Расстояние Земля-Луна: измерения, изменения и астрономическое значение

Distance from center of Earth to center of Moon
the navigation unit

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 (LD or ), 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 , 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 (roughly the distance from Earth to the Sun). Lunar distance is commonly used to express the distance to near Earth object encounters. Lunar semi major axis is an important astronomical datum; the few millimeter precision of the range measurements determines semi major axis to a few decimeters; it has implications for testing gravitational theories such as general relativity, and for refining other astronomical values, such as the mass, radius, and rotation of Earth. The measurement is also useful in characterizing the lunar radius, as well as the mass of and distance to the Sun. Millimeter precision measurements of the lunar distance are made by measuring the time taken for laser beam light to travel between stations on Earth and retroreflectors placed on the Moon. The Moon is spiraling away from Earth at an average rate of per year, as detected by the Lunar Laser Ranging experiment.

The instantaneous lunar distance is constantly changing. The actual distance between the Moon and Earth can change as quickly as 75, or more than in just 6 hours, due to its non circular orbit. There are other effects that also influence the lunar distance. Some factors include:

The formula of Chapront and Touzé for the distance in kilometres begins with the terms: The effect of radiation pressure from the Sun contributes an amount of ±3.6 to the lunar distance. Although the instantaneous uncertainty is a few millimeters, the measured lunar distance can change by more than from the mean value throughout a typical month. These perturbations are well understood and the lunar distance can be accurately modeled over thousands of years.

Through the action of tidal forces, the angular momentum of Earth's rotation is slowly being transferred to the Moon's orbit. The result is that Earth's rate of spin is gradually decreasing (at a rate of 2.4), and the lunar orbit is gradually expanding. The rate of recession is 3.830. There is geological evidence that the average lunar distance was about (332,000 km or 205,000 mi) during the Precambrian Era; 2500 million years BP. The widely accepted giant impact hypothesis states that the Moon was created as a result of a catastrophic impact between Earth and another planet, resulting in a re accumulation of fragments at an initial distance of (24,000 km or 15,000 mi). This theory assumes the initial impact to have occurred 4.5 billion years ago.

The oldest method of determining the lunar distance involved measuring the angle between the Moon and a chosen reference point from multiple locations, simultaneously. The synchronization can be coordinated by making measurements at a pre determined time, or during an event which is observable to all parties. Before accurate mechanical chronometers, the synchronization event was typically a lunar eclipse, or the moment when the Moon crossed the meridian (if the observers shared the same longitude). This measurement technique is known as lunar parallax. For increased accuracy, the measured angle can be adjusted to account for refraction and distortion of light passing through the atmosphere.

Early attempts to measure the distance to the Moon exploited observations of a lunar eclipse combined with knowledge of Earth's radius and an understanding that the Sun is much further than the Moon. By observing the geometry of a lunar eclipse, the lunar distance can be calculated using trigonometry. The earliest accounts of attempts to measure the lunar distance using this technique were by Greek astronomer and mathematician Aristarchus of Samos in the 4th century BC and later by Hipparchus, whose calculations produced a result of (376,000 or 233,000). This method later found its way into the work of Ptolemy, who produced a result of (409,000 or 253,000) at its farthest point.

An expedition by French astronomer A. C. D. Crommelin observed lunar meridian transits on the same night from two different locations. Careful measurements from 1905 to 1910 measured the angle of elevation at the moment when a specific lunar crater (Mösting A) crossed the local meridian, from stations at Greenwich and at Cape of Good Hope. A distance was calculated with an uncertainty of 30, and this remained the definitive lunar distance value for the next half century.

By recording the instant when the Moon occults a background star, (or similarly, measuring the angle between the Moon and a background star at a predetermined moment) the lunar distance can be determined, as long as the measurements are taken from multiple locations of known separation. Astronomers O'Keefe and Anderson calculated the lunar distance by observing four occultations from nine locations in 1952. They calculated a semi major axis of 384,407.6 ( ± ). This value was refined in 1962 by Irene Fischer, who incorporated updated geodetic data to produce a value of 384,403.7 ( ± ).

The distance to the moon was measured by means of radar first in 1946 as part of Project Diana. Later, an experiment was conducted in 1957 at the U. S. Naval Research Laboratory that used the echo from radar signals to determine the Earth Moon distance. Radar pulses lasting 2 were broadcast from a 50 feet (15 m) diameter radio dish. After the radio waves echoed off the surface of the Moon, the return signal was detected and the delay time measured. From that measurement, the distance could be calculated. In practice, however, the signal to noise ratio was so low that an accurate measurement could not be reliably produced. The experiment was repeated in 1958 at the Royal Radar Establishment, in England. Radar pulses lasting 5 were transmitted with a peak power of 2 megawatts, at a repetition rate of 260 pulses per second. After the radio waves echoed off the surface of the Moon, the return signal was detected and the delay time measured. Multiple signals were added together to obtain a reliable signal by superimposing oscilloscope traces onto photographic film. From the measurements, the distance was calculated with an uncertainty of
These initial experiments were intended to be proof of concept experiments and only lasted one day. Follow on experiments lasting one month produced a semi major axis of 384,402 ( ± ), which was the most precise measurement of the lunar distance at the time.

An experiment which measured the round trip time of flight of laser pulses reflected directly off the surface of the Moon was performed in 1962, by a team from Massachusetts Institute of Technology, and a Soviet team at the Crimean Astrophysical Observatory. During the Apollo missions in 1969, astronauts placed retroreflectors on the surface of the Moon for the purpose of refining the accuracy and precision of this technique. The measurements are ongoing and involve multiple laser facilities. The instantaneous precision of the Lunar Laser Ranging experiments can achieve small millimeter resolution, and is the most reliable method of determining the lunar distance. The semi major axis is determined to be 384,399.0 km.