Talk:Tidal acceleration

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Contents

[edit] Evidence

This mechanism has been working for 4.5 billion years, since oceans first formed on the Earth. There is geological and paleontological evidence that the Earth rotated faster and that the Moon was closer to the Earth in the remote past.

What is this evidence that the earth rotated faster and the moon was closer? I'm not disputing it, but I would love to see this evidence. -- D. F. Schmidt (talk) 16:59, 23 August 2005 (UTC)

Good question. I think one piece is that the Earth's core is spinning slightly faster. This is consistent with the theory since the core is loosely coupled to the mantle and crust (since there is a fluid layer in between) and tidal forces are much stronger on the outer shell with its greater radius. Further, as I recall the deceleration of the Earth and the increasing seperation between Earth and Moon can and have both been measured to significant accuracy.
I have no idea what paleontological evidence could exist out there. Perhaps a fossil record of algae layers? Faster days would imply thinner layers though you'd need to adjust for what is thought to be lower solar output for the time. -- KarlHallowell 17:48, 23 August 2005 (UTC)
Incidentally, this claim should be backed up. Also remind the reader with a short phrase that the oceans dissipate energy. Maybe
This mechanism has been working for 4.5 billion years, since oceans first formed on the Earth and began dissipating energy through the tides.
-- KarlHallowell 18:09, 23 August 2005 (UTC)

Paleontological evidence is mentioned in [1]. Specifically, that 620 Mya the day was 21.9±0.4 hours, as deduced from rhythmites (alternating layers in sandstone). The average recession rate of the Moon was 2.17±0.31 cm/year from then until now, about half of the present recession rate. The citation is Williams, G. "Geological constraints on the Precambrian history of Earth's rotation and the Moon's orbit". Reviews of Geophysics 38, 37 (2000). The Moon was formed 50 million years after the formation of the solar system by the collision of a Mars-sized planetisimal striking the Earth, causing the Earth to rapidly rotate with a roughly 6-hour day, as deduced from computer modelling. The oceans may have been formed by 150 million years (from the Origins miniseries on Nova on U.S. Public Broadcasting Stations [2]). The evidence is that the oldest zircon crystals (which is proof of continental crust) have a high amount of 18O, which means they were formed in water. A controversy exists between whether the oceans were formed by volcanic outgassing of steam or by comet strikes. But they could not have been formed solely by comets because comets measured so far have twice the amount of heavy water (deuterium oxide) than the present ocean has. I have only recently begun my search for these citations. Luckily, the Nova broadcast was last night, August 23. — Joe Kress 22:15, August 24, 2005 (UTC)

Excellent! I'm a bit too busy right now to help, but I'll put it on my watchlist FWIW. -- KarlHallowell 23:23, 24 August 2005 (UTC)

[edit] Moment of inertia

As a consequence, the polar diameter of the Earth increases, and since the mass and density remain the same, the volume remains the same; therefore the equatorial diameter is decreasing. As a consequence, mass moves closer to the rotation axis of the Earth. This means that its moment of inertia is decreasing.

I learned about this moment of inertia not long ago in college (this spring, actually), but I thought another thing: Since there are more people than there were before, two possibilities:

  • Moment of inertia increases because mass increases around the fringe

or

  • Rotation rate decreases because the rotational momentum remains the same

But maybe it's a blend of the two, and maybe they come to no net effect, in light of what is mentioned here. But still too much is being assumed. How can we know experimentally that the mass and volume and density remain the same? What if there are changes that are so minuscule so as to be undetectable. It has been known to happen. For instance, we can't detect microorganisms with our eyes, but we can with a microscope. In like manner, perhaps we cannot tell that these measurements are changing because our equipment simply doesn't allow us to? -- D. F. Schmidt (talk) 17:16, 23 August 2005 (UTC)

The key isn't whether the Earth is exactly the same mass, but whether mass changes are significant compared to the changing shape of Earth. It has been speculated that most of Earth's oceans were formed over the past few billion years by an accumulation of small comets. But even this accumulation of mass is dwarfed by the changing shape of Earth. -- KarlHallowell 18:01, 23 August 2005 (UTC)

[edit] Looking for algorithm

Hi,

I have been looking for accurate information on this subject to write a good Java class for a while. I am especially searching for day length on paleological scale (millions of years) and accurate data/equations. As it seems there is very few information on this subject on the web. Could anyone drop me an email at silvere@digitalbiosphere.com if he finds the correct equation or a pdf article to send me ?

Big thanks.

The info I cited above in Evidence is an average over 620 million years. Tidal acceleration is highly dependent on the particular continental configuration, but continents drift over millions of years, so tidal acceleration will constantly vary over time. I've seen some attempts to model the ocean basins for earlier continental configurations, but because most tidal friction takes place in shallow seas, those attempts would seem to be almost guesses with no assurance that the results are even in the right ballpark. — Joe Kress 04:04, 5 November 2005 (UTC)
Given that we know so little about the detailed bathymetry of the ocean and continental shelves say a billion years ago the best that you can do is use statistical arguments. The resonant structure of the ocean does depend on the topography etc but as the continents drift these are likely to have moved around in a random manner. The rate at which energy is dissipated is important but at present most of the energy is lost as soon as the tidal wave reaches a nearby resonant continental shelf (this usually takes less than 60 hours). Given there is nothing special about the present ocean, similar frictional damping is likely to have happened in the past. (There is also a small but significant amount of tidal friction in the solid earth but that would need another article).
What really changed in the past was the strength of the tidal forcing (the Moon was nearer) and the rotational speed of the Earth which was larger (a day originally lasted for about eight, maybe ten, hours). Increased strength by itself produces increased tidal friction and tidal acceleration. However because of the increased rotation rate, tidal wavelengths would heve been a lot shorter and the efficiency with which they were excited by the long wavelength (half the Earth's circumference) tidal forcing would have been a lot lot smaller (it depends on the square). The net effect is that tidal accelerations may have been less over the last two billion years but increased before that when the extra tidal forcing term wins. David Webb 22:07, 18 August 2006 (UTC)
p.s. while I am on-line - what on earth is the "Explanation" section doing at the top of the main page? Is it someone's pet beef that the Moon is really another planet (like Pluto's companion)? David Webb 22:07, 18 August 2006 (UTC)
Good point. I've made some changes there, but it could still use more work. Deuar 16:04, 23 August 2006 (UTC)

[edit] Angular momentum

I am confused about whether the earth's angular momentum remains constant or gradually decreases. The qualitative description in this article suggests that it is gradually decreasing but the quantitative description says it remains constant. Are the two sections discussing the same angular momentum? If so, which is it - constant or decreasing? 155.91.45.231 22:34, 10 November 2005

The last paragraph of the quantitative description is not discussing the same angular momentum discussed elsewhere. It only refers to the change in Earth's moment of inertia due to a change in its shape, like an ice skater bringing her arms inward. This portion of Earth's angular momentum is constant, but the rest of Earth's angular momentum is decreasing due to tidal friction. How to clarify this is problematic. To compound the confusion, the angular momentum of the Earth-Moon system is constant, so the decrease is Earth's rotational angular momentum is transferred to the Moon's orbital angular momentum as an increase. That last paragraph also places too much emphasis on relative changes in earth's polar and equatorial radii. Earth's north pole radius does not change, but radii at other high northern latitudes do (Canada and Scandinavia). Whether the south pole radius (Antarctica) is now changing or changed in the past has not been established. — Joe Kress 05:50, 11 November 2005 (UTC)

[edit] Proposed merge with Tidal Friction

Seems a good idea given the sparseness of the tidal friction article. However, it should be noted that the current tidal acceleration article talks almost exclusively about the Earth-Moon system. -- KarlHallowell 14:48, 31 December 2005 (UTC)

Perhaps the Tidal friction article should be revamped into "Tidal heating" to discuss things like Io's and Enceladus's heat source. Tidal friction as such is already being discussed in some detail here at tidal acceleration. Deuar 10:28, 29 May 2006 (UTC)
Tidal acceleration involves a transfer from one bodies rotational angular momentum to another bodies orbital angular momentum and, given Newtons's laws, this is only possible if tidal energy is lost to friction somewhere in the system. Thus tidal acceleration and tidal friction are just two sides of the same coin - and in my view should be combined. David Webb 21:18, 18 August 2006 (UTC)

[edit] Energy balance

The angular momentum and energy subsection was difficult to follow, and incorrect, so I have implemented a fix. Admittedly this is a rather confusing issue. However, there is a quantitative issue which I am not familiar with, and could use a definitive explanation:

How much energy is lost due to friction of the tides on Earth, and how important is it?
No, it was correct but you mis-understood Tom Peters 09:47, 28 May 2006 (UTC)
Well, it's better now, anyway. My "approximately conserved" statement is a bit embarassing. Late night shorthand that didn't work out :-(
There is still a problem with the way it is now. It is stated:
The excess rotational energy dissipates through friction of the tidal waters along shallow coasts, and is lost as heat.
What excess? Gravity is a conservative force, so the gravitational torques should neatly transfer the Earth's rotational energy to the Moon's orbital energy without the need for any friction. This friction appears to be an un-related extra. For exmple at PhysicsWorld, there is a quantitative calculation without any mention of friction [3]. I would suggest "Additionally, some rotational energy ... " Deuar 14:03, 28 May 2006 (UTC)
A recent overview of the subject by a world-renowned authority, Walter Munk ("Once again: once again—tidal friction", Progress in Oceanography 40 (1997), 7-35), leaves no doubt that the Moon's torque on the ocean's tides is dissipated as heat. Indeed, if it is not dissipated as heat, then it does not affect the Moon's motion. "In a steady state situation, the net work done by the Moon on the water is balanced entirely by net dissipation of oceanic tides." Here, 'work' has its normal physics definition of force times distance or torque and 'dissipation' means the generation of heat. Earth's rotation would not be able to drag tides ahead of the Moon without friction and hence heat. Without heat, the Moon's torque on the tides would pull the Earth's tides back into synchronization with the Moon. Heat exactly balances and maintains torque. — Joe Kress 22:05, 28 May 2006 (UTC)

The friction is not related to the Moon's migration, but may be relevant for the Earth's slowdown. Since it is known that the Moon is moving out, then it must be obtaining energy from the Earth (total energy increases with orbit size), and it can't do that from friction. But the friction must be there. Does anyone know how big is it's effect on the Earth's rotation compared to the loss of angular momentum + energy to the moon? Deuar 20:51, 26 May 2006 (UTC)

If you are competent to write on these matters, you should be able to compute that yourself. Tom Peters 09:47, 28 May 2006 (UTC)
Well I always wonder - suppose I see an inconsistency. Is it better to fix it according to what appears right, or leave it wrong? Deuar 14:03, 28 May 2006 (UTC)
Munk provides a formula that directly relates tidal dissipation (heat) to the Moon's acceleration:
D = - (dn/dt)(Ω - n)[r²MME]/[3(M+ME)],
where n, M, and r are the Moon's orbital velocity, mass, and distance, and Ω and ME are Earth's angular velocity and mass. He assumes that the lunar acceleration of lunar longitude dn/dt = -25"/cy², which is somewhat smaller than the lunar laser ranging value of -25.858"/cy². — Joe Kress 22:05, 28 May 2006 (UTC)

Thanks for the recent added explanations on receding Moon and energy dissipation. This is the first time I really have the impression I understand the phenomenon. And looks so simple now. Good work! −Woodstone 18:14, 29 May 2006 (UTC)

[edit] edits by Joe Kress 30 May 2006

Joe, I find your latest edits not at all an improvement:

  • "net tide ... (integrated over all oceans)" does not clarify anything. I doubt that one can integrate a tide. IMNSHO just "tide" would be as accurate, and much more to the point.
  • "tidal friction (dissipated as heat)": friction (a force) can not be dissipated as heat. Friction working on the rotating Earth dissipates energy in the form of heat. Also the extra qualifier "tidal" does not help at all here: in which respect is "tidal" friction different from just "friction"? The original text was more accurate and understandable.
  • "(within 48 hours)": where does this come from? Are you sure it is not 47 or 49 hours? I don't think specifying an exact value contributes much here.
  • Under historical evidence, you removed the line of reasoning that leads to the conclusion that the day was shorter. Now there is a big leap of thought between finding rhythmites, and the result of the day length. IMNSHO the explicative reasoning is necessary to bridge this gap.

I intend to revert these edits, unless you can clarify these points. Tom Peters (Wikipedia apparently already logged me out again) 82.170.18.66 22:43, 30 May 2006 (UTC)

Tom (after moving your edit to the end of the page):
  • The problem with "tide" is that there is no such thing as an equilibium tide (an ocean in the form of a prolate spheroid) on Earth for the Moon to pull on. Earth's continents break up any equilibrium tide as they pass under the Moon. Instead tides of much greater amplitude rotate around each ocean basin. The Moon pulls on large tides that are both ahead of and behind it. An integration over the world's oceans is indeed preformed by computer, effectively subtracting these large tides from each other in order to find the net difference, only 3.23 cm. I intend to add a paragraph about this.
  • I am using friction in the sense of one body rubbing against another. In normal usage, when you rub your hands together, for example, you get heat. The precise physical sequence would only complicate matters. But it is critical that heat dissipation be mentioned, and your wording was ackward. Friction normally exists between two solid bodies, but here the friction is between a liquid and a solid, so I think "tidal" is an appropriate modifier.
  • "Within 48 hours" comes from Munk as cited. Specifically, he stated that "In a steady state situation, the net work done by the Moon on the water is balanced entirely by net dissipation of oceanic tides. With a global tide energy of 4 x 105 TJ, [a dissipation of 2.4 TW] implies that once every 48 hours all of the tide energy is renewed!" However, the calculation actually yields 46.3 hours, so Munk was a bit loose. A less precise "within two days" would be more appropriate.
  • I only removed a reference to numerical integration because the solar system becomes chaotic before some tens of millions of years, so it cannot be used as proof of a constant year over billions of years. I have now consulted the citation and can add their argument, for whatever it's worth (that the constant of gravitation has not changed).
— Joe Kress 06:33, 31 May 2006 (UTC)
Presumably the most likely scenario for year length changes is from perturbations by other planets changing a, not from a changing constant of gravitation, and this is what numerical integration was trying to check (I haven't read the article, my uni doesn't seem to subscribe to that journal). Even though semi-major axis is what is most resistant to orbital resonances. If significant changes had been seen then, yes their details could not be trusted due to the solar system's chaotic behaviour, but the general presence or absence of changes is fairly trustworthy. It's a matter of finding out whether the Earth is in an integrable or non-integrable part of phase space. In any case, I don't think it's worth belaboring this point in a tidal article, since tidal forces would not be expected to have much effect (the Earth's rotational angular momentum is peanuts compared to its orbital angular momentum, and you wouldn't expect tides on the Sun raised by the Earth to be significant). Deuar 10:21, 31 May 2006 (UTC)


[edit] What about the Sun?

Well, there's quite a difference between shift-tilda and control-tilda, so I'll try again.

In discussing the tides due to the Moon, those due to the Sun ought to be mentioned as the effect is about half that of the Moon. Likewise, it should be mentioned that the tides as observed are the consequence of resonances in the ocean basins as built up by the history of the tidal forces, which (as is mentioned) would produce only a small rise alone.

In thinking about rotational and orbital resonances, I first thought that there might be "wells" that perhaps could not be escaped from, thus Mercury in a 3:2 resonance with only a small perturbation (there being no oceans of mercury slopping about, Hg or H2O) might be trapped in that state, whereas the wells associated with 354, 364, 363,... revolutions/orbit would be shallow. And what of the bizarre resonance of Venus, that turns the same (shrouded) face to Earth on closest approach? Then I convinced myself that the energy dissipation by friction into heat being irreversible, the resonance would be broken eventually. After pausing to confuse myself by wondering what would happen if the orbit and rotation were in the opposite senses, it seems clear to me that the slowing of rotation would not be constant but would wobble as resonances were entered and exited. That is, to start with the Earth's revolution would be too rapid so that it would shove the tidal bulge forwards and via frictional losses (with the bulge's position being held back by the Moon's gravity) would be slowed. Later, after slowing past the exact resonance the spin would be behind the Moon's schedule and so the slowing would abate.

This raises another point. Even with a 1:1 resonance of rotation and orbit, the Moon would not hover above a constant point of the Earth's surface but wander a little. Unless the orbit was exactly circular and there were no other masses in the Universe to peturb matters...

In general, I think explanations involving phrases such as "due to the conservation of ..." should be avoided because they are appeals to magical reasoning, as if there is some Universal Accountant observing all and enforcing its rules. A rocket advances, not because of conservation of momentum (even though it is upheld) but because of the pressures in the reaction chamber being unbalanced by the vent hole. Understanding this chain of reasoning is one thing, reciting "conservation of momentum" another.

Regards, NickyMcLean 23:45, 8 June 2006 (UTC)

I completely agree with you regarding not invoking conservation laws as an explanation. Hear, hear!
Regarding resonances, there is no reason for the resonance to be ever broken by small perturbations. An external perturbation transfers energy into the body's wobble, which is later lost through tidal friction and the body becomes nicely locked again. Provided the external perturbations give the body much less wobble energy per year than it can lose in a year it remains at the bottom of the well, only ever slightly wobbling.
Also, in almost all cases, the rotation slows asymptotically down to the locked rate without oscillating around it, because the system is usually overdamped. Deuar 17:00, 9 June 2006 (UTC)
I thnk you are misguided. Conservation laws determine the quantities of energy, angular momentum, etc that can be exchanged. The gravitational force is there, and there are boundaries on its work determined by the conservation laws. From conservation you can draw conclusions on what happens. Everything happens at once but there are different approaches to explain all that, which all lead to the same results. There is nothing "magical" about this reasoning: it is a quantitative sum. You cannot make conserved quantaties disappear from the system. So for instance you are forcced to conclude that the Moon moves away from the Earth. Regarding tidal locking: eventually the Moon will not be wobbling around some intermediate position, but will stay put over the surface of the Earth: the orbit will indeed be circular. Tom Peters 00:09, 10 June 2006 (UTC)
The "wobbles" I was referring to are due to perturbations by other bodies than Earth,Sun and Moon. Sure, they're tiny and possibly even un-observable from Earth with current instruments, but it's just a matter of principle. They have no qualitative effect. Deuar 12:36, 10 June 2006 (UTC)
Gravitational perturbations by the other planets and asteroids on the Earth and Moon are both detectable and have been calculated very precisely. See Jihad Touma, Jack Wisdom, "Evolution of the Earth-Moon system" (pdf, 2.33 MB), _Astronomical Journal_ 108 (1994) 1943-61, which obviously includes tidal friction. — Joe Kress 06:00, 11 June 2006 (UTC)
Regarding conservation laws, of course they're a correct and useful way to do the calculation and lead to the same results. duh. I've just found that when discussing things with people who are not familiar with physics, invoking conservation laws is usually not particularly insightful for them. A rather blank expression appears on their face, and i've lost them. On the other hand talking about forces and torques, action-reaction, etc. seems to be much more intuitive and work better. imho ;-) Deuar 12:36, 10 June 2006 (UTC)

[edit] Amplitude

This article states:

  • Earth's net equilibrium tide has an amplitude of only 3.23 cm.

In contrast, the article tide states:

  • The theoretical amplitude of oceanic tides due to the Moon is about 54 cm at the highest point

This is rather a big difference. The latter result comes form the referenced article: Myths about Gravity and Tides. The calculation is shown extensively and is verifiable. Where does the result in this article come from? −Woodstone 13:37, 9 June 2006 (UTC)

3.23 cm comes from Munk as cited. It is the net equlibrium tide measured from satellite data. The Myths figure is calculated for a hypothetical ocean-covered Earth. One obvious reason for the difference is the different Earth models. This indicates how far removed the simplistic ocean-covered Earth is from reality. Coincidentally, that same satellite data shows that the maximum tide in the open ocean (not that at shore) is around 80 cm (at only a few locations). According to Munk, tidal dissipation due to the Sun is 1 TW whereas that due to the Moon is 3 TW, hence the Sun's affect is 1/3 that of the Moon, not 1/2. One reason for the difference is that 1/3 includes all harmonics, not just the prolate spheroid M2 'harmonic'. Another difference is that the dominant solar tide is S1, which has only one bulge per day, not two. — Joe Kress 06:20, 10 June 2006 (UTC)
I have confirmed that 3.23 cm is correct because earlier figures of 3.21 cm and 3.64 cm appear in "The Earth's Variable Rotation: Geophysical Causes and Consequences" by Kurt Lambeck (1980). However, S1 appears to be a typo — it should be S2, which would be a semi-diurnal tide like M2. — Joe Kress 06:00, 11 June 2006 (UTC)
Thanks for the explanations. Perhaps some of it should be placed in the tide article (and in this one). It still leaves the question of the tidal acceleration in the sun-earth system and how it combines with the moon-earth effect. The earth's rotation cannot be in step with both. What would the theoretical final rotation be? −Woodstone 09:34, 11 June 2006 (UTC)

Currently, the Moon's tidal effect is the larger, however with time the Earth's revolution slows and the Moon drifts out so that its effect weakens. But, once the Moon's orbit 'around' the Earth (it is actually always concave towards the Sun) attains a simple ratio with the Earth&Moon around the Sun, its orbit will be disrupted. Currently the Moon's orbital period is between 13 and 12 cycles/year and presumably (disregarding Velikovsky) it had survived the 13/year resonance on the way to the current state. Smaller ratios are stronger resonances, and, with the Moon more distant from the Earth, its "binding energy" would be less. As a further point, I have read somewhere that one effect of the Sun on the Earth is to increase the rate of the Earth's spin (yes yes, slightly) via some atmospheric effect. Evidently, the the atmosphere is assymetrical in that the dawn side is cooler than the sunset side, but offhand, I can't think of mechanism that might have a spin effect. Weather patterns do affect the spin, but they are temporary (yes, I can wave the "conservation of momentum" flag too) - likewise movements of magma, earthquakes, continental rise/fall/drift, etc. NickyMcLean 05:08, 14 June 2006 (UTC)

The above does not answer my question. Let me rephrase. After earth's rotation has slowed down so it is locked with the moon's orbit, there is still a monthly tide on earth, caused by the sun. This would continue to slow down the earth's rotation. As a result, it then turns the other way relative to the moon. So the tide from the moon would start to run in opposite direction as the one from the sun. At a certain point the net effect of the two decelerations would cancel and the rotation would just wobble slightly around that value. Is this a correct analysis? What would the final rotation time be? −Woodstone 07:50, 14 June 2006 (UTC)
The referenced article Myths About Gravity and Tides puts the tidal lock for the Earth-Moon system at a day of fifty hours. But the solar tide would continue to slow the Earth whereupon the Moon would be wound back towards Earth finally disintegrating at the Roche limit. There would be no stable state along the way in that argument. NickyMcLean 20:44, 14 June 2006 (UTC)
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