Fifteen Eighty Four

Academic perspectives from Cambridge University Press


A mirror on the Moon: 50th anniversary of the Apollo-11 mission

Theo Gerkema


In this memorable photograph (courtesy of NASA), we see astronaut Buzz Aldrin holding in his right hand a sophisticated mirror: the Laser Ranging Retro-Reflector (LR3). This mirror has now been standing on the Moon for 50 years.

By sending a laser beam from the Earth to the mirror, and measuring the time it takes for the light to return, the distance to the Moon can be accurately calculated because we know the speed of light. This sounds simple in principle, but the execution and interpretation of this kind of measurement is far from straightforward.

First of all, the beam has to be pointed accurately to a tiny mirror over a vast distance. Moreover, there is in fact no such thing as “the” distance to the Moon: it varies a lot due to the lunar orbital characteristics (notably the ellipticity). On average, it is about 385000 km (i.e., 60 times the Earth’s radius), but it varies by as much as 50000 km. Notwithstanding these enormous variations, it has been possible to deduce with remarkable accuracy that the Moon recedes from the Earth at a net rate of 3.8 cm per year.

NASA cropped

Something of this order of magnitude was already expected on theoretical grounds even before the Apollo mission took place – based, in part, on Babylonian clay tablets! It is not that the Babylonians were measuring the distance to the Moon – accomplished astronomers though they were – but they documented diligently where and when total solar eclipses took place.

Modern astronomical calculations can reconstruct these events, but assuming the present length of day would place them westward of the actual location. From this discrepancy, the change in the length of day can be inferred as an increase of about 2 milliseconds per century.

Classical mechanics provides the link between the slowing of the Earth’s spin and the recession of the Moon (via the principle of conservation of angular momentum): if one is known, the other can be calculated. The slowing of the Earth’s spin also implies a loss of kinetic energy of the Earth.The beneficiary of this loss is the tide: every second, 3.2×1012 J is put into the (lunar) tides. This number, too, follows from the lunar recession rate. Thus, the Apollo mission to the Moon helped us a step forward in understanding the tides on Earth.

From a geological perspective, the present recession rate seems unusually large. Numerical modelling on paleotides – the tides during the geological past when the continents were shaped differently and located elsewhere – indicates that tides were mostly weaker, implying a smaller energy input and a smaller lunar recession rate.



Theo Gerkema, Department of Estuarine and Delta Systems, NIOZ Royal Netherlands Institute for Sea Research, and Utrecht University, Yerseke, The Netherlands

About The Author

Theo Gerkema

Theo Gerkema is a senior researcher in the Department of Estuarine and Delta Systems at the Royal Netherlands Institute for Sea Research (NIOZ). He graduated as a theoretical physi...

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