[rmolnav]

1) “Centrifugal” force isn NOT a forbidden word whatsoever: it is just a poorly understood and poorly explained force. I´m not going to deliver now any further explanation about why I say so, perhaps in another post if found convenient.
But please consider what follows: clear examples of real centrifugal forces appear.
2) Why is Earth from pole to pole smaller than between opposite points of the equator?
Because Earth´s rotation originates centrifugal forces which tend to increase equator´s diameter. Not only at oceans: also solid parts “suffer” that kind of force and get deformed. No doubt about it.
3) What happens if we consider now two celestial objects rotating around a common axis? For same reason, ALL material parts of both objects are subjected to centrifugal forces. The further from common axis, the stronger the force. All particles tend to get further from the axis of rotation.
4) What is causing that rotation? This is clear for everybody: apart from certain suitable initial conditions, gravitatory mutual attraction causes the rotation (centripetal force, “twin” force  -rather mother force- of the centrifugal one …).
Frequently, to simplify, this attraction is considered to work between centers of gravity of each of the two considered objects. But it is not actually so.
Making only “half” of that simplification, we can say that EACH material particle of one of the objects is attracted by the other object, even considering particles of equal masses, differently: the further the particle from the other object, the smaller the attraction …
5) Globally, totals of those centripetal and centrifugal forces are equal. Otherwise the distance between the objects would not keep constant.
But their spatial distributions are opposite from each other. At “inner” parts of both objects gravitatory atraction is bigger than centrifugal one, and at “outer” parts centrifugal forces are stronger than gravitatory ones (relative to the other object).
This fact originates deformation of those objects, even of their solid parts. Needless to say sea surface is much easily deformed than solid parts.
6) The Moon/Earth case is a “tricky” one. Most knowledge “sources”, when dealing with Earth´s movements, mention translation (actually an annual rotation around the sun), the daily rotation … and then they mention the several very slow changes of Earth´s axis direction, and similar very long period changes … But I consider that the third most important movement of Earth is its 28/29 days rotation of both Moon and Earth … Moon´s movement wouldn´t be possible without Earth´s one, and this last one causes the 2nd daily Earth´s tide. Few people mention that movement, I think because the axis of rotation is kind of hidden: it crosses the Earth, but NOT through its center of gravity, but at some point between that center and Earth´s surface. By itself this rotation causes bulges at both parts nearer and further to the Moon, but bigger at further one (it is also further from axis of rotation). But attraction from the Moon is bigger at the side nearer to it.
The result is two similar high tides, one “below” the Moon, and the other on the antipodes. There is actually some delay: due to the quick tangential movement of sea because of Earth daily rotation, high tides try to catch up with their theoretical positions but don´t “succeed” …
This last fact has curiously had very big importance in Earth´s history (perhaps even in the beginning of life), especially at its early stages when Moon was much much closer, Earth´s own rotation was much much quicker, and subsequently tides were much much stronger. But this is not the moment to go any further about that.

[PmbPhy]

pmb,
How does gravity push water away from the moon?

I learned this years ago from Newtonian Mechanics by A.P. French. I don't recall the details of the derivation though. I only make sure that I follow a derivation at least once and then after that I can have confidence in knowing that it's right. I'll scan the derivation in and post it later on today and reread it myself. Until then Wiki explains it nicely. See:
http://en.wikipedia.org/wiki/Tidal_force#Mathematical_treatment

Especially Fig. 4

[rmolnav]

In Reply #21 a wikipedia link is given. It surprises me the don´t mention the centrifugal forces originated by Earth´s rotation around the Moon/Earth rotation axis, as I exposed at Reply #20.
They just say (in my words) that gravitational (due to the Moon) acceleration at ocean nearer side is bigger than at intermediate solid parts of the Earth, and last one is bigger than at the further side of the Earth. And those facts produce kind of opposite acceleration there, relative to main Earth´s body, causing the second high tide.
I´ve previously heard that argument, but consider it insufficient.
If those three zones of the Earth experience only those gravitational accelerations from the Moon, why ALL of them don´t cause a movement of the Earth towards the Moon?

[PmbPhy]

I scanned the section of Gravity From the Ground Up by Bernhard Schutz which covers ocean tides. It's on my companies website at http://www.newenglandphysics.org/Science_Literature/Journal_Articles/schutz_tides.pdf

[rmolnav]

In pdf linked in reply #23, I can see that Schutz also mentions only the different gravitatory pulls from the Moon …
I repeat the question on my post #22:
"If those three zones of the Earth experience only those gravitatory accelerations from the Moon, why ALL of them don´t cause a movement of the Earth towards the Moon? “
Tomorrow I´ll try to explain my “theory” of the centrifugal force used in my first post, which I consider necessary to have a correct explanation of the issue. I´m slow when typing in English, and have no time now. But just an analogy that I consider useful:
Imaging an athlete of hammer trow speciality. He or she can´t keep verticality when throwing the hammer. It is necessary to lean a little backwards. Otherwise the hammer could not be rotated. Both the athlete and the hammer will rotate around an axis situated near the forward part of the athlete´s body.
If the hair of the athlete is long and not  fixed by some device, instead of keeping its normal downward direction due to its weight, it will move back and upwards …
That cannot be due to anything similar to what stated by Schutz relative to tides: CENTRIFUGAL force is the cause.

[PmbPhy]

In pdf linked in reply #23, I can see that Schutz also mentions only the different gravitatory pulls from the Moon …

Did you read that PDF file carefully? Did you see an error in it?

Why do you believe that centrifugal force plays such an important role in ocean tides?

That cannot be due to anything similar to what stated by Schutz relative to tides: CENTRIFUGAL force is the cause.

Let me get this right. You actually believe that tides are caused entirely by centrifugal forces? If so then that's clearly wrong. It can't be correct because the existence of tides corresponds to the position of the moon and centrifugal forces can't account for that. It also can't account for the periodicity of tides either.

[PmbPhy]

That cannot be due to anything similar to what stated by Schutz relative to tides: CENTRIFUGAL force is the cause.

You appear to think that tidal forces are caused by centrifugal forces and that's simply not true. That would mean that there'd be no tides since the centrifugal force on matter at any place on earth doesn't change with the time of day like ocean tides do.

[PmbPhy]

That cannot be due to anything similar to what stated by Schutz relative to tides: CENTRIFUGAL force is the cause.

You appear to think that tidal forces are caused by centrifugal forces and that's simply not true. That would mean that there'd be no tides since the centrifugal force on matter at any place on earth doesn't change with the time of day like ocean tides do.

[rmolnav]

I know centrifugal force can be considered as an inertial, actually kind of ficticious force … But not only that way.
Imagine a solid spherical object rotating as artificial satellite around Earth. As all we know, the hole object is globally subjected only to one gravitatory centripetal force, which is producing an acceleration. Being that acceleration perpendicular to the object velocity, it doesn´t change its linear velocity, only its direction, in such a way that the object rotates. To simplify we can consider the orbit is circular.
That is possible only with suitable values  of angular speed and distance: those values have to match. The gravitatory force divided by object´s mass has to be equal to the square of the angular speed multiplied by the radius (distance from Earth).
For a given angular speed, centripetal acceleration of that satellite is proportional to the distance, but gravitatory acceleration is inversely proportional to the square of the distance.
If we made the simplification of considering the hole mass of the satellite concentrated in its center of gravity, for a given angular speed there would be a distance suitable to get the object moving as a satellite.
In that case, no centrifugal force would actually be affecting the object. That force, in the fashion I´m  using this concept, derives from action/reaction principle: if Earth is producing a gravitatory, centripetal force on the object, this is also producing another equal opposite force on the Earth. But the object does´t suffer that reaction force.
But the object has a size. Different parts of it are at different distances from Earth. Subsequently gravitational forces are different. But the hole object is kind of obliged to rotate at the same angular speed … New internal forces appear affecting different parts of the object!
Let us imagine the object divided into many thin cylindrical slices (with radius equal to distance to Earth). All parts of each slice rotate with same radius. If there were no internal forces, only a central slice could continue rotating with the given global angular speed, but the rest could not.
All parts of the object interact with contiguous ones, but we can consider central parts of the object “ run the show”: they are rotating at the “ correct” speed, and forcing the rest to keep their pace. 
Each slice experiences the gravitatory force at that distance, and additional internal forces from contiguous slices. The sum of all those forces has to produce the centripetal acceleration which makes it rotate at the given angular speed.
Going from center slice to further side, slices are being forced by contiguous closer ones to rotate with a centripetal acceleration bigger than what only gravity would produce on each slice. That is acheived by inner direct tensile forces, from closer slices to further contiguous ones. And that fills the centripetal acceleration “gaps”. Due to action/reaction principle, further slices produces an opposite and equal force on closer ones. Those forces  are CENTRIFUGAL, not ficticious but real, and affect all those slices of the object.
Something similar happens going from center slice to closer side. In this case gravitatory forces get bigger and bigger than what required to produce the centripetal force at the given angular speed. Further slices force contiguous closer ones to rotate with a  centripetal acceleration smaller than what produced by gravity there. That is achieved by direct internal tensile forces from further slices on closer ones, which is also a CENTRIFUGAL, real force.
Those “ internal” imbalances are the cause of the tendency of any celestial object rotating around another (actually around a common axis of rotation) to get an ovoid shape, causing many interesting phenomena, some of them mentioned by Schutz previously linked work as a pdf. And, as far as I can see, they are also the actual cause of the two Earth´s high tides.
I have other arguments that further “ prove” my (?) theory, related to tide cycle due to the other “couple” Sun/Earth, but this post is already too long …
By the way, Schutz (or whoever has written “Investigation 5.1: Tides and eclipses“ at mentioned work), make a bizarre calculation when comparing Sun and Moon gravitatory effects, that I also find wrong ...
     

[rmolnav]

Sorry. An "n" is missing at "But the object does**´t suffer that reaction force". It is clear, isn´t it?

[rmolnav]

After my last posts I´ve found my point can be put in a simpler way:
Each slice is affected by its own gravity, and internal stresses from both nearer and further contiguous slices. The net result of all forces has to produce the centripetal acceleration to make the slice rotate at the given angular speed.
The closer the slice, the bigger the gravitatory force (it increases inversely proportionally to the square of the distance), but the smaller the centripetal force necessary to produce the given angular speed (proportionally to the radius or distance). The dynamic equilibrium of satellite rotation can only be achieved if the net force produced on each slice by contiguous ones (either direct or reaction forces) is in an outward direction: a CENTRIFUGAL force, which affects all slices bar central one, where net force from contiguous slices is null (gravitatory force equal to what necessary to produce the given angular speed).

[rmolnav]

I HAD NOT SEEN Reply #       :
"You appear to think that tidal forces are caused by centrifugal forces and that's simply not true. That would mean that there'd be no tides since the centrifugal force on matter at any place on earth doesn't change with the time of day like ocean tides doI".

That is utterly erroneous. In any low latitude area, when Moon is almost just over there, even solid earth get deformed, in this case mainly due gravitatory pull from the Moon. And it happens the same at antipodes, there mainly due to centrifugal force. Logically, the deformation is smaller than at open oceans, where "fluidity" of water makes deformation much easier ... Even we ourselves weigh a little less, similar to what happens at the equator, compared to our weight at poles.
Something similar, but smaller, happens at noon and midnight, in relation to Sun/Earth effects. 

[PmbPhy]

That is utterly erroneous.

And you are utterly wrong. You're claiming that tidal forces, i.e. ocean tides, are due solely do to centrifugal forces which means that the moon has nothing to do with it because centrifugal forces are not caused by the moon.

You may not like it and you may not understand it but the descriptions in those PDF files are the correct description for tidal forces. There is no doubt about it whatsoever. If you think that those derivations are wrong then you are seriously mistaken.

 You have the derivations right in front of you and they've been there for days now and you've made no attempt to state what's in those derivations that's wrong. I.e. you haven't proved that the derivations and therefore the conclusions are wrong.
Keep it civil - Mod

[rmolnav]

Reply #31:
"... You're claiming that tidal forces, i.e. ocean tides, are due solely do to centrifugal forces which means that the moon has nothing to do with it because centrifugal forces are not caused by the moon".
Sorry, but i have NOT claimed what you say. What in several ways I have said is that ocean tides are mainly due to an imbalance between gravitatory pull from the Moon (the closer, the higher the pull), and centrifugal forces due to the fact that it is not 100% right that Moon is rotating around Earth: both are rotating around a common barycentral axis, and the further from that axis, the bigger the centrifugal force.
And I´m not promoting my own idea and "not inviting critical debate about it ...". F.e., twice I have invited anybody to answer the question:
"If those three zones of the Earth experience only those gravitatory accelerations from the Moon, why ALL of them don´t cause a movement of the Earth towards the Moon? “
To be honest, I admit that perhaps I"ve been too assertive. and I beg your pardon. It would have been due to the fact that I feel pretty sure about the issue. Logically I know I could be wrong. If any of you think it is so, please kindly show it to me with facts and arguments, not with sweeping, not accurate generalizations. 

[rmolnav]

If anybody think I was utterly wrong at #30, as said at #31, please kindly google "tidal earth crust deformation" ...
There are plenty of studies considering a fact that deformation.

[rmolnav]

No reply in two days ... I do hope somebody could be considering my point, without seeing clearly wether I´m right or wrong.
Please kindly compare #29 with what follows. People with some knowledge on calculation of internal stresses of structure materials know that the way I dealt with the issue there is basic on that field.
Another analogy to make it clearer for people not familiar with the matter:
Imaging just a steel cylindrical bar hanging from one of its ends. If we made a horizontal cut, the lower part would fell down. Why it didn´t fall before? Because of internal tensile stresses: upper side of the section was pulling lower one, exactly with a force equal to the weight of lower part of the bar.
If we had made the cut a little lower, we could say the same. In this case the weight of lower part would be a little less: just the weight of the slice between the two cuts.
As the slice is not experiencing any acceleration, the sum of all forces applied to it is null. The sum of internal stresses it suffers from contiguous material, plus its own weight, has to be null.
If we produced any upward acceleration to the hanging point, internal stresses would increase in such a way that the sum of weight of the slice plus stresses from contiguous material would give a net force that divided by slice mass would be equal to the acceleration.
Very similar is what happens in the case of two objects rotating around a common axis. In this case each slice of one of the objects is subjected to gravitational attraction from the other object, and that force plus net forces from contiguos slices, divided by the slice mass, has to be equal to the square of angular speed multiplied by the radius (or distance), actual centripetal acceleration at rotatory movements.
Please kindly go now back to #29 ... As far as I can see, it should be clear for most people. 
   

[PmbPhy]

No reply in two days ...

That's because when we see that someone can't understand an argument and/or correctly back up there's then we usually give up. In this case you still haven't done what's required of you and that's to find an error in the derivations that are in those PDF files that I posted which are from various textbooks.

[rmolnav]

Sorry, but what said in #35 is NOT true. F. e., THREE times I have previously asked:
"If those three zones of the Earth experience ONLY those gravitatory accelerations from the Moon, why ALL of them don´t cause a movement of the Earth towards the Moon? “
It´s you, and rest of readers, who haven´t reply that question. Do you think that question is absurd and doesn´t deserve to be answered?
Within the theory in mentioned PDF, that question could be answered saying that those forces are producing the centripetal accelerations of the rotating movement. But, as I´ve already shown in different ways, in different earth areas gravitational pull from the moon and rotatory centripetal force are NOT equal to each other ... Forces from internal stresses have to be considered.
ANOTHER error, as far as I can see:
In mentioned PDF, tidal forces are considered to be derived  from just the variation of pull from the moon with the distance. That´s why they conclude that although gravitational force decrease to the square of the distance, tidal force decrease to the third power of the distance.
Beeing honest, I have to say I can´t refute their mathematical explanation ... But I insist: stuff different from just gravitatory pull and distance have to be considered to explain tides. Such us internal stresses as I´ve already said, some of them centrifugal. And also what follows.
Even considering a bellow the moon ocean bulge, that could be cause just by pull from the moon, we could call it high tide only in comparison to what happens 90 degrees away, where low tide. But the reason is not just a difference in what they call tidal forces (smaller pull where further from the moon). Even if the pull were the same at both places, tides would happen.
Why? Because main cause of ocean surface shape is OTHER force which has also to be considered: gravitatory one from earth itself. That alone would produce a spherical shape. Adding moon pull bellow it (now I´m "forgetting" inner stresses), the result is kind of less weight of the water there. BUT 90 DEGREES AWAY from there moon´s pull doesn´t actually affect water weight, and we have low tide.
Tides are kind of a dynamic equilibrium that results from MORE forces than just pull from the moon and its variation with the distance ...
 

[rmolnav]

A couple of things more.
Firstly, I beg your pardon for my many English errors. Perhaps they make more tiring to read my posts. It takes me long to write them, and when written I am not sufficiently patient to check them carefully before sending ...
I´m afraid PmbPhy didn´t completely read #34.

But what said there is BASIC Physics. Standard Finite Element Methods to calculate structures are based on what said there: ALL internal and external forces affecting each small finite element of any object have to be considered. If not in balance, deformations and/or movements (with acceleration) happens ...
By the way: in #34, for people not familiar with the subject, I considered the hanging bar initially without any acceleration (still, but it could also be in movement at constant speed). Afterwards with an upward acceleration produced by an artificial force applied to the hanging point: internal stresses would increase.
Needless (?) to say that if we let the bar fall down freely, internal stresses would disappear. The unique force which would be affecting each slice would be its weight, with the result of "g" acceleration there ...
The sum of ALL forces affecting ANY part of the object, and the resulting acceleration, has to match. 

 

[rmolnav]

Two days more and … I´m going to post a “divertimento” on the issue , hoping it may be interesting to some folks.
Nature is far more complex than what seems at first sight. Ocean surface shape depends on not just a few physical phenomena.
I´ll try and list what, as far as I know, affects it, in a decreasing order of importance. I hope not to forget anything. If any disagreement, please let me know, and we can discuss the issue.
1) Gravity from earth itself. If our planet is considered alone, without any movement, without any other celestial object gravitationally affecting it, etc, sea surface “should" be spherical …
2) I say “should” because that is only in theory: gravity is not uniform over sea surface, because amount and density of inside material varies …
That produces sea local level differences much much bigger than tidal differences.
3) Let us “allow” earth daily rotation … Due to centrifugal forces, equator diameter gets bigger than distance from pole to pole.
4) If we now include moon/earth rotation, then we have main part of tides, which we have been discussing. We shouldn´t forget that local conditions (mainly size and shape of continents) produce changes on “theoretical” tides, because water is not completely free to “obey” the forces we have been discussing.
5) Now earth translation (actually rotation around the sun): it produces tides similar to moon related ones, but smaller. These don´t change with the clock. For similar reasons to lunar tides, a high tide happens “bellow” the sun, at noon, and another at antipodes, at midnight. Also with a certain gap due to the fact that the water bulges cannot catch up with their theoretical position …
Needless to say that when lunar tides syncronize with sun ones, we have the strongest actual tides. This happens when full and new moons.
6) Meteorological conditions also affect: atmospheric pressure, winds, etc.
7) I haven´t mentioned water temperature, as if it did´t change with space and time … That isn´t actually so, and the result is that some additional, but relatively small changes happen.
An additional curiosity in this respect. Local increase in temperatures of ocean upper part (f.e., at El Niño zone) are beeing detected thanks to “gravitational” Physics … The temperature increase produces there tiny bulges that are detected with sophisticated satellites (f.e., GRACE, a couple of satellites), thanks to very very tiny changes in the distance to each other, derived from gravitational changes.
The software they use must be “unbelievable”: how can they tell apart the many different gravitatory existing factors?