Lunar distance (astronomy)

Lunar distance (LD or Δ ⊕ L { extstyle Delta _{oplus L}} ), also called Earth–Moon distance, Earth–Moon characteristic distance, or distance to the Moon, is a unit of measure in astronomy. It is the average distance from the center of Earth to the center of the Moon. More technically, it is the mean semi-major axis of the geocentric lunar orbit. It may also refer to the time-averaged distance between the centers of the Earth and the Moon, or less commonly, the instantaneous Earth–Moon distance. The lunar distance is approximately 400 thousand kilometres (250 thousand miles). Lunar distance (LD or Δ ⊕ L { extstyle Delta _{oplus L}} ), also called Earth–Moon distance, Earth–Moon characteristic distance, or distance to the Moon, is a unit of measure in astronomy. It is the average distance from the center of Earth to the center of the Moon. More technically, it is the mean semi-major axis of the geocentric lunar orbit. It may also refer to the time-averaged distance between the centers of the Earth and the Moon, or less commonly, the instantaneous Earth–Moon distance. The lunar distance is approximately 400 thousand kilometres (250 thousand miles). The mean semi-major axis has a value of 384,402 km (238,856 mi). The time-averaged distance between Earth and Moon centers is 385,000.6 km (239,228.3 mi). The actual distance varies over the course of the orbit of the Moon, from 356,500 km (221,500 mi) at the perigee to 406,700 km (252,700 mi) at apogee, resulting in a differential range of 50,200 km (31,200 mi). Lunar distance is commonly used to express the distance to near-Earth object encounters. Lunar distance is also an important astronomical datum; the precision of this measurement to a few parts in a trillion has useful implications for testing gravitational theories such as general relativity, and for refining other astronomical values such as Earth mass, Earth radius, and Earth's rotation. The measurement is also useful in characterizing the lunar radius, the mass of the Sun and the distance to the Sun. Millimeter-precision measurements of the lunar distance are made by measuring the time taken for light to travel between LIDAR stations on the Earth and retroreflectors placed on the Moon. The Moon is spiraling away from the Earth at an average rate of 3.8 cm (1.5 in) per year, as detected by the Lunar Laser Ranging Experiment. By coincidence, the diameter of corner cubes in retroreflectors on the Moon is also 3.8 cm. The instantaneous lunar distance is constantly changing. In fact the true distance between the Moon and Earth can change as quickly as 75 meters per second, or more than 1000 km in just 6 hours, due to its non-circular orbit. There are other effects that also influence the lunar distance. Some factors are described in this section. 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 2–3 cm for the average distance. 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 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. Although the instantaneous uncertainty is sub-millimeter, the measured lunar distance can change by more than 21000 km 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, angular momentum is slowly being transferred from the Earth's rotation to the Moon's orbit. The result is that Earth's rate of spin is imperceptibly decreasing (at a rate of 2.3 milliseconds/century), and the lunar orbit is gradually expanding. The current rate of recession is 3.805±0.004 cm per year. However, it is believed that this rate has recently increased, as a rate of 3.8 cm/year would imply that the Moon is only 1.5 billion years old, whereas scientific consensus assumes an age of about 4 billion years. It is also believed that this anomalously high rate of recession may continue to accelerate. It is predicted that the lunar distance will continue to increase until (in theory) the Earth and Moon become tidally locked. This would occur when the duration of the lunar orbital period equals the rotational period of Earth. The two bodies would then be at equilibrium, and no further rotational energy would be exchanged. However, models predict that 50 billion years would be required to achieve this configuration, which is significantly longer than the expected lifetime of the solar system.