Lunar distance

The instantaneous Earth–Moon distance, or distance to the Moon, is the distance from the center of Earth to the center of the Moon. In contrast, the Lunar distance (LD or ${\textstyle \Delta _{\oplus L}}$), 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 average lunar distance is approximately 385,000 km (239,000 mi), or 1.3 light-seconds. It is roughly 30 times Earth's diameter and a non-stop plane flight traveling that distance would take more than two weeks. Around 389 lunar distances make up an 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. 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 measuring the lunar radius, as well as the distance to the Sun.

Millimeter-precision measurements of the lunar distance are made by measuring the time taken for laser light to travel between stations on Earth and retroreflectors placed on the Moon. The precision of the range measurements determines the semi-major axis to a few decimeters. The Moon is spiraling away from Earth at an average rate of 3.8 cm (1.5 in) per year, as detected by the Lunar Laser Ranging experiment.

Because of the influence of the Sun and other perturbations, the Moon's orbit around the Earth is not a precise ellipse. Nevertheless, different methods have been used to define a semi-major axis. Ernest William Brown provided a formula for the parallax of the Moon as viewed from opposite sides of the Earth, involving trigonometric terms. This is equivalent to a formula for the inverse of the distance, and the average value of this is the inverse of 384,399 km (238,854 mi). On the other hand, the time-averaged distance (rather than the inverse of the average inverse distance) between the centers of Earth and the Moon is 385,000.6 km (239,228.3 mi). One can also model the orbit as an ellipse that is constantly changing, and in this case one can find a formula for the semi-major axis, again involving trigonometric terms. The average value by this method is 383,397 km.

The actual distance varies over the course of the orbit of the Moon. Values at closest approach (perigee) or at farthest (apogee) are rarer the more extreme they are. The graph at right shows the distribution of perigee and apogee over six thousand years.

Jean Meeus gives the following extreme values for 1500 BC to AD 8000:

The instantaneous lunar distance is constantly changing. The actual distance between the Moon and Earth can change as quickly as 75 meters per second, or more than 1,000 km (620 mi) in just 6 hours, due to its non-circular orbit. There are other effects that also influence the lunar distance. Some factors are listed in the sections below.

The distance to the Moon can be measured to an accuracy of 2 mm over a 1-hour sampling period, which results in an overall uncertainty of a decimeter for the semi-major axis. However, due to its elliptical orbit with varying eccentricity, the instantaneous distance varies with monthly periodicity. Furthermore, the distance is perturbed by the gravitational effects of various astronomical bodies – most significantly the Sun and less so Venus and Jupiter. Other forces responsible for minute perturbations are: gravitational attraction to other planets in the Solar System and to asteroids; tidal forces; and relativistic effects. The effect of radiation pressure from the Sun contributes an amount of ±3.6 mm to the lunar distance.