[rmolnav]

Let us imagine video diagram timed 2:23 with a vertical line some 2/3 Earth´s radius at right side of its center: the axis of this rotation.
Earth parts at the left of that axis require a total force per unit of mass proportional to its distance to that axis, in order to get required centripetal acceleration at ach considered spot. But gravitational pull from Moon is the farther the smaller (to the square of the distance to the Moon). That imbalance can be compensated only by internal stresses: parts closer to the axis have to add an inward pull on contiguous farther parts … Then we have Newton´s 3rd Law, and each part pulls inner contiguous one with same but opposite (and REAL) force, that is, outwards, "fllying from a center" (axis of rotation), CENTRIFUGAL …

I wish we ALL had a better knowledge of nature, or at least more imagination ...
I´ve long been arguing in line with what above, and neither myself, nor anybody else so far (unless they kept it "in secret") have imagined what below, and realized that what quoted is WRONG !!
Some people actually said it was wrong, but not for the correct reason. Most of them just considered that centrifugal forces are never real, but only apparent of ficticious ... And I gave many examples of REAL centrifugal forces ...
But recently I learnt that the 28/29 days circular movement of the couple Earth/Moon around their barycenter, though for the Moon is a rotation, for the Earth is NOT: Earth only REVOLVES around mentioned barycenter ...
That implies that all Earth points, center of mass included, follow equal circular paths.
Subsequently, my explanation, that would be valid for the Moon (it rotates at 2π radians/some 28 days angular speed), is NOT for the Earth !!
And possible imbalances between Moon´s pull on each point (either where solid or liquid parts), that could cause centrifugal forces, are not so straightforward to tell (?) ...
I´m trying to sort that out, but not easy ... For all my discussions on the subject, I´ve read many, many articles. But I NEVER saw any reference to what above !!

[rmolnav]

But recently I learnt that the 28/29 days circular movement of the couple Earth/Moon around their barycenter, though for the Moon is a rotation, for the Earth is NOT: Earth only REVOLVES around mentioned barycenter ...
That implies that all Earth points, center of mass included, follow equal circular paths.
Subsequently, my explanation, that would be valid for the Moon (it rotates at 2π radians/some 28 days angular speed), is NOT for the Earth !!
And possible imbalances between Moon´s pull on each point (either where solid or liquid parts), that could cause centrifugal forces, are not so straightforward to tell (?) ...
I´m trying to sort that out, but not easy ...

As a continuation of #80, I can say that, as far as I can understand, I´ve already sorted it out ...
Another day I´ll further elaborate on the issue, but now I´m going to put here main points.
Curiously, as Earth only revolves around the barycenter, all particles of the Earth follow equal circular paths, its center of mass included, logically at same angular speed (2π radians every some 28 days). So, centripetal accelerations required for the circular movement of each particle are the same in value, but the direction of each one is towards the center of its circular path.
As those accelerations can´t match with Moon´s pull on each particle, there is an imbalance, similar (but more complex) to what in #79. That imbalance only can be countered by internal stresses. If we analyze them along line Moon´s C.G./barycenter/Earth´s C.G., and similarly orientated lines, we find (as in #79) that particles closer to the Moon have to add a pull on contiguous farther parts … And due to Newton´s 3rd Law, each part pulls inner contiguous one with same but opposite (and REAL) force, that is, outwards from Moon.
Whether those last forces should be called "centrifugal" is arguable ... But they, in any case, together with all Moon´s pulls on each particle,  stretch considered line of particles, both where solid Earth, and where water.
Other similarly orientated lines of material suffer similar stretches, but smaller ...
Deformations were solid Earth depend on elasticity. But water logically is more free to move, and that´s the cause of high tide so called "bulges".

[rmolnav]

Curiously, as Earth only revolves around the barycenter, all particles of the Earth follow equal circular paths, its center of mass included, logically at same angular speed (2π radians every some 28 days). So, centripetal accelerations required for the circular movement of each particle are the same in value, but the direction of each one is towards the center of its circular path.
As those accelerations can´t match with Moon´s pull on each particle, there is an imbalance, similar (but more complex) to what in #79. That imbalance only can be countered by internal stresses. If we analyze them along line Moon´s C.G./barycenter/Earth´s C.G., and similarly orientated lines, we find (as in #79) that particles closer to the Moon have to add a pull on contiguous farther parts … And due to Newton´s 3rd Law, each part pulls inner contiguous one with same but opposite (and REAL) force, that is, outwards from Moon.

I think I¨ve already managed to grasp the actual mechanism of internal stresses in cases, like Earth attracted by Moon, when the object revolves, but doesn´t rotate.
ALL MATERIAL POINTS not only follow equal circular paths, logically at same speed, but even they ALWAYS are at farthest (from Moon) point of their own path …
Then, ALL centripetal forces required for the circular movement of each particle are equal both in value and in direction: ALWAYS parallel to line Earth´s C.G./barycenter/Moon´s C.G., and towards the Moon.
If we imagine the revolving object cut into slices (all its material equally far from Moon), and analyze in detail all forces (gravitational, interactions, and the ones required for their circular movements, ALL PER UNIT OF MASS), we find that mentioned "differential gravitational forces" are what remain kind of "free" (not necessary for the circular movements), and either stretch solid Earth, or move water (and change pressure) towards the Moon (where excessive Moon´s pull), or in the opposite direction (where excessive centrifugal force).
Being all centripetal forces equal, "excessive" pull at closer slices is transmitted outwards (at same  rate as Moon´s pull decreases) ... Between each pair of contiguous slices opposite pulls occur (Newton´s 3rd Law), that could be arguably called centripetal and centrifugal ...
So, "differential gravitational forces" tool (usually called "tidal forces") kind of hides a "chain of transmission" of forces between contiguous particles, centrifugal forces included, what affect the whole revolving object.
I used to think "how on Earth so many people, even scientists, say those differential gravitational forces are the unique deep cause of tides, without even mentioning any circular movement, let alone centrifugal forces ?? ... Centrifugal forces HAVE TO be taken into consideration !!!"
And THEY WERE, but without most people (including me) noticing ... !!!

[rmolnav]

As a continuation of #82, just a detail to avoid anybody could get mislead.
When talking about position of material points relative to the Moon, we have to keep in mind that what is being analyzed is exclusively the  Moon /Earth "dance" around  their barycenter... The daily spinning of Earth has to be disregarded.

[rmolnav]

If we imagine the revolving object cut into slices (all its material equally far from Moon), and analyze in detail all forces (gravitational, interactions, and the ones required for their circular movements, ALL PER UNIT OF MASS), we find that mentioned "differential gravitational forces" are what remain kind of "free" (not necessary for the circular movements), and either stretch solid Earth, or move water (and change pressure) towards the Moon (where excessive Moon´s pull), or in the opposite direction (where excessive centrifugal force).
Being all centripetal forces equal, "excessive" pull at closer slices is transmitted outwards (at same  rate as Moon´s pull decreases) ... Between each pair of contiguous slices opposite pulls occur (Newton´s 3rd Law), that could be arguably called centripetal and centrifugal ...
So, "differential gravitational forces" tool (usually called "tidal forces") kind of hides a "chain of transmission" of forces between contiguous particles, centrifugal forces included, what affect the whole revolving object.

As most likely not everybody buys what quoted, I´m going to put what follows, that I sent last year to a scientist by email, when discussing on the issue. I´m sure this analogy can help understanding:
"Surely you also played what in Spain we call "el látigo", literally in English the whip: a row of several boys, each left hand grasping right hand of contiguous inner boy … "Inner" because they run around one of them at a center, trying to keep the row in a radial line at a certain equal angular speed.
Let us consider five boys, A, B, C, D, and E, A being on a fixed point.
Let us suppose each boy hand-to-hand distance is 1 m (logically, the same between their C.G.), they weight of each 40 kg, and they rotate at 1 radian/sec.
Centripetal acceleration of E has to be 1x1x4 = 4 m/sec2. Centripetal force, 4x40 =160 newtons. It only can by exerted by right hand of D pulling inwards left hand of E.
Centripetal acceleration of D has to be 1x1x3 = 3 m/sec2. Required centripetal force: 3x40 =120 newtons. But he is "suffering" two opposite pulls: one outwards (centrifugal) exerted by E, of 160 newtons (3rd Newtons´Principle), and another inwards, exerted by C. If net force on D has to be 120 newtons inwards, right hand of C has to pull left hand of D with an inward force of 120+160=280 newtons.
Also due to 3rd Newton´s Principle, that means right hand of C is pulled outwards (centrifugal) by left hand of D with a force of 280 newtons ...
… C : 1x1x2 = 2 m/sec2 … 2x40 = 80 newtons … 280+80= 360 newtons.
… B : 1x1x1 = 1 m/sec2 … 1x40 = 40 newtons … 360+40= 400 newtons.
The result is boys, especially their arms, get stretched.
All those hand-to-hand transmitted forces are similar to what happens between contiguous pieces of material of above mentioned "columns" perpendicular to axis of rotation. Though in last case there is another important "source" of centripetal forces, Moon´s attraction, it can´t exert required forces along those columns, because Moon´decreases with distance, and required centripetal force increases with distance from axis of rotation.
There is also the difference that own Earth´s gravity effect, important for tides, does´t  significantly affect rotation of boys (energy wasted in friction could be reduced to a minimum with boys skating on ice). There are also other centrifugal forces due to daily Earth´s own rotation, which produces a permanent bulge around the equator.  But what exposed above is the real scenario in comparison with if Earth were just not rotating around Moon/Earth.barycenter, with the purpose of analyzing forces caused by that rotation alone.
The result of all those forcers is both a stretch of solid Earth´s parts, and the pseudo-equilibrium of oceans with its "theoretical" spherical shape very slightly changed, with two bulges".
By that time I had not yet learnt that Earth doesn´t actually rotate, only revolves. Then, the comments to the analogy should be changed.
On the one hand, in the game required centripetal forces increase proportional to the radius, but all particles of Earth follow identical circles, what requires same centripetal accelerations ...
On the other hand, in the game only "internal" stresses supply force for centripetal accelerations, but in our real case Moon gravitational pulls (on each Earth´s particle) are main cause of centripetal accelerations. But not uniformily ...
BUT, similarly to the game, between contiguous slices of any imaginary "column" of material parallel to line of centers of G. Moon/Earth, opposite pulls have to turn up to compensate the imbalance, in such a way that the net force acting on each slice (three vectors to add: Moon´s gravitational pull, and two opposite pulls from contiguous particles), divided by its mass, gives the required centripetal acceleration, the same across the Earth as previously said.
Then, centrifugal forces resulting distribution is kind of a "mirror" image of gravitational pull distribution. At Earth C.G. there are not "spare" forces (all Moon´s pull is spent in centripetal acceleration), but at closer and farther points that balance does´t occur: at closer points there is an "excess" of gravitational pull, and in farther points a deficit, what results in "spare" outwards forces ("arguably" centrifugal ... perhaps another day I´ll come back to that).
BOTTOM LINE: the well known diagram with average pull at C.G., bigger vector pull at closer side, and smaller one at further side, which after deducing average bigger vector changes direction to side opposite to the Moon ...
       

[rmolnav]

Not having seen any further comment to my last posts, I imagine some of you agree with them, but surely many don´t buy my explanations really convinced.
As I continued discussing the topic in other sites, especially youtube pages, I´ve found some nuances to add to my explanations, to try and convey "my" (?) ideas ...
I do agree differences in gravitational forces (so called “differential g.f.”) are necessary condition to have real "tidal forces”, but not sufficient, let alone both concepts should be considered synonymous.
Let us imagine our planet were cut through into two equal parts, by a plane perpendicular to moon-earth line.
The center of mass of closer part would be obviously closer to moon than the farther one, and gravitational force acting on it would be higher.
IF NO OTHER REAL FORCE acted on them (apart from own gravity and internal stresses within each half), they would move towards the moon with different accelerations, following 2nd Newton´s Law.
But, on the one hand, their solid parts are kind of stuck, and they exert internal stresses on each other. And both solid and liquid parts of the two halves are attracted towards earth C.G.
On the other hand, both follow equal circular movements, as earth doesn´t rotate around moon-earth barycenter: it revolves.
Those two identical circular movements require equal centripetal forces, expected to be provided by moon´s pull.
But moon´s pull on closer half is bigger than necessary, and farther one is smaller.
The bulk of moon´s pull on closer half produces its centripetal acceleration. No centrifugal force associated to that fraction: 3rd Newton´s Law tell us closer half exerts an equal pull ON THE MOON. But the excess of moon´s pull on that half is transmitted to the farther half, same way we saw it happens between children at their "whip" game (see last post).
That transmitted pull is precisely what the farther half needs to get same centripetal acceleration, due to the fact that moon´s pull on that part is insufficient.
And  3rd Newton´s Law implies that farther half, apart from its own pull ON THE MOON (which couldn´t be called centrifugal force), also exerts an outward pull ON CLOSER HALF, as part of the reaction to its total centripetal force. That outward force is a real CENTRIFUGAL force: if it were not real, that closer half wouldn´t move the way it does: it would move towards the moon, getting separated from the other half !!!
Whatever the position of the imaginary dividing plane, similar things could always be said.
THOSE internal stresses are the real “tidal forces”: they stretch our planet. And water, being more “free” than solid parts, moves to form the two opposite bulges, as an “infinitesimal” deformation (a few meters of sea level difference some 10,000 km apart) of the spheric shape it would have with only own earth gravity ...
We have to keep in mind that moon´s effect, rather than a dynamic phenomenon, is a succession of static situations. If earth didn´t have its daily rotation, the bulges would form very, very slowly, because moon-earth “dancing” lasts 28/29 days per cycle … And that is what counts, if we analyze only that “dance”. Adding afterwards earth daily rotation, we have the tidal bulges trying to keep in line with moon´s position ...


     

[rmolnav]

Seen from outside, as my stand refutes  what so many people (scientists included) say, most probably "should be" the wrong one ... But there are several details that could explain those so frequent, total or partially  errors:
1) Many folks don´t keep in mind Newton´s Motion Laws apply also to any part of objects, and internal stresses appear, as explained in my last posts (and long ago, e.g. #28)
2) Many ignore or forget that earth´s C.G. is actually following a continuously "curled" path around the sun: earth-moon barycenter is what follows an elliptical orbit.
And that implies additional curvature of earth parts (apart from what due to daily rotation), what required additional centripetal forces ...
3) And 3rd Newton´s Law reactions to those forces "may" be real centrifugal forces, as explained in my last posts.
But many consider those only as "apparent" and/or fictitious forces, that "could not" cause real effects such as tides. I´ve been refuting that since my first post here, #20 in May 2015 !!
By the way, a few months ago a scientist from NOAA, when discussing about a rather old publication of them about tides, told me:
"The publication you are referring to ... It used terminology of science and forces which were common in the 1950s.  Such as centrifugal force.  Centrifugal force was always an "imaginary force" (not a real / measurable force).  But that type of description made the concepts easier to understand and explain.  That  description and use of centrifugal force continued to be common practice until the 1970-80's.  At that point, the terminology shifted and the textbooks used in grade schools were changed to use a more modern terminology and description of this "effect" being a result of inertia rather than an "imaginary force"."
4) And, curiously, the mathematical operation of subtracting gravitational force at earth C.G. from local g.f. at each place gives correct results ... But NOT because that "artificial" operation is what actually happens ...
As explained in my last post, subtracting at each part the required centripetal force there from gravitational force, we get a kind of spare force, that is transferred from the considered material part to the rest of the earth, as internal stresses.
THOSE forces are what actually cause the tides.
BUT, as earth doesn´t rotate around the barycenter, only revolves, centripetal forces are the same across the whole earth. And as at earth C.G. gravitational force is equal to centripetal force (neither surplus nor deficit there), subtracting g.f. there gives same result as subtracting required centripetal force at each place.
Curiously, as moon is tidal locked to earth, it doesn´t revolve but rotates. There differences between gravitational forces and required centripetal forces are relatively higher, because last ones also vary with distance, in this case proportionally to the distance (in sense opposite to g.f.).
And differential gravitational forces mathematical "trick" would give erroneous values when analyzing tidal forces in the moon.       

[smoker42]

Because of the Moon

[rmolnav]

That outward force is a real CENTRIFUGAL force: if it were not real, that closer half wouldn´t move the way it does: it would move towards the moon, getting separated from the other half !!!

Sorry. I meant “it would intend to move towards the moon ...” That centrifugal force would be much, much smaller than gravitational attraction between the two halves.
I was more precise before, when saying:
“IF NO OTHER REAL FORCE acted on them (apart from own gravity and internal stresses within each half), they would move towards the moon with different accelerations, following 2nd Newton´s Law”
By the way, even with mutual attraction, those accelerations would also be centripetal, changing the revolving fashion of the two halves. That attraction would initially keep them “together”, but they would slide on each other ...

[opportunity]

If the tides are caused by the gravity of the moon, why is there a high tide on the side of the Earth furthest from the moon as well as on the closest side?

Peter Conway

Asked by Peter Conway


                                        Visit the webpage for the podcast in which this question is answered.

[chapter podcast=1000585 track=14.01.07/Naked_Scientists_Show_14.01.07_1001836.mp3]  ...or Listen to the Answer[/chapter] or [download as MP3]

As much as I want to read all the posts, the answer is simple.....the earth spins.....so when the pull is strongest with the moon, obviously there's a drag on the Earth, yet to keep the earth on a stable spin there has to be an equal counter-weight on the opposite side.

[rmolnav]

the answer is simple.....the earth spins.....so when the pull is strongest with the moon, obviously there's a drag on the Earth, yet to keep the earth on a stable spin there has to be an equal counter-weight on the opposite side.

The idea of the necessity of a counter-weight to keep stability is correct ... But:
1) The question is actually HOW that necessity is physically fulfilled.
2) If with "spin" you refer to the daily Earth rotation, that movement should be dismissed when analyzing root causes of tides. Moon-Earth couple movement is actually a cycle of 28/29 days. If Earth didn´t have its daily spin, the two tidal bulges would also occur. And the reason of that is what we are discussing.
Logically, as Earth does spin daily, mentioned bulges are continuously trying to keep in line with Moon, and that causes tides, but as a kind of secondary reason.
By the way, Earth daily spin causes the so called equatorial bulge, much, much bigger than the two tidal bulges we are discussing about: equator diameter is more than 40 km bigger than the distance between N and S poles !! Centrifugal forces are involved here too.
And Moon and Sun related tides occur on top of that deformed sphere.

[opportunity]

the answer is simple.....the earth spins.....so when the pull is strongest with the moon, obviously there's a drag on the Earth, yet to keep the earth on a stable spin there has to be an equal counter-weight on the opposite side.

The idea of the necessity of a counter-weight to keep stability is correct ... But:
1) The question is actually HOW that necessity is physically fulfilled.
2) If with "spin" you refer to the daily Earth rotation, that movement should be dismissed when analyzing root causes of tides. Moon-Earth couple movement is actually a cycle of 28/29 days. If Earth didn´t have its daily spin, the two tidal bulges would also occur. And the reason of that is what we are discussing.
Logically, as Earth does spin daily, mentioned bulges are continuously trying to keep in line with Moon, and that causes tides, but as a kind of secondary reason.
By the way, Earth daily spin causes the so called equatorial bulge, much, much bigger than the two tidal bulges we are discussing about: equator diameter is more than 40 km bigger than the distance between N and S poles !! Centrifugal forces are involved here too.
And Moon and Sun related tides occur on top of that deformed sphere.

It's worked itself out, right?

[rmolnav]

It's worked itself out, right?

When I first saw what quoted, I didn´t send any further comment because, rather than a Physics question, it´s kind of a Philosophy one ...
Somehow you are right, because nature works by itself, regardless of our actions and theories.
But, watch out, we are analyzing facts a posteriori. But if gravitational and Newton Motion Laws were different (or the initial conditions), things would have happened differently, and existing  equilibrium could have not been reached: the Moon, if existing as a single object at all, could have either gone away to the space, or fallen back onto the Earth ... Or tides could be quite different, or not be happening at all ...
And it´s quite reasonable to analyze how and why things are actually happening as they are. If everybody have had the attitude your comment implies, sciences would not have gone where they now are, and we could still be in the stone age !! 

[opportunity]

I'll take that as a compliment 

I don't have any tickets on myself. Coudos to your "attitude detector".

Apologies though for not explaining the physics of stable spinning objects. I wrongly thought it was already understood.

[rmolnav]

I wish we ALL had a better knowledge of nature, or at least more imagination ...
I´ve long been arguing in line with what above, and neither myself, nor anybody else so far (unless they kept it "in secret") have imagined what below, and realized that what quoted is WRONG !!
Some people actually said it was wrong, but not for the correct reason. Most of them just considered that centrifugal forces are never real, but only apparent or ficticious ... And I gave many examples of REAL centrifugal forces ...
But recently I learnt that the 28/29 days circular movement of the couple Earth/Moon around their barycenter, though for the Moon is a rotation, for the Earth is NOT: Earth only REVOLVES around mentioned barycenter ...
That implies that all Earth points, center of mass included, follow equal circular paths.
Subsequently, my explanation, that would be valid for the Moon (it rotates at 2π radians/some 28 days angular speed), is NOT for the Earth !!
And possible imbalances between Moon´s pull on each point (either where solid or liquid parts), that could cause centrifugal forces, are not so straightforward to tell (?) ...
I´m trying to sort that out, but not easy ... For all my discussions on the subject, I´ve read many, many articles. But I NEVER saw any reference to what above !!

I´m quoting that because a couple of weeks ago I saw some surprising prove that even eminent physicists can be (or could have been) as wrong as I used to be, in relation with that question of Earth´s revolving instead of rotating, in its "dance" with the Moon.
If somebody has any doubt about that, please consider what follows.
It´s a little tricky, because of the daily Earth´s spin, which not having anything to do with Moon/Earth dynamics, has to be dismissed.
Imagine our meridian is Greenwich, it is 6:00 p.m., and the Moon is at its zenith (subsequently in first quarter).
Next day at same time the Moon would be some 360º/24 eastwards. That means that if Earth were not spinning daily, our meridian would be keeping its position relative to far stars, after that time moving in opposition to the Moon.
The same would happen in subsequent days.
So, Earth does revolve around Moon/Earth barycenter, it does NOT rotate ...

[rmolnav]

Next day at same time the Moon would be some 360º/24 eastwards.

Sorry for the lapsus. I should have said "... some 360º/28 ..."

[Yusup Hizirov]

If, the tidal hump on Earth was created by the Moon - that would not be an ellipse but a "drop". (The force of gravity is added, not compensated).
What prevents a drop of water hanging on an apple, create two tidal hump?

[Colin2B]

What prevents a drop of water hanging on an apple, create two tidal hump?

The apple is not rotating around a barycentre with another mass

[Yusup Hizirov]

In some places there is only one tide per day, where does the barycenter go?
Can one sea move on a barycenter, and another sea does not?

[Colin2B]

In some places there is only one tide per day, where does the barycenter go?
Can one sea move on a barycenter, and another sea does not?

That’s like asking if a wheel axle goes!
Clearly from the earth/moon rotational frame, they both rotate around a common barycentre, but from an earthcentic frame the barycentre rotates around the earth.
For the rest I’ll answer in the other thread where you are misunderstanding the papers you quote.