The enigma of the increase in the Earth-Moon distance is solved

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In 1755, the philosopher Immanuel Kant published a remarkable pamphlet entitled Universal natural history and theory of the heavens: Essay on the constitution and mechanical origin of the whole structure of the universe based on Newtonian principles. Not only did he set out what would become the Kant-Laplace model for the cosmogony of the Solar System, theorize a cosmos maybe infinite but mostly filled with galaxies similar to the Milky Way, “Universe-islands” in the words of Kant, but he also predicted that the distance between the Moon and the Earth was to increase with time.

From Kant to Darwin

Perfectly master of the concepts of physical Newtonian, in the absence of Newtonian mathematics developed at the same time by Leonhard Euler and d’Alembert, Kant understands that the law of conservation of cinematic moment and the existence of friction of the oceans deformed by the tidal forces of the Moon, due to the rotation of the Earth, lead to dissipate the kinetic energy of rotation on itself of our blue Planet. The slowing down of the rotation of the Earth causing its angular momentum to decrease, it must lead to an increase in that of the Moon around the Earth to ensure the conservation of the total angular momentum Earth+Moon and therefore an increase in the distance between the two celestial bodies — on all these elementary notions of mechanics, one can consult the Physics courses two Nobel Prizes Feynman and Pram.

During Kant’s lifetime, but in the half-century that followed, d’Alembert, Lagrange and Laplace intensively developed tidal theory on mathematical foundations and it is on these bases also that the English astronomer and mathematician George Howard Darwin (1845-1912) solidly embodied, around 1880, Kant’s ideas on the slowing down of the Earth’s rotation and the gradual receding of the Moon. For the record, and as his name suggests, Georges is indeed one of the children of Charles Darwin (1809-1882) the famous naturalist and paleontologist English whose work on theevolution of species living organisms have revolutionized biology.

These works of Darwin accompany his cosmogonic theory of the Moon, a very interesting theory but the exposition of which would lead us too far. You can get a glimpse of it in the treatise on geophysics of the great British astronomer, mathematician and geophysicist Harold Jeffreys who would also contribute to the theory of his compatriot George Darwin to whom the treatise is dedicated.

The ideas of Kant and Darwin will finally be firmly verified during the XXe century and a turning point in this regard will come thanks to the lunar program, American and Soviet, which will deposit on the Moon retro-reflectors returning photons 180° lasers and which will therefore make a round trip from their emission on earth. Since 1969, therefore, we have had a telemetry laser between the Moon and the Earth which made it possible to demonstrate that stars were well away from each other with an estimated speed of 3.83 cm/year.

The geological archives were not left out either because we have some fossils of corals that have like growth rings depending on the duration of the day on Earth and also that of the year. It has thus been shown that during the period of Devonian, (more precisely about 380 million years ago) a year had 400 days but its duration was almost the same as today. It was therefore necessary to deduce that the duration of the day was only about 22 hours and therefore that the rotation of the Earth had indeed slowed down, which as we have seen implies that the Moon was closer in the past to the Earth.

Fifty years after Neil Armstrong’s first step, the instruments deployed on the Moon by the Apollo 11 mission are still used by French scientists. Thanks to reflective panels placed on the lunar ground, they measure the distance that separates our planet from its satellite. The key is valuable lessons on the rotation of the Moon or the composition of its core. © CNRS

A Moon born 1.4 billion years ago?

However, by inserting in the equations from Darwin’s theory of the motions of the Moon and the Earth the value measured by laser ranging, it is found that the Moon and the Earth must have been in contact about 1.4 billion years ago. This result is in good qualitative agreement with the theory that the Moon is born from a collision between the Earth and a planet the size of Mars, the famous Theiabut quantitatively, it is not at all good because we know that the Moon is more than 4 billion years old and that it would have been born from the Earth-Theia collision about 4.4 billion years ago .

We have therefore been faced for about 50 years with a paradox that has been called the Gerstenkorn event, that is to say a contact between the Earth and the Moon 1.4 billion years ago, a contact which does not is certainly not produced at that time.

A research team from the Paris-PSL Observatory within the Institute of Celestial Mechanics and Ephemeris Calculation (IMCCE) has looked into this problem and has just announced that it has solved the enigma. in an article published in A&A Letters but of which one can find a free access version on arXiv.

Previous attempts to resolve the contradiction by improving the theory of the tides, notably the ocean models of Webb (1982) which had represented fundamental advances in showing the appearance of resonances mechanical (similar to those that swing a swing when the frequency of excitation is good) between ocean waves and forcing of tidal forces, leading to a large increase in the dissipation of Earth’s rotational energy, had still failed to account for neither the tidal rate current nor of the age of the Moon.

Continents interacting with tidal waves

In fact, the comparison with experience is not straightforward and, until now, there was a risk of circular reasoning. Indeed, with regard to the history of the movements of the Earth-Moon system, there are also cyclostratigraphic archives in the sediment in relation to deposits associated with tidal rhythmites, linked to the variation in tidal deposition between neap and spring tides, as well as the famous Milankovitch climate cycles. However, to interpret these data, it is also necessary to have a modelization of these movements in relation to celestial mechanics up to a certain point.

So that the empirical models of Earth-Moon history that are widely used today by geologists are problematic. Finally, as explained in a press release from the IMCCE, empirical models do not make it possible to deduce physical information about the Earth-Moon system.

The tides are mainly the result of the attraction of the moon and the sun and the rotation of the earth on itself. Satellite measurements make it possible to obtain animations which visualize the variations in the height of the seas, represented by levels of gray. These level variations are the sum of many components, called tidal waves. The animations highlight the properties of the tide wave M2, effect of the attraction of the moon (period, amplitude, wavelength, vibration nodes and speed of propagation) and of the tide wave K1, effect the inclination of the lunar orbit with respect to the equator (phase opposition and critical latitude). © CreditsScientific authors: Le Provost Christian and Lyartd Florent (Legos, UMR CNRS, Toulouse) Director: Ternay Jean-François (CNRS AV) Production: Legos, CNRS AV Distributor: CNRS Images

To overcome these difficulties, the astronomers and geophysicists from the IMCCE have refined their modeling taking into account over millions and billions of years of Continental Drift. Movements of continental blocks not only change the timing ofinertia of the Earth over time, which influences the rotation of the Earth and the movements of its axis of rotation, but also modifying the shape of the oceans, they lead to waves of propagation of the tides and dissipations of energy more complex than initially considered.

In the end, the researchers not only eliminated the contradiction represented by the Gerstenkorn event, but also obtained a remarkable consistency between the predictions of the new modeling and the history of the evolution of the Earth-Moon distance.

The IMCCE press release setting out this discovery concludes with the following comments:

This study is interdisciplinary and will have a very broad impact in several fields (geophysics, geology, astronomy). It provides the first physical model of the evolution of the Earth-Moon system which agrees perfectly with the current tidal dissipation and the age of the Moon, resolving a fifty-year-old paradox. In addition, this model fits the available geological data very well. It will thus most likely become the standard reference for geoscientific studies. This study clearly demonstrates that the cyclostratigraphic approach is very relevant to find the past rotational state of the Earth. It even consolidates the entire cyclostratigraphic field. This model differs from those previously published by allowing resonances of larger amplitudes. This is essential in adjusting the current dissipation rate. These results will therefore also consolidate the theory of ocean tides, showing the important effect of these oceanic resonances. Moreover, they can be generalized to the ocean tides of extrasolar planets “.

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