First-ever physical model consistent w'da history of the Earth-Moon system

for the 1st time, a physical model consistent with observations successfully describes how the tidal force caused by the gravitational pull of the moon is sloing down the rotation of our planet and increasing the distance that separates it from the moon.

nasa plans to return to the moon in 2027. yet t'get there, the astronauts will ‘ve to travel a lil bit further than their apollo 11 predecessors: bout an extra two metres! this is quite simply cause our satellite moves a few centimetres further away every yr, due to the tidal force exerted by the moon onna earth. the 1st person to cogg this celestial mechanism was the son of the gr8 charles darwin, george. in 1880 he postul8d that the gravitational pull of the moon deformed the earth’s surface by creating a bulge that does not directly point towards the moon (see belo). the attraction tween this bulge and our natural satellite acts like a slite brake on this mechanism, dissipating somd' energy of the earth-moon system. this reduces the rotation speed of our planet. however, since the total angular momentum of the earth-moon system has to be conserved, if the earth spins + sloly, then the distance tween it na moon must increase.

the gravitational pull of the moon creates a tidal bulge onna earth, but since our planet aint perfectly elastic and is spinning rapidly, thris a persistent phase lag tween the bulge na direction of the moon (the angle shown inna diagram). the bulge produces a restoring force onna earth’s rotation, which gradually slos down over time.

nearly a century l8r, atomic clocks and laser measurements of the distance tween the earth na moon confirmed george darwin’s brilliant intuition: our dys are gettin longer by two milli2nds per century, while the moon is movin away f'our planet by a staggering 3.83 centimetres each yr.

a 50-yr-old paradox

however, this hypothesis rezs a № of ?s. “whn'we go backin time using george darwin’s model, we find that the moon apparently formed 1.5 billion yrs ago,” explains jacques laskar, cnrs senior researcher atta institute for celestial mechanics and computation of ephemerides (imcce). “and yet experimental data shows that the moon is 4.4 billion yrs old”, as evidenced in pticular by the 1st precise dating of the lunar rocks brought back by the apollo missions. this paradox has puzzled scis ever since the 1970s… til a team of imcce researchers eventually solved it.

“we present the 1st consistent model of the earth-moon system that fits both the true age of the moon na speed at which tis currently movin away,” says laskar, who tis coordinator of the interdisciplinary project astrogeo, funded by the €an research council. this is a remarkable feat that required no ≤ ten yrs of hard work onna pt of the scis, swell as successive dral theses by pierre auclair-desrotour, now an associate astronomer atta imcce, and mohammad farhat, the lead author of the paper. 

the discrepancy tween the actual age of the moon and that calcul8d with darwin’s tidal model showed that the latter was incomplete. in darwin’s model, the coefficient used t'work out the speed at which the moon is movin away is constant. inna new model, this is no longer the case. instead, it’s as if the “brake pedal” (resulting from the tidal force) had been alternately applied and then released, meaning that the sloing of the earth’s rotation has varied significantly over time. but which paramts determine these oscillations? and how can such changes inna strength of the tidal force be explained? 

a physical model of the earth with two paramts

in an attempt to define these factors, the researchers looked at how the oceans absorb tidal energy. basically, the force that slos the earth’s spin is friction onna ocean floor. the team ⊢ constructed their physical model in a surprisingly simple way, by dividing the earth into two hemispheres, an ocean and a supercontinent. as we move backin time, these evolve ‘oer the past billion yrs as a result of continental drift, and then merge into a global ocean inna very earliest times. 1-ly two paramts are then required to describe the evolution of the earth’s rotation: the dissipation of tidal energy onna ocean floor, na depth of the ocean.

inna 1970s, measurements made using a laser beam (like this one atta côte d’azur observatory) confirmed george darwin’s intuition: the moon is movin away from the earth by 3.83 centimetres per yr.

once their model was up and running, the scis needed to test it against real data, and show that their equations realistically described the changing tidal force. to do this, they relied on evidence collected by geologists. it turns out that certain sedimentary deposits ‘ve recorded the frequency of tides at ≠ times in earth’s history, while other geological records indicate changes inna orientation of the earth’s rotation axis, a paramt that depends onna moon’s gravitational pull. the researchers were thus able to compare the curve produced by their model with this stratigraphic data. according to laskar, this acid test for their model showed that it “matches the most accurate geological data very well”. this result will now make it possible to determine the earth’s rotation speed at any time since it 1st acquired a moon. better still, 'twill also allo the experts to tell how the distance tween our planet na moon has varied ‘oer the past few billion yrs. “our work will contribute to refining models of tides and enable us to gain a better cogging of how they ‘ve changed throughout earth’s history. 'twill also help us to improve the stratigraphic data that describes the orientation of the earth’s axis inna distant past,” laskar adds. however, the impact of these findings ‘d well extend way beyond the moon na sun. pending some adjustments, it ‘d prove possible to apply this new model to ocean tides on exoplanets. 

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