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Lunar laser ranging

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Title: Lunar laser ranging  
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Subject: Geodesy, Axial precession, Satellite geodesy, LLR, Lunar theory
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Lunar laser ranging

The ongoing Lunar Laser Ranging Experiment measures the distance between the Earth and the Moon using laser ranging. Lasers on Earth are aimed at retroreflectors planted on the Moon during the Apollo program (11), and the time for the reflected light to return is determined.

Early tests, Apollo, and Lunokhod

The first successful tests were carried out in 1962 when a team from the Massachusetts Institute of Technology succeeded in observing reflected laser pulses using a laser with a millisecond pulse length. Similar measurements were obtained later the same year by a Soviet team at the Crimean Astrophysical Observatory using a Q-switched ruby laser.[1] Greater accuracy was achieved following the installation of a retroreflector array on July 21, 1969, by the crew of Apollo 11, while two more retroreflector arrays left by the Apollo 14 and Apollo 15 missions have also contributed to the experiment. Successful lunar laser range measurements to the retroreflectors were first reported by the 3.1m telescope at Lick Observatory, 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.

The unmanned 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.[2] Lunokhod 2's array continues to return signals to Earth.[3] The Lunokhod arrays suffer from decreased performance in direct sunlight, a factor which was considered in the reflectors placed during the Apollo missions.[4]

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 Grasse, France; and the Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) at the Apache Point Observatory in New Mexico.


The distance to the Moon is calculated approximately using this equation:

Distance = (Speed of light × Time taken for light to reflect) / 2.

In actuality, the round-trip time of about 2½ seconds is affected by the relative motion of the Earth and the Moon, the rotation of the Earth, lunar libration, weather, polar motion, propagation delay through Earth's atmosphere, the motion of the observing station due to crustal motion and tides, velocity of light in various parts of air and relativistic effects.[5] Nonetheless, the Earth-Moon distance has been measured with increasing accuracy for more than 35 years. The distance continually changes for a number of reasons, but averages about 384,467 kilometers (238,897 miles).

At the Moon's surface, the beam is only about 6.5 kilometers (four miles) wide[6] and scientists liken the task of aiming the beam to using a rifle to hit a moving dime 3 kilometers (approximately two miles) away. The reflected light is too weak to be seen with the human eye: out of 1017 photons aimed at the reflector, only one will be received back on Earth every few seconds, even under good conditions. They can be identified as originating from the laser because the laser is highly monochromatic. 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 one hundredth of an inch.[4][7] As of 2002 work is progressing on increasing the accuracy of the Earth-Moon measurements to near millimeter accuracy, though the performance of the reflectors continues to degrade with age.[4]


Some of the findings of this long-term experiment are:

  • The Moon is spiraling away from Earth at a rate of 3.8 cm per year.[6] This rate has been described as anomalously high.[8]
  • The Moon probably has a liquid core of about 20% of the Moon's radius.[3]
  • The universal force of gravity is very stable. The experiments have put an upper limit on the change in Newton's gravitational constant G of less than 1 part in 1011 since 1969.[3]
  • The likelihood of any "Nordtvedt effect" (a composition-dependent differential acceleration of the Moon and Earth towards the Sun) has been ruled out to high precision,[9][10] strongly supporting the validity of the Strong Equivalence Principle.
  • Einstein's theory of gravity (the general theory of relativity) predicts the Moon's orbit to within the accuracy of the laser ranging measurements.[3]

The presence of reflectors on the Moon has been used to rebut claims that the Apollo landings were faked. For example, the APOLLO Collaboration photon pulse return graph, shown here, has a pattern consistent with a retroreflector array near a known landing site. On the other hand the reflectors on the Lunokhod rovers prove that such instruments can be installed during unmanned missions.

Photo gallery

In popular culture

On the May 24, 2010 episode of The Big Bang Theory, "The Lunar Excitation," the characters bounce a laser off the reflector on the moon.

See also


External links

  • Lunar and Planetary Institute
  • University of Texas at Austin, Center for Space Research
  • "Lunar Retroreflectors" by Tom Murphy
  • Grasse, France
  • Lunar Laser Ranging from International Laser Ranging Service
  • UW Today, January 14, 2002
  • "What Neil & Buzz Left on the Moon" by Science@NASA, July 20, 2004
  • CNN, July 21, 1999

Template:Apollo program hardware

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