The distance from the Moon

The method currently used to evaluate the distance from the Moon dates back to 1962, when a team from MIT (Massachusetts Institute of Technology) in collaboration with soviet astronomers from the Crimean Astrophysical Observatory carried out an experiment to measure the round-trip time of a laser pulse reflected on the surface of the Moon. The evolution of this experiment was completed thanks to the Apollo missions of 1969, when the astronauts placed reflective mirrors on the lunar surface in order to improve the accuracy of the measurement. Lasers traveling to the Moon involve multiple structures and are part of the Lunar Laser Ranging.
The distance measurement from this project is 384402 km with an error of 1.1 millimeters(1), which in terms of light time corresponds to just under 1.3 seconds.
The pre-laser method is also inspired by the same principle: in 1957 the US Naval Research Laboratory sent 2 μs radar pulses from a radio antenna with a diameter of about 15 meters. After the echo produced by the waves on the surface of the Moon, the experiment detected the return signal and measured the delay time, from which to derive the distance from our satellite. Unfortunately, this experiment was subject to an excessively high error with respect to the signal and therefore the result produced was not considered reliable(2).
The experiment was repeated the following year, in 1958, by the Royal Radar Establishment in Great Britain. In that case, radar pulses of 5 μs were sent with a maximum power of 2 megawatts and a frequency of 260 pulses per second(3).
After these two tests, the radar method, suitably refined by the results of the two previous experiments, produced a compatible result, although not as precise as the result they would have obtained a few years later with the laser method: 384402 ± 1.2 km(4).
The least precise modern system is that of occultations. In this way the astronomers John O'Keefe and Pamela Anderson calculated in 1952 a value of 384407.6 ± 4.7 km(5). This result was improved in 1962 by Irene Fischer, who obtained a value of 384403.7 ± 2 km(6).
The most ancient methods, however, are that of the lunar eclipse, as done by Aristarchus of Samos in the 4th century BC., and later by Hipparchus. Ptolemy also produced his results. The oldest of all is the parallax method, that is, the simultaneous measurement from different positions of the angle between the Moon and a given reference point. Obviously in this way it is necessary to synchronize all observers.
  1. Battat, J. B., Murphy, T. W., Adelberger, E. G., Gillespie, B., Hoyle, C. D., McMillan, R. J., ... & Swanson, H. E. (2009). The Apache Point Observatory Lunar Laser-ranging Operation (APOLLO): two years of millimeter-precision measurements of the Earth-Moon range. Publications of the Astronomical Society of the Pacific, 121(875), 29. doi:10.1086/596748
  2. Yaplee, B. S., Roman, N. G., Craig, K. J., & Scanlan, T. F. (1959). A lunar radar study at 10-cm wavelength. In Symposium-International Astronomical Union (Vol. 9, pp. 19-28). Cambridge University Press. 
  3. Hey, J. S., & Hughes, V. A. (1959). Radar observations of the moon at 10-cm wavelength. In Symposium-International Astronomical Union (Vol. 9, pp. 13-18). Cambridge University Press. 
  4. Yaplee, B. S., Knowles, S. H., Shapiro, A., Craig, K. J., & Brouwer, D. (1965). The mean distance to the Moon as determined by radar. In Symposium-International Astronomical Union (Vol. 21, pp. 81-93). Cambridge University Press. doi:10.1017/S0074180900104826
  5. O'Keefe, J. A., & Anderson, J. P. (1952). The earth's equatorial radius and the distance of the moon. The Astronomical Journal, 57, 108. doi:10.1086%2F106720
  6. Fischer, I. (1962). Parallax of the moon in terms of a world geodetic system. The Astronomical Journal, 67, 373. doi:10.1086%2F108742

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