The Earth's rotation slowing down and the Moon spiraling away

[lpetrich]

The Earth's rotation is very gradually slowing down, and the Moon is very gradually spiraling away.

Ancient shell shows days were half-hour shorter 70 million years ago
noting journal paper
Subdaily‐Scale Chemical Variability in a Torreites Sanchezi Rudist Shell: Implications for Rudist Paleobiology and the Cretaceous Day‐Night Cycle - Winter - 2020 - Paleoceanography and Paleoclimatology - Wiley Online Library

This work was done on a reef-forming rudist bivalve's shell. It involved taking tiny samples of it and then analyzing them. Composition and isotope-abundance variations could then be analyzed to find evidence of daily and yearly variation. The year was 372 days long back then, as opposed to 365.26 days today.

From  Earth's rotation, our planet's rotation has slowed at 2.3 milliseconds per century over the last 2800 years, and that is the rate that one finds from that shell.

The authors of that work hope to examine older shells with their technique, to get a better picture of the Earth's rotation rate over geological time.

http://articles.adsabs.harvard.edu//full/1972Ap%26SS..16..212P/0000223.000.html
Title: Paleontological Evidence on the Earth's Rotational History Since Early Precambrian
Authors: Pannella, G.
Journal: Astrophysics and Space Science, Volume 16, Issue 2, pp.212-237
Bibliographic Code: 1972Ap&SS..16..212P

This paper a look back further. Some shells from 450 million years ago record day lengths of about 400 days/year. Here also, 2.3 msec/cy.

 

[lpetrich]

How did the moon end up where it is?

The Moon is observed to be slowly spiraling away, at about 3.8 cm/year. But there is a problem. Assuming constant tidal-drag friction makes the Moon start spiraling outward at about 1.5 billion years ago, and most of the dated Moon rocks are much older than that. So the Earth must have had less tidal friction.

The implication is that today's tides must be abnormally large, causing the 3.8cm recession rate. The reason for these large tides is that the present-day North Atlantic Ocean is just the right width and depth to be in resonance with the tide, so the natural period of oscillation is close to that of the tide, allowing them to get very large. This is much like a child on a swing who moves higher if pushed with the right timing.

But go back in time – a few million years is enough – and the North Atlantic is sufficiently different in shape that this resonance disappears, and so the moon's recession rate will have been slower. As plate tectonics moved the continents around, and as the slowing of Earth's rotation changed the length of days and the period of tides, the planet would have slipped in and out of similar strong-tide states. But we don't know the details of the tides over long periods of time and, as a result, we cannot say where the moon was in the distant past.

A way out is to look for evidence of Milankovitch astronomical cycles in sediments. They are produced by a combination of spin precession and orbit precession, though the spin precession is faster than the orbit precession. Faster rotation means a larger equatorial bulge, and thus faster precession.

Proterozoic Milankovitch cycles and the history of the solar system | PNAS
Looking at some 1.4-billion-year-old sediments in China, some researchers inferred an Earth-Moon distance of 341,000 km (present: 384,000 km), and also a day length of 19 hours. That means an average spindown rate of 1.3 msec/cy.

 

[lpetrich]

Geological Constraints on the Precambrian History of Earth's Rotation and the Moon's Orbit (2000) - approximate agreement with the results in it, like in Table 1.

Days on Earth Really Are Getting Longer Thanks to The Moon - They Used to Be Just 18 Hours - more on the OP's result.

Also notes
From rocks in Colorado, evidence of a ‘chaotic solar system’
which notes
Theory of chaotic orbital variations confirmed by Cretaceous geological evidence | Nature
The planets pull on each other, and they cause each other's orbits to precess. This precession has some weak chaos in it, but it could be noted in those 87-million-year-old sediments.

 

[DBT]

I guess the Moon will spiral away at an increasing rate with distance?

 

[barbos]

I guess the Moon will spiral away at an increasing rate with distance?

No, rate should decrease.

 

[DBT]

I guess the Moon will spiral away at an increasing rate with distance?

No, rate should decrease.

Why is that?

 

[barbos]

I guess the Moon will spiral away at an increasing rate with distance?

No, rate should decrease.

Why is that?

tidal force is proportional to F=~1/R^3 where R is a distance to the Moon.
Energy loss is proportional to F^2 so 1/R^6. orbital energy of the moon increases proportional to (-1/R) only.
Tital forces losses fall too fast.

 

[DBT]

Why is that?

tidal force is proportional to F=~1/R^3 where R is a distance to the Moon.
Energy loss is proportional to F^2 so 1/R^6. orbital energy of the moon increases proportional to (-1/R) only.
Tital forces losses fall too fast.

Ah, of course...the Earth and Moon eventually showing each other the same face.

 

[barbos]

Why is that?

tidal force is proportional to F=~1/R^3 where R is a distance to the Moon.
Energy loss is proportional to F^2 so 1/R^6. orbital energy of the moon increases proportional to (-1/R) only.
Tital forces losses fall too fast.

Ah, of course...the Earth and Moon eventually showing each other the same face.

Not necessarily in this case, also not relevant. Tidal forces just fall too fast with distance. I mean when Moon gets 2 times father than it is now, process will become 64 times slower.

 

[DBT]

Ah, of course...the Earth and Moon eventually showing each other the same face.

Not necessarily in this case, also not relevant. Tidal forces just fall too fast with distance. I mean when Moon gets 2 times father than it is now, process will become 64 times slower.

Well, I was thinking what happens in the very long term. Tidal lock, the sun expanding into a red giant, etc.