are examples of disciplines for which observatories have been constructed. Th ...

, and

McDonald Observatory McDonald Observatory is an astronomical observatory located near unincorporated community of Fort Davis in Jeff Davis County, Texas, United States. The facility is located on Mount Locke in the Davis Mountains of West Texas, with additional faci ...

in Texas soon followed. The uncrewed Soviet ''

Lunokhod 1 ''Lunokhod 1'' (Russian language, Russian: Луноход-1 "Moonwalker 1"), also known as Аппарат 8ЕЛ № 203 ("Device 8EL No. 203") was the first rover (space exploration), robotic rover lunar rover, on the Moon and the first to freel ...

'' and ''

Lunokhod 2 ''Lunokhod 2'' ( ("Moonwalker 2"), also known as Аппарат 8ЕЛ № 204 ("Device 8EL No. 204")) was the second of two uncrewed space mission, uncrewed lunar rover (space exploration), rovers that landed on the Moon by the Soviet Union as ...

'' 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 The National Aeronautics and Space Administration (NASA ) is an independent agencies of the United States government, independent agency of the federal government of the United States, US federal government responsible for the United States ...

Lunar Reconnaissance Orbiter The Lunar Reconnaissance Orbiter (LRO) is a NASA robotic spacecraft currently orbiting the Moon in an eccentric Polar orbit, polar mapping orbit. Data collected by LRO have been described as essential for planning NASA's future human and robotic ...

located the Lunokhod 1 rover on images and in April 2010 a team from University of California ranged the array. ''Lunokhod 2'' array continues to return signals to Earth. The Lunokhod arrays suffer from decreased performance in direct sunlight—a factor considered in reflector placement during the Apollo missions. 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 Nice ( ; ) is a city in and the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative city limits, with a population of nearly one million Apache Point Observatory Lunar Laser-ranging Operation 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 ...

(APOLLO) at the

Apache Point Observatory The Apache Point Observatory (APO; obs. code: 705) is an astronomical observatory located in the Sacramento Mountains in Sunspot, New Mexico, United States, approximately south of Cloudcroft. The observatory is operated by New Mexico State Un ...

New Mexico New Mexico is a state in the Southwestern United States, Southwestern region of the United States. It is one of the Mountain States of the southern Rocky Mountains, sharing the Four Corners region with Utah, Colorado, and Arizona. It also ...

. In the 2010s several new retroreflectors were planned. The

MoonLIGHT Moonlight consists of mostly sunlight (with little earthlight) reflected from the parts of the Moon's surface where the Sun's light strikes. History The ancient Greek philosopher Anaxagoras was aware that "''the sun provides the moon with its ...

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. MX-1E was set to launch in July 2020, however, as of February 2020, the launch of the MX-1E has been canceled. India's

lunar lander successfully placed a sixth reflector on the Moon in August 2023. MoonLIGHT will be launched in early 2024 with a

Commercial Lunar Payload Services Commercial Lunar Payload Services (CLPS) is a NASA program to hire companies to send small robotic landers and rovers to the Moon. Most landing sites are near the lunar south pole where they will scout for lunar resources, test in situ resource ...

(CLPS) mission.

Principle

The distance to the Moon is calculated using the equation: . Since the

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 In lunar astronomy, libration is the cyclic variation in the apparent position of the Moon that is perceived by observers on the Earth and caused by changes between the orbital and rotational planes of the moon. It causes an observer to see ...

polar motion Polar motion of the Earth is the motion of the Earth's rotation, Earth's rotational axis relative to its Earth's crust, crust. This is measured with respect to a reference frame in which the solid Earth is fixed (a so-called ''Earth-centered, Ea ...

weather Weather is the state of the atmosphere, describing for example the degree to which it is hot or cold, wet or dry, calm or stormy, clear or cloud cover, cloudy. On Earth, most weather phenomena occur in the lowest layer of the planet's atmo ...

, speed of light in various parts of air, propagation delay through

Earth's atmosphere The atmosphere of Earth is composed of a layer of gas mixture that surrounds the Earth's planetary surface (both lands and oceans), known collectively as air, with variable quantities of suspended aerosols and particulates (which create weathe ...

, the location of the observing station and its motion due to crustal motion and

tide Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another. Tide tables ...

s, and relativistic effects. The distance continually changes for a number of reasons, but averages between the center of the Earth and the center of the Moon. The orbits of the Moon and planets are integrated numerically along with the orientation of the Moon called physical

libration In lunar astronomy, libration is the cyclic variation in the apparent position of the Moon that is perceived by observers on the Earth and caused by changes between the orbital and rotational planes of the moon. It causes an observer to see ...

. At the Moon's surface, the beam is about wide and scientists liken the task of aiming the beam to using a rifle to hit a moving dime away. The reflected light is too weak to see with the human eye. Out of a pulse of 3×10¹⁷ photons aimed at the reflector, only about 15 are received back on Earth, even under good conditions. They can be identified as originating from the laser because the laser is highly

monochromatic A monochrome or monochromatic image, object or palette is composed of one color (or values of one color). Images using only shades of grey are called grayscale (typically digital) or black-and-white (typically analog). In physics, mon ...

. As of 2009, the distance to the Moon can be measured with millimeter precision. 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.

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 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. * The same program integrates the 3-axis orientation of the Moon called physical

Libration In lunar astronomy, libration is the cyclic variation in the apparent position of the Moon that is perceived by observers on the Earth and caused by changes between the orbital and rotational planes of the moon. It causes an observer to see ...

. The range model includes * The position of the ranging station accounting for motion due to

plate tectonics Plate tectonics (, ) is the scientific theory that the Earth's lithosphere comprises a number of large tectonic plates, which have been slowly moving since 3–4 billion years ago. The model builds on the concept of , an idea developed durin ...

Earth rotation Earth's rotation or Earth's spin is the rotation of planet Earth around its own Rotation around a fixed axis, axis, as well as changes in the orientation (geometry), orientation of the rotation axis in space. Earth rotates eastward, in progra ...

precession Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In o ...

nutation Nutation () is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behaviour of a mechanism. In an appropriate reference fra ...

, and

. * Tides in the solid Earth and seasonal motion of the solid Earth with respect to its

center of mass In physics, the center of mass of a distribution of mass in space (sometimes referred to as the barycenter or balance point) is the unique point at any given time where the weight function, weighted relative position (vector), position of the d ...

. * 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. *

Lorentz contraction Lorentz is a name derived from the Roman surname, Laurentius, which means "from Laurentum". It is the German form of Laurence. Notable people with the name include: Given name * Lorentz Aspen (born 1978), Norwegian heavy metal pianist and keyboa ...

of the Moon. *

Thermal expansion Thermal expansion is the tendency of matter to increase in length, area, or volume, changing its size and density, in response to an increase in temperature (usually excluding phase transitions). Substances usually contract with decreasing temp ...

and contraction of the retroreflector mounts. For the terrestrial model, the IERS Conventions (2010) is a source of detailed information.

Results

Lunar laser ranging measurement data is available from the Paris Observatory Lunar Analysis Center, the International Laser Ranging Service archives, 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. *The Moon is spiraling away from Earth at a rate of . This rate has been described as anomalously high. *The fluid core of the Moon was detected from the effects of core/mantle boundary dissipation. *The Moon has free physical librations that require one or more stimulating mechanisms. *Tidal dissipation in the Moon depends on tidal frequency. * The Moon probably has a liquid core of about 20% of the Moon's radius. The radius of the lunar core-mantle boundary is determined as . *The polar

flattening Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid) respectively. Other terms used are ellipticity, or oblateness. The usual notation for flattening is f ...

of the lunar core-mantle boundary is determined as . *The free core

of the Moon is determined as . *Accurate locations for retroreflectors serve as reference points visible to orbiting spacecraft.

Gravitational physics

* Einstein's theory of gravity (the

general theory of relativity General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physi ...

) predicts the Moon's orbit to within the accuracy of the laser ranging measurements. *

Gauge freedom In the physics of gauge theory, gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant Degrees of freedom (physics and chemistry), degrees of freedom in field (physics), field variab ...

plays a major role in a correct physical interpretation of the relativistic effects in the Earth-Moon system observed with LLR technique. * 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, strongly supporting the

strong equivalence principle The equivalence principle is the hypothesis that the observed equivalence of gravitational and inertial mass is a consequence of nature. The weak form, known for centuries, relates to masses of any composition in free fall taking the same tr ...

. * The universal force of

gravity In physics, gravity (), also known as gravitation or a gravitational interaction, is a fundamental interaction, a mutual attraction between all massive particles. On Earth, gravity takes a slightly different meaning: the observed force b ...

is very stable. The experiments have constrained the change in Newton's

gravitational constant The gravitational constant is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general relativity, theory of general relativity. It ...

''G'' to a factor of per year.

Gallery

File:ALSEP AS14-67-9386.jpg, Apollo 14 Lunar Ranging Retro Reflector ( LRRR) File:LunarPhotons.png,

APOLLO Apollo is one of the Twelve Olympians, Olympian deities in Ancient Greek religion, ancient Greek and Ancient Roman religion, Roman religion and Greek mythology, Greek and Roman mythology. Apollo has been recognized as a god of archery, mu ...

collaboration photon pulse return times File:Wettzell Laser Ranging System.jpg, Laser ranging facility at Wettzell fundamental station,

Bavaria Bavaria, officially the Free State of Bavaria, is a States of Germany, state in the southeast of Germany. With an area of , it is the list of German states by area, largest German state by land area, comprising approximately 1/5 of the total l ...

Germany Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total popu ...

File:Goddard Spaceflight Center Laser Ranging Facility.jpg, Laser Ranging at

Goddard Space Flight Center The Goddard Space Flight Center (GSFC) is a major NASA space research laboratory located approximately northeast of Washington, D.C., in Greenbelt, Maryland, United States. Established on May 1, 1959, as NASA's first space flight center, GSFC ...

References

External links

"Theory and Model for the New Generation of the Lunar Laser Ranging Data"
by Sergei Kopeikin
Apollo 15 Experiments - Laser Ranging Retroreflector
by the

Lunar and Planetary Institute The Lunar and Planetary Institute (LPI) is a scientific research institute dedicated to study of the Solar System, its formation, evolution, and current state. The Institute is part of the Universities Space Research Association (USRA) and is ...

"History of Laser Ranging and MLRS"
by the

University of Texas at Austin The University of Texas at Austin (UT Austin, UT, or Texas) is a public university, public research university in Austin, Texas, United States. Founded in 1883, it is the flagship institution of the University of Texas System. With 53,082 stud ...

, Center for Space Research
"Lunar Retroreflectors"
by Tom Murphy

in Grasse, France
Lunar Laser Ranging
from International Laser Ranging Service
"UW researcher plans project to pin down moon's distance from Earth"
by Vince Stricherz, UW Today, 14 January 2002
"What Neil & Buzz Left on the Moon"
by Science@NASA, 20 July 2004
"Apollo 11 Experiment Still Returning Results"
by Robin Lloyd,

CNN Cable News Network (CNN) is a multinational news organization operating, most notably, a website and a TV channel headquartered in Atlanta. Founded in 1980 by American media proprietor Ted Turner and Reese Schonfeld as a 24-hour cable ne ...

, 21 July 1999
"Shooting Lasers at the Moon: Hal Walker and the Lunar Retroreflector"
by Smithsonian National Air and Space Museum, YouTube, 20 Aug 2019 {{Authority control Apollo program hardware Tests of general relativity