The unforgiving distance from the moon

In Europe, the year 1999 was marked by a stunning astronomical event, the total solar eclipse of August 11, considered the most observed eclipse in human history. Maybe you are among them. And you would have done well, because this kind of phenomenon would not happen again indefinitely! Why ?

Because the Moon is currently moving away from the Earth at a speed of 3.83 cm per year, as shown by precise measurements made using laser shots reflected from reflectors placed on the Moon by various space missions. Added to this is an increase in the length of the day by 1/74,000 of a second every year. Two phenomena, only one comet: the moon! The tidal forces they exert on our planet, by deforming the Earth's crust and oceans, dissipate energy and slow the Earth's rotation while transferring the energy to our satellite. Modern models describe the evolution of this pair since their creation more than 4 billion years ago. Surprise: The frequency of breakups varies a lot over time. Let us detail this phenomenon.

Tidal effect

Consider first a planet and its moon, devoid of oceans, orbiting each other in circular paths. At their respective centers of gravity, the centrifugal force resulting from their mutual rotation is completely compensated by the gravitational force that attracts them. But on the surface, this is no longer the case; These two forces are no longer in balance. It is their result that we call “tidal force.” On a planet, this tidal force tends to raise its surface along the planet-moon axis, and the effect is opposite in perpendicular directions. As a result, the planet becomes elongated in the direction of its satellite. The extent of deformation is very small: the crustal height is up to 20 cm.

If the planet and its moon orbited together synchronously, that is, they always showed the same face to each other, we would still be there: very slightly distorted celestial bodies. But when the planet's rotation on itself is faster than the satellite's rotation around the planet, the bulges cause it to move on the latter's surface. To determine what is happening, compare the speed at which tidal forces travel across the Earth's surface (0.45 kilometers per second) to the rate of propagation of seismic waves (4 kilometers per second). Since the former is much lower than the latter, the bulges can follow the motion of the satellite.

Late pill

In fact, these deformations do not occur without friction, without dissipation of energy, which causes delay and causes the position of the bulges to be displaced relative to the axis of the planet and the Moon. If the planet is rotating faster, they are ahead of that axis, in the direction of the planet's rotation. This small gap may not seem like much, but it is responsible for the distance between two celestial bodies and the slowing down of the planet's rotation.

In fact, compared to the situation in which the planet is not deformed by the tide, since the gravitational force between two masses varies as the square of the distance between them, the tidal edge closer to the satellite is subject to a stronger gravitational pull on its side than the more distant bulge. These two forces are not exactly aligned with the axis, and a torque effect is produced on the planet which opposes its rotation and thus slows it down. From the point of view of the satellite, the two gravitational forces it encounters from these bulges, opposing under the law of action and reaction of the forces mentioned above, combine to accelerate it along its circular path: a slow increase in its speed also increases the centrifugal force and the satellite moves away from the planet .

This deceleration and acceleration will continue until all the rotations become synchronized as we mentioned at the beginning of this paragraph, but, by the minute, if the tidal effect exists in both directions (from satellite to planet and vice versa), it is not of the same amplitude. The tidal forces of A on B are actually proportional to the product of the mass of A times the radius of B and the cube of the distance between them. Since the Earth's mass is eighty times greater than the Moon's and the latter's radius is approximately four times smaller, the lunar tides were more intense than Earth's tides, and the dissipation was also much stronger, as with a smaller Moon, the deceleration was much stronger. That is why today the Moon's rotation is actually synchronized with the Earth: it always presents us with the same face.

The sea, the sun and the orbits

To properly understand Earth's tides, many other influences must be taken into account. Thus, the Sun contributes up to 30% of the Earth's tidal forces and is the origin of spring and tides. Moreover, the inclination of the Earth's axis of rotation relative to the plane of the Earth's and Moon's orbits, and the elliptical and variable nature of the Moon's path also influence this phenomenon. Finally, with water on the Earth's surface, liquid bulges will be added to the solid ridges, significantly modifying the situation.

First, the movement of water masses dissipates a lot of energy due to friction with the ocean floor or turbulence caused by tidal currents. Hence, to see if these water bulges could track the Moon's motion, we need to look at the speed of gravitational waves, more commonly called “bulges”! This is equal to the product of the square root of the acceleration due to gravity and the depth of the ocean. With an average depth of about 4 km, its speed is 0.2 km per second, more than half the force of the tide. Our hills could no longer follow the Moon, and if the Earth were completely covered by water, we would be practically perpendicular to the Earth-Moon axis!

Finally, there are the continents. What is true at the local level – tidal amplitude can be greatly increased by the phenomenon of resonance, in the Bay of Mont Saint-Michel for example – also applies at the global level. Depending on the arrangement of the continents, and taking into account the Coriolis force that deflects ocean currents, we may or may not have echoes under the influence of lunar tidal forces. When this is the case, dissipation increases and with it the Earth's rotation slows down.

A team from the Institute of Celestial Mechanics and Ephemeris Calculus recently succeeded in combining all these elements and more (such as the fact that the ocean floor sags slightly when the liquid edge passes over it) to predict the Earth-Moon distance and height. Day (associated with right rotation) on Earth. In particular, it took into account continental drift by modeling it using a moving hemispherical layer on the Earth's surface, at least up to a billion years in the past, a date for which we no longer have any data. they. She also added that in the very distant past, 3 billion years ago, the Earth was covered in water.

Their results reflect very well the estimates from stratified data. They showed that the evolution of the day and the distance between the Earth and the Moon were anything but regular, and that periods of strong slowdowns like today, due to oceanic resonance, overshadowed a long (between 1 and 3 billion years) quieter period. and in the future?

Even with the current significant slowdown, synchronization of cycles will not occur for a few tens of billions of years. On the other hand, in just a million years, the Moon will be far enough away from Earth that a total solar eclipse will be nothing more than a distant memory!