It has implications for testing gravitational theories such as general relativity [2] and for refining other astronomical values, such as the mass,[3] radius,[4] and rotation of Earth.

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.

Ernest William Brown provided a formula for the parallax of the Moon as viewed from opposite sides of the Earth, involving trigonometric terms.

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.

Jean Meeus gives the following extreme values for 1500 BC to AD 8000:[12] [15][16] The instantaneous lunar distance is constantly changing.

The actual distance between the Moon and Earth can change as quickly as 75 meters per second,[20] or more than 1,000 km (620 mi) in just 6 hours, due to its non-circular orbit.

The distance to the Moon can be measured to an accuracy of 2 mm over a 1-hour sampling period,[22] which results in an overall uncertainty of a decimeter for the semi-major axis.

[22] Although the instantaneous uncertainty is a few millimeters, the measured lunar distance can change by more than 30,000 km (19,000 mi) from the mean value throughout a typical month.

[23] Through the action of tidal forces, the angular momentum of Earth's rotation is slowly being transferred to the Moon's orbit.

[32] Theoretically, the lunar distance will continue to increase until the Earth and Moon become tidally locked, as are Pluto and Charon.

However, models predict that 50 billion years would be required to achieve this configuration,[33] which is significantly longer than the expected lifetime of the Solar System.

Laser measurements show that the average lunar distance is increasing, which implies that the Moon was closer in the past, and that Earth's days were shorter.

[26] There is geological evidence that the average lunar distance was about 52 R🜨 (332,000 km or 205,000 mi) during the Precambrian Era; 2500 million years BP.

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).

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[37] and later by Hipparchus, whose calculations produced a result of 59–67 R🜨 (376000–427000 km or 233000–265000 mi).

After the radio waves echoed off the surface of the Moon, the return signal was detected and the delay time measured.

After the radio waves echoed off the surface of the Moon, the return signal was detected and the delay time measured.

Follow-on experiments lasting one month produced a semi-major axis of 384402±1.2 km (238,856 ± 0.75 mi),[47] which was the most precise measurement of the lunar distance at the time.

[48] 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.

[21] During this event, participants were invited to record a series of five digital photographs from moonrise until culmination (the point of greatest altitude).

The method took advantage of the fact that the Moon is actually closest to an observer when it is at its highest point in the sky, compared to when it is on the horizon.

Modern cameras have achieved a resolution capable of capturing the Moon with enough precision to detect and measure this tiny variation in apparent size.