[David Cooper]

You keep mixing up basic concepts

E.g.:

The centrifugal force is calculated from the barycentre. I want to know if the centripetal force is also calculated from there ...

Why do you say "The centrifugal force is calculated from the barycentre" ? It is not always so, and neither is the centripetal force ...

How is that mixing up basic concepts? You've provided a way of calculating centrifugal force which works from the barycentre. If you don't want it to be calculated from there, why don't you show me where you do want to calculate it from and how to do it from that place.

But in each case, being equal but opposite, both of them must be calculated from same point: the center of curvature of the trajectory of the object ...

So the moon's pull on the Earth does indeed come from the barycentre within the Earth rather than from the moon when we implement this in a program. Except that you've now referred to the centre of curvature of the trajectory of the object, and, depending on how you interpret that, that could mean that it changes over time as it follows an elliptical path in such a way that the point in question is no longer in line with the other body, which would be even more bonkers - we can't have the centripetal force coming from any direction other than the other body.

You've just described differential gravity and you're giving centrifugal force no role. Nature adds the forces without doing any maths

Wrong! What nature actually adds is inertial forces (centrifugal forces in our case) to gravity, with their values at each location (no maths necessary). 
But to subtract gravities from distant locations our "intelligent" minds are required, and nature can´t do it !!

You're saying that nature adds imaginary forces to gravity without doing maths, and that's not far wrong because there's no centrifugal force to add. But gravity from one direction still has to be combined with gravity from another, and that addition/subtraction is done automatically without any kind of intelligence working with numbers. The number crunching is only needed in our mathematical simulations of events, and your method needs that just as much as mine.

[rmolnav]

Quote
But in each case, being equal but opposite, both of them (centripetal and centrifugal f.) must be calculated from same point: the center of curvature of the trajectory of the object ...
So the moon's pull on the Earth does indeed come from the barycentre within the Earth rather than from the moon when we implement this in a program. Except that you've now referred to the centre of curvature of the trajectory of the object, and, depending on how you interpret that, that could mean that it changes over time as it follows an elliptical path in such a way that the point in question is no longer in line with the other body, which would be even more bonkers - we can't have the centripetal force coming from any direction other than the other body.

"Center of curvature" is not a "grey area" to me (as you say centripetal force is to you ... I ONLY could interpret that term the way, as I have more than once said here, "curvature", "center of curvature" and "radius of curvature" are defined in Maths ... Otherwise it would lead me to wrong conclusions !
And, regarding last quoted sentence, if you think so you must agree with the solution given to 3rd problem of:
http://ipho.org/problems-and-solutions/1996/IPhO_1996_Theory.pdf
Is it so ? Because they are considering centrifugal force paramount when resolving the proposed tidal problem.
Is it not so ? Please kindly tell us where you find what you consider erroneous, so that we could see what I quoted is ...

...a chunk of very readable, instantly comprehensible information from his book which are very obvious to me. I could have written that myself

because you are actually very knowledgable on Physics and Maths ...

Where is your evidence that I despise someone that I have no dislike of whatsoever?

Well, to despise one of the very roots of somebody´s stand on his or her speciality is to kind of despise them. And several times you have done so. E.g.:
"Here, we see that the scientist may not have a firm understanding of the tides himself though - all he's doing here is trying to get rid of the idea of centrifugal force by referring to the real mechanism that is behind centrifugal force, but he hasn't realized that this isn't the mechanism behind the tides"
Why don´t you contact and show them your opposite ideas, as I did several times ??
Then you could tell us their answers, as I also did.
As you say,

Lovely - he knows a lot about the tides, but misunderstands the tidal forces that drive them. Experts don't always get everything right - they are not gods.

... but you are much, much farther from being somehow kind of "close to god" than them.
By the way, my discussions with them showed that :

Logically, you should be (I am) trusting reason rather than authority.

because reason presided them ...
Quite different situation than our discussion, because you keep misunderstanding even very basic Physics and Maths concepts, "despising" even household dictionary definitions, no matter how many times are posted here !!

[rmolnav]

Well, to despise one of the very roots of somebody´s stand on his or her speciality is to kind of despise them. And several times you have done so.

Another example of that type of "despising" is the fact that you lofty ignore what I also posted here several times, because mentioned scientist is the author (or, at least one of them) of
https://tidesandcurrents.noaa.gov/restles3.html ...
...where they say:
"1. The Effect of Centrifugal Force. It is this little known aspect of the moon's orbital motion which is responsible for one of the two force components creating the tides. As the earth and moon whirl around this common center-of-mass, the centrifugal force produced is always directed away from the center of revolution. All points in or on the surface of the earth acting as a coherent body acquire this component of centrifugal force".
Again, why don´t you contact and show them your opposite ideas, as I did several times ??
Then you could tell us their answers, as I also did.
By the way, with those discussions with them I polished up my understanding of the actual Physics of the tides, with details also confirmed by other eminent scientists. And I posted here links to their sites where that is clearly shown. You could try and contact them too, to increase the odds of receiving an unswer ...

[David Cooper]

"Center of curvature" is not a "grey area" to me (as you say centripetal force is to you ... I ONLY could interpret that term the way, as I have more than once said here, "curvature", "center of curvature" and "radius of curvature" are defined in Maths ... Otherwise it would lead me to wrong conclusions !

If you have a changing curvature (as with an ellipse), the point you consider to be the centre of curvature will vary depending on how much of that line you use for the calculation, each section of it disagreeing with the next and leading to a fudged average centre if you try to pin it down to a single point for both. If you take an entire ellipse, then the centre is half way between the two foci. I have no idea what the rules are about which of the possible ways of defining the centre of curvature in such a situation and I have no desire to go hunting for them. My computer runs XP which has had no updates for a couple of years and is vulnerable to security risks (making searches dangerous), and it also tends to freeze when I open more than a couple of tabs (or to watch video), so it's more convenient just to ask people to spell out what they're doing rather than to have to reboot over and over again while hunting for simple information which is not as simple to find as you might imagine. Even if I do find rules for something, there is no guarantee that they are the same rules that you are following.

And, regarding last quoted sentence, if you think so you must agree with the solution given to 3rd problem of:
http://ipho.org/problems-and-solutions/1996/IPhO_1996_Theory.pdf
Is it so ? Because they are considering centrifugal force paramount when resolving the proposed tidal problem.
Is it not so ?

(I reluctantly took the risk with opening that, though PDFs are pretty safe. It froze my machine for only a short time, so I was able to access its content. What I've found there looks useful - some stuff that will be relevant to the simulation.)

The question says: "We simplify the problem by making the following assumptions." It does not say that the method it expects you to use in solving it is the correct mechanistic explanation of events - it is actually testing people's ability to apply the rules of a particular approach which happens to be an abstraction. It does not say that they consider centrifugal force paramount when resolving the proposed tidal solution - it merely pushes you into using a rotating frame to analyse the events, and it does so in order to test your understanding of the rules of working with rotating frames. Note that it requires you to treat the Earth and moon in isolation so as to avoid complications, and that it requires them to be at a constant distance apart.

Well, to despise one of the very roots of somebody´s stand on his or her speciality is to kind of despise them.

You should choose a better word - despise means hate strongly, and I have no hatred or dislike of the person or his stand whatsoever. I simply label it as wrong because it is wrong.

And several times you have done so. E.g.:
"Here, we see that the scientist may not have a firm understanding of the tides himself though - all he's doing here is trying to get rid of the idea of centrifugal force by referring to the real mechanism that is behind centrifugal force, but he hasn't realized that this isn't the mechanism behind the tides"

Disdain might be the word you're looking for, but even that isn't appropriate - to err is human, and all I've done is point out that he has made a mistake in one area.

Why don´t you contact and show them your opposite ideas, as I did several times ??

I don't go around bothering scientists to point out errors that they've made which they may be fully aware of already.

... but you are much, much farther from being somehow kind of "close to god" than them.

I have no doubt that when they get into the fine details of how the tidal forces convert into actual tides with the complications of some places having one tide per day while others have up to 128 of them, their expertise will dwarf my meagre knowledge. But on the issue of the actual tidal forces right at the start of the process, if they aren't doing differential gravity and are instead doing the warped physics of an abstraction involving rotating frames, then my judgement of that part is superior to theirs. Most scientists agree with differential gravity though, so we're only talking about a minority who are applying the wrong approach.

By the way, my discussions with them showed that :

Logically, you should be (I am) trusting reason rather than authority.

because reason presided them ...

If you were trusting reason, you'd recognise that their explanation doesn't work for all the reasons that have been pointed out to you in this thread, such as centrifugal force not being able to lift material at opposite sides of the Earth with one lot caused by the Earth following a curve with the sun on its inside while at the same time it follows a curve with the moon on its inside (while the sun and moon are to opposite sides of the Earth). You just ignore that case and act as if it isn't relevant, but it destroys your mechanism - the Earth can't be following two different curved paths at the same time which curve in opposite directions. If you were rational, you'd have abandoned your explanation right there and accepted that it's plain wrong.

Quite different situation than our discussion, because you keep misunderstanding even very basic Physics and Maths concepts, "despising" even household dictionary definitions, no matter how many times are posted here !!

I understand the physics and maths of what's actually happening, and that's the part that counts. You don't understand the actual physics, but imagine that you do because you are misapplying rules which you trust more than reality - you just apply rules blindly without actually thinking for yourself.

Another example of that type of "despising" is the fact that you lofty ignore what I also posted here several times, because mentioned scientist is the author (or, at least one of them) of
https://tidesandcurrents.noaa.gov/restles3.html ...
...where they say:
"1. The Effect of Centrifugal Force. It is this little known aspect of the moon's orbital motion which is responsible for one of the two force components creating the tides. As the earth and moon whirl around this common center-of-mass, the centrifugal force produced is always directed away from the center of revolution. All points in or on the surface of the earth acting as a coherent body acquire this component of centrifugal force".

No - it's merely an example of me calling something wrong because it's wrong. It is possible that the scientist you refer to has gained an incorrect understanding because he has been trained in the maths of the abstraction of rotating frames and he has been misled by that into thinking that it is a mechanistic description of the actual physics involved. I doubt he's ever stopped to question that belief. If he did, he would likely change position on it very quickly because he'd think it through, see the places where it fails, and instead of searching the net to find authorities who say the same thing, he'd try to work out what the real mechanism is, quickly realising that it's simply differential gravity, and then he'd make a note that he needs to rewrite one of his many pages some day (if he can find the time) to put it right.

Again, why don´t you contact and show them your opposite ideas, as I did several times ??

Again, I don't like bothering busy scientists about things like that, and I don't like to pounce on them in that way to tell them they've got something wrong either, not least because a hundred other people might be doing the same thing over the same mistake. Scientists are busy with their work and don't need to be interrupted over trivia. If anyone has been misled by that page, that will come out in places like this forum and they can be shown the errors. If they are rational, they will recognise the errors and learn. If they are not rational, they will fail to recognise the errors and will appeal to authority instead.

Then you could tell us their answers, as I also did.[/b]

If you have already established a friendly conversation with the scientist and are confident that he is happy to discuss things with you (and isn't actually swearing as he types his replies), then you could put the problems to him and ask him how his mechanism applies in the cases where it most clearly fails.

You could try and contact them too, to increase the odds of receiving an unswer ...

If there's any difficulty in you receiving an answer, what does that tell you? It suggests to me that the person is busy and doesn't need anyone else jumping in to ask the same questions. If you are trying to communicate with him though, you should ask him about one of the situations where his mechanism breaks and point out that differential gravity doesn't break. Ask him if he's sure he's backed the right horse. Put the case to him where the Earth is directly between the moon and Sun with centrifugal force lifting water at two opposite sides and ask him how that's possible. Is there any way for his mechanism to handle two barycentres, or is it restricted to a single rotating frame with different mechanisms accounting for different bulges depending on which barycentre you decide to use.

You've read his work in detail, whereas I've merely looked through the page you linked to. Does he at any point tell you that differential gravity is not the correct explanation? Does he even mention it at all? It's possible that he's completely unaware of it because he isn't a cosmologist.

[rmolnav]

Again: more RUBBISH !
As I´ve said several times, you don´t deserve the time and effort I´m "wasting" discussing with you, because most of what you say is a lot of:
- Absurdities (if not due to serious reason flaws, due to what follows).
- Lies: in order to have something to say against my stand, you, time and again, claim I said things I´VE NEVER SAID. You must have run out of "reasonable" arguments !
- Signs of poor education. E.g.: not even in my wildest dreams I could have imagined to listen from an adult educated on Maths "… the point you consider to be the centre of curvature will vary depending on how much of that line you use for the calculation” (let alone after having been sent the definition of that basic concept more than once !!)

BUT I´m going to refer to something you say it could mislead other people:
 

You've read his work in detail, whereas I've merely looked through the page you linked to. Does he at any point tell you that differential gravity is not the correct explanation? Does he even mention it at all? It's possible that he's completely unaware of it because he isn't a cosmologist.

I haven´t actually read the book in detail, and don´t know if he somewhere refers directly to the so called “differential gravity”. But he says:
"The Effect of Centrifugal Force. It is this little known aspect of the moon's orbital motion …”
If, as you claim, Logics is your forte, how can´t you tell that he clearly knows there is another “explanation” of tides, which ignores that “little known” effect ??
And he is not the only scientist I have referred to here. I´ve  also posted the title of a youtube video where directly one of the conferences given by Neil F. Comins was recorded:
What if the Moon Didn't Exist? — Neil F. Comins
Surely you haven´t watched it, have you ? Otherwise you shouldn´t argue the way you do.
In the first part of it NFC deals with tides.  As it is too long, and with the purpose of helping people lazy (or with little time) to watch it, following information can be heard and seen ...
In a World Expo in Nagoya (2005?) Japan chose the Moon as the "nucleus" of their pavilion. And they asked NFC (logically, as one of top authorities on the matter) to deliver the conference of the linked youtube video.
The director of the event was changed a couple of weeks before inauguration, and NFC was sent what, according to the new director, the conference should include.
He replied the director it was WRONG (he found more than 15 errors). He says the director answered “Scientists can reasonable disagree in these matters” … even adding “I´m not making up this” (!!), like saying he could understand the audience could consider that unbelievable, but that it was true …
All that starts at 06:00, with following app. timing:
07:20 - He says is going to include a clip with one of those 15 errors (from a "History Channel" video in line with new director ideas).
08:00 - He even says that explanation is “fairly universal” and that ...
08:11 - … it is COMPLETELY WRONG.
08:20 - 08:47 Mentioned clip: one of the many videos one can find out there that consider the so called “differential gravity” as the UNIQUE cause of tides …
09:13 - He explains what I´ve said here many times, though logically much better than me: centrifugal force also intervenes (though he avoids that controversial term and says "outward" force).
09:25 - 09:39 He even clearly says that to consider moon orbits the earth is also WRONG … They both are rather “waltzing” as a couple … idea I´ve also brought up here several times, last one on 1st and 2nd parts of my series “MY ULTIMATE GO?” …
And he continues saying, and discussing with the audience, other details relative to tides, for some more time (10 min?).
So, he does know:

Most (?) scientists agree with differential gravity ...

Please everybody keep in mind that, according to his web page:
"Neil is an astrophysicist, astronomer, professor of physics and astronomy at the University of Maine, author of at least 20 published books on astronomy and space (many more according to the Amazon web site), and public speaker. He has "appeared" on over a hundred radio shows aired around the world, as well as numerous television shows".
Some of you will also remember that not long ago I mentioned he is also the author of:
"Sources of Misconceptions in Astronomy", by Neil F. Comins (University of Maine).
and that he himself said:
"... For the past eighteen months I have been working with students taking the above-mentioned introductory college astronomy course in an effort to understand the origins of their misconceptions about astronomy ..."
Could he be wrong? For sure ... As you say, he is not god! But the odds of that happening must be smaller than 1:1000 !!
Therefore, it is not me but YOU who ...

If you were rational, you'd have abandoned your explanation right there (or even long ago) and accepted that it's plain wrong.

[David Cooper]

Again: more RUBBISH !

Then stop posting it.

As I´ve said several times, you don´t deserve the time and effort I´m "wasting" discussing with you, because most of what you say is a lot of:
- Absurdities (if not due to serious reason flaws, due to what follows).

You're the one pushing absurdities, but you're incapable of recognising that.

- Lies: in order to have something to say against my stand, you, time and again, claim I said things I´VE NEVER SAID. You must have run out of "reasonable" arguments !

If you can't express yourself clearly, I have to guess what you mean, and a lot of the time I have to do that by assuming that the nonsense you do successfully express is actually your position.

- Signs of poor education. E.g.: not even in my wildest dreams I could have imagined to listen from an adult educated on Maths "… the point you consider to be the centre of curvature will vary depending on how much of that line you use for the calculation” (let alone after having been sent the definition of that basic concept more than once !!)

If you have a varying amount of curvature in a line, at one point it's steeper than another. At any given point, the local curvature can be extended to form a circle, and the centre of the circle generated from one point will not be the same as the centre of the circle generated from the next point. If you want to assert that there's a centre of curvature for a stretch of such a curve, all you can do is pick an average, and it'll be a different point depending on which stretch of the curve you use. If you really understand maths as well as you think you do, you should immediately understand what I'm talking about and not mistake it for rubbish, but I think it just goes straight over your head and you assume that you have a superior knowledge because you can't actually hack the maths at all.

BUT I´m going to refer to something you say it could mislead other people:
 

You've read his work in detail, whereas I've merely looked through the page you linked to. Does he at any point tell you that differential gravity is not the correct explanation? Does he even mention it at all? It's possible that he's completely unaware of it because he isn't a cosmologist.

I haven´t actually read the book in detail, and don´t know if he somewhere refers directly to the so called “differential gravity”. But he says:
"The Effect of Centrifugal Force. It is this little known aspect of the moon's orbital motion …”
If, as you claim, Logics is your forte, how can´t you tell that he clearly knows there is another “explanation” of tides, which ignores that “little known” effect ??

Where in that is there anything that I've misled anyone about? You've pointed to a bit where he is misleading people by referring to a fake mechanism. And it isn't clear from that that he's aware of another explanation - it could be that he thinks he has the only explanation and that everyone else just thinks it's an unsolved mystery.

And he is not the only scientist I have referred to here. I´ve  also posted the title of a youtube video where directly one of the conferences given by Neil F. Comins was recorded:
What if the Moon Didn't Exist? — Neil F. Comins
Surely you haven´t watched it, have you ? Otherwise you shouldn´t argue the way you do.

Of course I haven't watched it. The existence of a video of a scientist giving a talk about an incorrect mechanism doesn't magically make the incorrect mechanism work.

In the first part of it NFC deals with tides.  As it is too long, and with the purpose of helping people lazy (or with little time) to watch it, following information can be heard and seen ...

Video is the most time-consuming way to gather knowledge - highly inefficient.

08:20 - 08:47 Mentioned clip: one of the many videos one can find out there that consider the so called “differential gravity” as the UNIQUE cause of tides …
09:13 - He explains what I´ve said here many times, though logically much better than me: centrifugal force also intervenes (though he avoids that controversial term and says "outward" force).

The centrifugal force explanation is nothing more than a contrived abstraction. He can use whatever wording he likes, but there isn't going to be an outward force on the water on both sides of the Earth when the Earth's between the sun and moon. It's an abstraction which only seems to fit if you just consider two bodies. As soon as you add in more, it breaks. However, differential gravity works in all cases.
 

09:25 - 09:39 He even clearly says that to consider moon orbits the earth is also WRONG … They both are rather “waltzing” as a couple … idea I´ve also brought up here several times, last one on 1st and 2nd parts of my series “MY ULTIMATE GO?” …

The moon does orbit the Earth and the Earth orbits the moon. The barycentre is the average location of the Earth and of the moon.

So, he does know:

Most (?) scientists agree with differential gravity ...

Please everybody keep in mind that, according to his web page:
"Neil is an astrophysicist, astronomer, professor of physics and astronomy ...
Could he be wrong? For sure ... As you say, he is not god! But the odds of that happening must be smaller than 1:1000 !!

You clearly don't have a clue about how to calculate odds. Most scientists working in the relevant field agree with differential gravity. Finding a couple of exceptions does not swing the odds over in favour of their fake mechanism.

Therefore, it is not me but YOU who ...

If you were rational, you'd have abandoned your explanation right there (or even long ago) and accepted that it's plain wrong.

You're the one with the explanation that keeps breaking. I've backed the explanation that works in every case. If you think it would be rational for me to abandon the correct explanation because the incorrect one keeps breaking, you are... (how can I put this in order to be maximally kind?) ...a wonderful eccentric who makes the world a more colourful place. I celebrate the fact that you're out there making everyone happy by spreading comedy physics.

[rmolnav]

Quote
- Lies: in order to have something to say against my stand, you, time and again, claim I said things I´VE NEVER SAID. You must have run out of "reasonable" arguments !
If you can't express yourself clearly, I have to guess what you mean, and a lot of the time I have to do that by assuming that the nonsense you do successfully express is actually your position.

[/i]
Frequently you blame my expressing problems as the reason why you misunderstand what I say ... I could certainly do it better, but nobody will believe that is your main problem !!
Yesterday you quoted and said:

Quote
- Signs of poor education. E.g.: not even in my wildest dreams I could have imagined to listen from an adult educated on Maths "… the point you consider to be the centre of curvature will vary depending on how much of that line you use for the calculation” (let alone after having been sent the definition of that basic concept more than once !!)
If you have a varying amount of curvature in a line, at one point it's steeper than another. At any given point, the local curvature can be extended to form a circle, and the centre of the circle generated from one point will not be the same as the centre of the circle generated from the next point. If you want to assert that there's a centre of curvature for a stretch of such a curve, all you can do is pick an average, and it'll be a different point depending on which stretch of the curve you use. If you really understand maths as well as you think you do, you should immediately understand what I'm talking about and not mistake it for rubbish, but I think it just goes straight over your head and you assume that you have a superior knowledge because you can't actually hack the maths at all.

How on earth can you keep confusing concepts that way, and blaming my lack of clarity ??
Anybody can see the problem is YOURS, because I haven´t put here only explanations by me, but also definitions by household dictionaries (and several times), and you, unbelivibly, insist in your basic errors.
E.g.: directly referring to the mathematical concept of "curvature" and "center of curvature":

A) Post #432.
..That last component exerts what is called a centripetal force on the stone, because in an infinitesimal lapse of time any curved line is an infinitesimal arc of a circle, with same curvature as the line at that point ...
As somebody could not clearly understand that concept of “curvature” (most probably, you one of them):
"Curvature, in mathematics, (is) the rate of change of direction of a curve with respect to distance along the curve. At every point on a circle, the curvature is the reciprocal of the radius; for other curves (and straight lines, which can be regarded as circles of infinite radius), the curvature is the reciprocal of the radius of the circle that most closely conforms to the curve at the given point (see figure)”.
(Encyclopedia Britannica).

B) Post #455.
Quote from: David Cooper on 26/10/2018 22:57:24
Quote
- At locations where the ellipse is more/less curved than if it were a circle, the radius of curvature is smaller/bigger respectively.
More maths help needed for that then.
I already referred to those mathematical concepts (#432):
"Curvature, in mathematics, (is) the rate of change of direction of a curve with respect to distance along the curve. At every point on a circle, the curvature is the reciprocal of the radius; for other curves (and straight lines, which can be regarded as circles of infinite radius), the curvature is the reciprocal of the radius of the circle that most closely conforms to the curve at the given point (see figure)”. (Encyclopedia Britannica).

C) Post #467.

Quote from: David Cooper on 31/10/2018 21:17:56 Quote
But in each case, being equal but opposite, both of them (centripetal and centrifugal f.) must be calculated from same point: the center of curvature of the trajectory of the object ...
So the moon's pull on the Earth does indeed come from the barycentre within the Earth rather than from the moon when we implement this in a program. Except that you've now referred to the centre of curvature of the trajectory of the object, and, depending on how you interpret that, that could mean that it changes over time as it follows an elliptical path in such a way that the point in question is no longer in line with the other body, which would be even more bonkers - we can't have the centripetal force coming from any direction other than the other body.
"Center of curvature" is not a "grey area" to me (as you say centripetal force is to you ... I ONLY could interpret that term the way, as I have more than once said here, "curvature", "center of curvature" and "radius of curvature" are defined in Maths ... Otherwise it would lead me to wrong conclusions !

Either you, having run out of "reasonable" arguments, keep lying on purpose time and again, or you don´t even read my posts, or your problems in Logics (your speciality ??) are even much more serious than what I´ve thought several times ... !!

[David Cooper]

..That last component exerts what is called a centripetal force on the stone, because in an infinitesimal lapse of time any curved line is an infinitesimal arc of a circle, with same curvature as the line at that point ...

You don't even notice that I said the same thing but pointed out that if you apply the centripetal force from such a direction you are not applying it from the direction of the barycentre (or the other body beyond the barycentre and in line with it). If you really do want to apply it in these wrong directions throughout most of the orbit, then you should simply have confirmed that is how you want to apply the force. It won't work though - it will not produce the required orbit. That is why I was looking for other possible interpretations of "centre of curvature" that you might have intended and which might produce a more viable result, but now it's abundantly clear that you do mean the most obvious thing and that you won't be able to produce the right orbit with it. Again it reveals that you don't understand your own method - you've just taken it on trust that it works (somehow) from a few scientists who have backed the wrong horse.

Either you, having run out of "reasonable" arguments, keep lying on purpose time and again, or you don´t even read my posts, or your problems in Logics (your speciality ??) are even much more serious than what I´ve thought several times ... !!

The problem is that if I interpret your words in the most direct way, they lead into a load of absolute cobblers that doesn't work, so I look for alternative possible explanations behind the rubbish you're writing, and I do so in the hope that you might actually understand your own mechanism, but you clearly don't. The centrifugal force must either be applied from the barycentre or the other body and not from any of the infinite series of other points that are centres of curvature related to a host of points along the orbit. You are wandering about all over the place because you have very little grasp of how your method works - you are largely making it up as you go along.

[rmolnav]

Just a couple of things, for now ...

Quote from: rmolnav on Yesterday at 08:10:51
..That last component exerts what is called a centripetal force on the stone, because in an infinitesimal lapse of time any curved line is an infinitesimal arc of a circle, with same curvature as the line at that point ...
You don't even notice that I said the same thing but pointed out that if you apply the centripetal force from such a direction you are not applying it from the direction of the barycentre (or the other body beyond the barycentre and in line with it). If you really do want to apply it in these wrong directions throughout most of the orbit, then you should simply have confirmed that is how you want to apply the force.

[/i]
UTTERLY WRONG what in italics! Time and again, you show your lack of basic education on Maths and Physics ...
It´s not a question of how I "want to apply the force.", it is a question of a "rational" analysis of facts.
Perhaps due to your previous and quite erroneous statements saying things such as that gravity could not be "labelled" as centripetal force (let alone a part of it !!), you keep mixing basic concepts.
Haven´t you ever thought of the possibility that the pull vector causing the revolving/rotation could be broken down into two components orthogonal to each other, with quite different effects on the movement, most of the times not pointing at the origin of the pull ?? ...
If we "logically" chose the directions of those components one perpendicular to the orbit at considered point, and the other tangential, ONLY the former is the one which bends the orbit and causes centripetal acceleration, and it obviously points at the center of curvature there ...
"Logically" once more, that component of the gravity pull is the one which EXERTS (gravity essence doesn´t change !!) what in Physics (since first levels) is called "centripetal force".
And if you don´t understand my words, have a go with any of the definitions I´ve previously linked. 

The problem is that if I interpret your words in the most direct way, they lead into a load of absolute cobblers that doesn't work

That is just a handy excuse ... As I said yesterday:

How on earth can you keep confusing concepts that way, and blaming my lack of clarity ??
Anybody can see the problem is YOURS, because I haven´t put here only explanations by me, but also definitions by household dictionaries (and several times), and you, unbelivibly, insist in your basic errors.

[rmolnav]

Quote
... So, he does know:
Quote from: David Cooper on 01/11/2018 22:49:47
Most (?) scientists agree with differential gravity ...
(though I´d rather say most people ...)
Please everybody keep in mind that, according to his web page:
"Neil is an astrophysicist, astronomer, professor of physics and astronomy ...
Could he be wrong? For sure ... As you say, he is not god! But the odds of that happening must be smaller than 1:1000 !!

You clearly don't have a clue about how to calculate odds. Most scientists working in the relevant field agree with differential gravity. Finding a couple of exceptions does not swing the odds over in favour of their fake mechanism.[/quote]

AND YOU CLEARLY ignore that in SCIENCE it is not the majority what counts ...
Neil F. Comins is professor of physics and astronomy at the University of Maine. His books include Discovering the Universe, tenth edition (2014), What If the Earth Had Two Moons? (2010), Heavenly Errors: Misconceptions About the Real Nature of the Universe (Columbia, 2003), and What If the Moon Didn't Exist? (1993). ...
Some ten years after the publication of last book, in a World Expo in Nagoya (2005?) Japan chose the Moon as the "nucleus" of their pavilion. And they asked NFC (logically, as one of top authorities on the matter) to deliver the conference of the linked youtube video.
The director of the event was changed a couple of weeks before inauguration, and NFC was sent what, according to the new director, the conference should include.
He replied the director it was WRONG (he found more than 15 errors). He says the director answered “Scientists can reasonable disagree in these matters” … even adding “I´m not making up this” (!!), like saying he could understand the audience could consider that unbelievable, but that it was true, and he delivered the conference as HE thought he should, including a clip with one of those 15 errors (from a "History Channel" video in line with new director ideas, defending differential gravity as THE cause ...). Youtube video timing:
08:00 - He even says that explanation is “fairly universal” and that ...
08:11 - … it is COMPLETELY WRONG.

[/b]

DO YOU REALLY THINK that, among all scientists supposedly as contrary to his view as you, none of them would have challenged NFC during last decades, similarly to what you are doing here ?? Because NFC stand on the issue is not only on youtube, but also on his book, it has been broadcasted by many TV channels ...
Most eminent scientists give conferences, publish books ... For them, if they thought NFC was quite wrong (as you dare say), that issue would have been a fantastic opportunity to make a lot of money ... (and fame, personal satisfaction, etc)
It seems you barely search the web, but I´ve done it a lot of times for the last three or four years in relation with tides (and centrifugal force indeed), and I´ve haven´t seen any scientist challenging NFC stand on tides ... Unfortunately, there still are many showing differential gravity theory, but none of them is a "first" level scientist ... Most either haven´t learn NFC´s stand yet, or don´t dare challenging him and keep silent...
And, besides NFC, NOAA scientists published the works I´ve referred to so many times, the authors of "French Tides" linked by PmbPhy too … And NO serious challenge whatsoever !
Don´t forget the strong discussion happened in recent decades in relation to the opposite ideas scientists had about causes of climate change ... It is quite another issue, but be sure that if many first line physicists thought NFC were quite wrong on that, we would have had quite an interesting "spectacle" on the media ...
That, and my own grasp of the facts (after my discussion especially with one of NOAA physicists), is why I said that NFC could certainly be wrong, but I guess the odds would be below 1:1000 ...

By the way, as I explained on 1st and 2nd parts of my series "MY ULTIMATE GO?", I agree with NFC as far as the "waltz" moon and earth are concerned. 
I would accept that moon orbits the earth though, but earth doesn´t orbit the moon, because ...
Oxford Dictionary definition of "to orbit":
1(of a celestial object or spacecraft) move in orbit round (a star or planet).
Living aside their limitation "round a star or planet", what is QUITE clear is that the moon is always far away from the closed trajectory of the earth ... And I suppose "round" meaning is understood by everybody ...
The fact that earth is so much massive than the moon, allows her to kind of "run the shots".
As I´ve said several times, earth´s revolving around the barycenter is just like the movement of a child´s wrist playing hulla-hoop (we can imagine the moon at the center of the hoop), and earth should not be considered in a "free fall" towards the moon whatsoever.
Though I understand that children move their wrist with their muscles, and both moon and earth pulls on each other are what makes them "dance". 
But the Dynamics of the phenomenon are different from when a "proper" orbiting, e.g. artificial satellites orbiting the earth.

[David Cooper]

Just a couple of things, for now ...

Quote from: rmolnav on Yesterday at 08:10:51
..That last component exerts what is called a centripetal force on the stone, because in an infinitesimal lapse of time any curved line is an infinitesimal arc of a circle, with same curvature as the line at that point ...
You don't even notice that I said the same thing but pointed out that if you apply the centripetal force from such a direction you are not applying it from the direction of the barycentre (or the other body beyond the barycentre and in line with it). If you really do want to apply it in these wrong directions throughout most of the orbit, then you should simply have confirmed that is how you want to apply the force.

[/i]
UTTERLY WRONG what in italics! Time and again, you show your lack of basic education on Maths and Physics ...

Have you any idea where all your centres of curvature are for each part of an ellipse? Please go and plot them out and see what shape results from that. Then ask yourself if you really want to apply centripetal force from the resulting line. Maybe you do, but if that's the case, all you have to do is say so, but I can't see it working. Perhaps the problem here is that you aren't able to visualise things correctly because you're not testing your ideas to the extreme - you always go the opposite way to give them the easiest tests possible where they provide the illusion of passing. You need to draw out an extreme ellipse for a moon, put the barycentre at one of the foci, then draw in a planet over it (the barycentre being inside the planet). Then take a point on the elliptical orbit where the moon is half way between apogee and perigee, then work out where the centre of curvature is for that point and see if a line between the two points (moon and centre of curvature) continues on in the direction of the barycentre or the planet. I think you'll find that it can easily be 80 degrees out from the right direction. I can process this stuff in my head with ease, but you appear to be incapable of doing so, with the result that you repeatedly think I'm talking nonsense because you're failing to push your mechanism to the extremes where it's faults become manifest. You haven't done the work.

It´s not a question of how I "want to apply the force.", it is a question of a "rational" analysis of facts.

It's a matter of what will actually produce the required results, and it looks so wrong to me that I don't see the point of wasting time writing code to try out an idea that looks so ridiculous. That's why I'm trying to pin you down on how your method applies. If I just believe what you appear to be saying now and write code that shows it to be nonsense, you'll just turn round and tell me that you didn't mean what I thought you'd said and that I'd programmed it to do the wrong thing. That's why I want you to spell out your method clearly, but you maybe don't want to do that because you don't want anyone to see what a pile of mouldy old pants it is.

Perhaps due to your previous and quite erroneous statements saying things such as that gravity could not be "labelled" as centripetal force (let alone a part of it !!), you keep mixing basic concepts.

Where did I say that? An elephant could be labelled as centripetal force if someone decides to label it as such. What I tried to do was show you that it's a mistake to think that applying that label to gravity works the same way as it does with something going round on the end of a string. Anyone with a half-decent grasp of physics will recognise the point that I was making and know that it is correct - there is no force operating in the opposite direction when gravity is the "string", quite unlike an actual string where "reactive centrifugal force" is generated. Centrifugal force only appears to exist when you view things artificially through rotating frames.

Haven´t you ever thought of the possibility that the pull vector causing the revolving/rotation could be broken down into two components orthogonal to each other, with quite different effects on the movement, most of the times not pointing at the origin of the pull ?? ...

If the pull on a planet comes from the moon, why would you want to split that into two pulls from different directions? Real physics should take the pull from the moon.

If we "logically" chose the directions of those components one perpendicular to the orbit at considered point, and the other tangential, ONLY the former is the one which bends the orbit and causes centripetal acceleration, and it obviously points at the center of curvature there ...

So you appear to be confirming that you have the centripetal force applying not from the object that generates the gravitational force, nor from the barycentre, but for a series of other points which usually aren't in line with either of them unless the orbit is precisely circular. That's exactly what I was wanting to know, and all you had to do was say yes. I can see too why you were so keen to cover that up and why it's taken so long to get that information out of you.

The problem is that if I interpret your words in the most direct way, they lead into a load of absolute cobblers that doesn't work

That is just a handy excuse ...

Well, I never expected it to be anything like so contrived.

As I said yesterday:

How on earth can you keep confusing concepts that way, and blaming my lack of clarity ??
Anybody can see the problem is YOURS, because I haven´t put here only explanations by me, but also definitions by household dictionaries (and several times), and you, unbelivibly, insist in your basic errors.

The problem is that you're pushing a bonkers mechanism that doesn't work in most cases, and when I try to pin down how it's supposed to work in the few cases where it might appear to fit the facts, you're not able to set out clearly how your method should be applied. There's an easy way to fix that, but I can't set it out clearly for you until you make it clear what it is.

AND YOU CLEARLY ignore that in SCIENCE it is not the majority what counts ...

If you read things I post about elsewhere, you'd know that I don't automatically trust the majority. Whatever the issue is, it needs to stand up logically and not just rest on the weight of authority. But if you are going to keep using authority as your backing, it would make more sense to point at the majority rather than a minority. If you want to argue that a minority is the correct one, pointing to the qualifications of the rebels is worthwhile as a way of pointing out that they aren't nutters, but it doesn't prove them right. To get any further with the argument, you need to abandon looking for a winner on the basis of authority (I certainly don't care about weight of authority, so I'm already half on your side there) and move instead to testing proposed mechanisms by applying reason to them. I have tested differential gravity by writing a program to apply it, and it clearly works (and makes sense). To test your side's mechanism, we need to do the same thing, writing a program to apply it. We appear to have established that you want the centrifugal force applied from the barycentre. I then asked if you want to apply the centripetal force from there too. You don't want to say yes to that because it looks ridiculous to have the moon's gravity applied to the Earth from the barycentre (inside the Earth) instead of from the moon, so you've tried to hide that by talking about it coming from the centre of curvature of the body's path instead. however, you haven't bothered to plot that out to see how badly it fits, and you're probably hoping no one else is capable of doing that in their head and of realising just how far out the angles of pull can be. It simply can't be right, which is why I'm questioning it, but you just tell me I don't understand the maths, even though I'm the only one of us who's actually applied it to find out where these centres of curvature actually are and what they aren't in line with.

He replied the director it was WRONG (he found more than 15 errors). He says the director answered “Scientists can reasonable disagree in these matters” … even adding “I´m not making up this” (!!), like saying he could understand the audience could consider that unbelievable, but that it was true, and he delivered the conference as HE thought he should, including a clip with one of those 15 errors (from a "History Channel" video in line with new director ideas, defending differential gravity as THE cause ...). Youtube video timing:
08:00 - He even says that explanation is “fairly universal” and that ...
08:11 - … it is COMPLETELY WRONG.

If it's completely wrong, how does it produce all the right behaviour in my simulation? It would be nice though if we could work together to produce a working simulation of his/your mechanism. That's what I'm trying to steer things towards now, but instead of trying to help with that, you're just attacking me over and over again in a manner that appears designed to prevent it being built.

DO YOU REALLY THINK that, among all scientists supposedly as contrary to his view as you, none of them would have challenged NFC during last decades, similarly to what you are doing here ?? Because NFC stand on the issue is not only on youtube, but also on his book, it has been broadcasted by many TV channels ...
Most eminent scientists give conferences, publish books ... For them, if they thought NFC was quite wrong (as you dare say), that issue would have been a fantastic opportunity to make a lot of money ... (and fame, personal satisfaction, etc)

Why would they bother? If it was an issue like global warming it would matter, but this has insufficient importance. They have better things to do with their time than correct someone who's wrong in a video on the Internet.

It seems you barely search the web, but I´ve done it a lot of times for the last three or four years in relation with tides (and centrifugal force indeed), and I´ve haven´t seen any scientist challenging NFC stand on tides ... Unfortunately, there still are many showing differential gravity theory, but none of them is a "first" level scientist ... Most either haven´t learn NFC´s stand yet, or don´t dare challenging him and keep silent...

Or they're doing more important work. But I like to see incorrect science being overturned, so if NFC has got this right, I want to see it. I don't care for watching videos though - I just want to see a simulation of his mechanism in action, and I'm asking you to supply the mechanism, which isn't an unreasonable request considering how forthright you've been about its rightness.

And, besides NFC, NOAA scientists published the works I´ve referred to so many times, the authors of "French Tides" linked by PmbPhy too … And NO serious challenge whatsoever !
Don´t forget the strong discussion happened in recent decades in relation to the opposite ideas scientists had about causes of climate change ... It is quite another issue, but be sure that if many first line physicists thought NFC were quite wrong on that, we would have had quite an interesting "spectacle" on the media ...

I don't think there would be any spectacle on the media - it would simply go unnoticed. If someone promotes a rival idea to mainstream science and that idea falls flat, it's a non-event.

[rmolnav]

I´m afraid you are wrong even on one of your main "flags":

I've backed the explanation that works in every case.

Perhaps what you are doing is a simulation that, at least for earth trajectory around the barycenter, it doesn´t reflect reality whatsoever. The source of gravitational pull (the moon) is not actually situated on a fixed location, one of the foci of an ellipse. It moves even much,much more than the earth !!
That´s the reason why I say (and certainly NFC), that the real thing is not an orbiting of earth round the moon, but the "dancing" of an attached couple, something dynamically different.
I tried and explained it, doing "my best", on 1st and 2nd parts of my series "MY ULTIMATE GO?" ... but most likely you haven´t even read it ... or are unable to understand it !
In any case, please have a look at least to the images on:
http://www.batesville.k12.in.us/physics/phynet/mechanics/gravity/answers/images/ch14_rev7.gif
That gravitational pull vector break down into two components orthogonal to each other is an absurd thing only to you ...

[rmolnav]

As I´ve already said, D.C. doesn´ deserve the time and effort I´m waisting discussing with him.
Due to that, sometimes I don´t reply to all erroneous details of his posts.
But my replies could interest others, and I´ve decided to reply (though with a delay of four or five days) what follows.

If you have a changing curvature (as with an ellipse), the point you consider to be the centre of curvature will vary depending on how much of that line you use for the calculation, each section of it disagreeing with the next and leading to a fudged average centre if you try to pin it down to a single point for both. If you take an entire ellipse, then the centre is half way between the two foci. I have no idea what the rules are about which of the possible ways of defining the centre of curvature in such a situation and I have no desire to go hunting for them

It is unbelievable how difficult is for you to learn even basic Maths …
Come on ! … It is your own language, and more than once I´ve included here the definition of “center of curvature”, which ALWAYS refers to a single point of any line.  And just the “center” of a closed line (if any), such as an ellipse, is something quite different !!

Even if I do find rules for something, there is no guarantee that they are the same rules that you are following.

I would rather say "there is no guarantee that, even if they were the same that I am following, you would apply them correctly” … As it happens with many dictionary definitions !!

The question says: "We simplify the problem by making the following assumptions." It does not say that the method it expects you to use in solving it is the correct mechanistic explanation of events

Come on! ALL CALCULATIONS we do (relative to real phenomena) have to be simplified by making some assumptions !!
But they have to be relative to details affecting only to the accuracy of the results, and not too much.
And what they assume is:
"(i) The earth and the moon are considered to be an isolated system,
(ii) the distance between the moon and the earth is assumed to be constant,

(iii) the earth is assumed to be completely covered by an ocean,

(iv) the dynamic effects of the rotation of the earth around its axis are neglected, and

(v) the gravitational attraction of the earth can be determined as if all mass were concentrated at the centre of the earth.

They could never affect the “essence” of the phenomenon, unless it were unwittingly. They would have proposed another and  artificial scenario, such as the ones you sometimes proposes …
Keep in mind that the “olympiade” was hold in a serious University, and eminent physicists were in charge … It could be quite different if something similar happened, e.g., here in our forum …
In any case, you were unable to say if you find any "olympic"  error ...

Note that it requires you to treat the Earth and moon in isolation so as to avoid complications, and that it requires them to be at a constant distance apart.

And YOU should note that moon and earth are basically "at a constant distance apart.” …Relatively very small changes don´t affect significantly to the “bottom” line. In their model, that is not an arbitrary decision to “avoid complications” whatsoever !!

Scientists are busy with their work and don't need to be interrupted over trivia. If anyone has been misled by that page, that will come out in places like this forum and they can be shown the errors. If they are rational, they will recognise the errors and learn. If they are not rational, they will fail to recognise the errors and will appeal to authority instead.

Only some of those scientists are too busy to answer, and not always. In fact, in some of their sites they clearly invite people to ask questions. They usually work in a team, and there is always somebody with enough time to answer, unless your question were too absurd !!
And, do you really think people can learn better in forums like ours (by the way, with members “king” like you), than discussing directly with eminent scientists ??

If you were trusting reason, you'd recognise that their explanation doesn't work for all the reasons that have been pointed out to you in this thread, such as centrifugal force not being able to lift material at opposite sides of the Earth with one lot caused by the Earth following a curve with the sun on its inside while at the same time it follows a curve with the moon on its inside (while the sun and moon are to opposite sides of the Earth)

Once again, you twist my words …
I would never "recognise that their explanation doesn't work … “ for what you say, because I (and neither them), as I explained on #411:
"I never said centrifugal force is the unique cause of any bulge (as you and L.R. sometimes say I claim), let alone I used terms such as "the centrifugal bulge", as one of you recently did ...
Last time I referred to that:
Quote from: rmolnav on 13/10/2018 11:49:35
Each bulge is the result of four nature physical "features": two of them gravity-related (caused by moon and sun), and two inertia-related (centrifugal forces inherent in earth´s "dance" with moon and its revolving around the sun) (edited)
... if applied to the "sunwards" bulge with the scenario sun -> earth´s CM -> barycenter -> moon (full or almost),
1) Sun exerts its stronger pull there.
2) The revolving of earth-moon couple around the sun makes inertia manifest itself as a centrifugal  force, logically in the sense sun -> earth´s closest side, what actually opposes to sun´s pull, but with a weaker  strength ...
3) In its "turn", earth´s revolving around the barycenter similarly makes inertia manifest itself as a centrifugal force, this time in the sense moon -> barycenter- > earth´s CM -> sun, that is, contributing to the formation of the bulge on mentioned area.
4) Moon also exerts its pull there, in the sense opposite to effect 3), but smaller.
THE ADDITION OF ALL THOSE FORCES is the total force exerted on the water there (apart from own weight).
As both sun and moon related net effects are in the sense away from earth CM, and they directly add up, we have one of the spring tide bulges".

I doubt he's ever stopped to question that belief. If he did, he would likely change position on it very quickly because he'd think it through, see the places where it fails, and instead of searching the net to find authorities who say the same thing, he'd try to work out what the real mechanism is, quickly realising that it's simply differential gravity, and then he'd make a note that he needs to rewrite one of his many pages some day (if he can find the time) to put it right.

They would neither "change position on it very quickly because he'd think it through", nor "see the places where it fails”, because, at least in the case above, YOU are the one who are unable to grasp what clearly explained to you …
No wonder. As we all have seen, you are unable of understanding correctly dictionary definitions of even basic concepts of Physics and Maths.

then you could put the problems to him and ask him how his mechanism applies in the cases where it most clearly fails.

Last paragraphs apply here too.

Put the case to him where the Earth is directly between the moon and Sun with centrifugal force lifting water at two opposite sides and ask him how that's possible.

Time and again, you alter “our” words … Neither any of them, nor myself, have ever said:
"... with centrifugal force (alone) lifting water at two opposite sides”,
and it would be another of YOUR absurdities to "ask him how that's possible” ...
 

[David Cooper]

I´m afraid you are wrong even on one of your main "flags":

I've backed the explanation that works in every case.

Perhaps what you are doing is a simulation that, at least for earth trajectory around the barycenter, it doesn´t reflect reality whatsoever. The source of gravitational pull (the moon) is not actually situated on a fixed location, one of the foci of an ellipse. It moves even much,much more than the earth !!

My simulation applies gravity on a moon directly from a planet (wherever the planet is at that moment) and on the planet directly from the moon (wherever the moon is at that moment), allowing them to wander wherever that gravity pulls them. The orbit comes directly out of that without me having to program it, and the barycentre is not calculated at all. The two bodies simply fall round each other and produce correct orbits. (If you make the planet much more massive than the moon, the planet contains the barycentre - I chose less extreme initial difference in mass for the planet and moon in the simulation which leads to the planet wandering around a bit visibly as the moon orbits it because the planet's movement hardly shows up otherwise.)

That´s the reason why I say (and certainly NFC), that the real thing is not an orbiting of earth round the moon, but the "dancing" of an attached couple, something dynamically different.

Your description of a dancing couple fits their behaviour in my simulation too - it's the exact same movement as a simulation of your method should produce (if you can work out its specifications).

I tried and explained it, doing "my best", on 1st and 2nd parts of my series "MY ULTIMATE GO?" ... but most likely you haven´t even read it ... or are unable to understand it !

You're the one who's dragging along, failing to understand 95% of what's been said in this thread.

In any case, please have a look at least to the images on:
http://www.batesville.k12.in.us/physics/phynet/mechanics/gravity/answers/images/ch14_rev7.gif
That gravitational pull vector break down into two components orthogonal to each other is an absurd thing only to you ...

You don't even realise that I apply that in my simulation. When I ask you where you're applying the centripetal force from, I'm asking for the big arrow and not either of the two component ones (which are artificial components used in the maths and not in the underlying physics).

If you have a changing curvature (as with an ellipse), the point you consider to be the centre of curvature will vary depending on how much of that line you use for the calculation, each section of it disagreeing with the next and leading to a fudged average centre if you try to pin it down to a single point for both. If you take an entire ellipse, then the centre is half way between the two foci. I have no idea what the rules are about which of the possible ways of defining the centre of curvature in such a situation and I have no desire to go hunting for them

It is unbelievable how difficult is for you to learn even basic Maths …
Come on ! … It is your own language, and more than once I´ve included here the definition of “center of curvature”, which ALWAYS refers to a single point of any line.  And just the “center” of a closed line (if any), such as an ellipse, is something quite different !!

As I pointed out before, by taking the most obvious interpretation (the correct one), it produces the wrong answer because the centripetal force should not be coming from any direction other than the other body. That is why I looked for other possible rational interpretations of the nonsense you were spouting. It turns out that my mistake was in thinking there was a rational interpretation to look for. I should just have told you straight that you were producing the wrong angle for the centripetal force because you can't hack the maths. I made allowances for you, thinking you couldn't possibly be making such a crazy error, and yet you were!

Even if I do find rules for something, there is no guarantee that they are the same rules that you are following.

I would rather say "there is no guarantee that, even if they were the same that I am following, you would apply them correctly” … As it happens with many dictionary definitions !!

Bit by bit, I'm learning that when you say something absolutely bonkers, you actually do mean it and that I should trust your words. I will not look for alternative explanations in future.

The question says: "We simplify the problem by making the following assumptions." It does not say that the method it expects you to use in solving it is the correct mechanistic explanation of events

Come on! ALL CALCULATIONS we do (relative to real phenomena) have to be simplified by making some assumptions !!

You read into the question the idea that the method it asks people to use is the correct mechanism to explain the workings of the system. It did not say that - you made that up all for yourself.

Keep in mind that the “olympiade” was hold in a serious University, and eminent physicists were in charge … It could be quite different if something similar happened, e.g., here in our forum …

They are trying to find awkward things to test people's ability to apply rules - in this case by making them apply the maths of a warped abstraction. That is a good test, but it is not intended to be taken as backing of the idea that the warped abstraction isn't warped and that it is the actual mechanism.

In any case, you were unable to say if you find any "olympic"  error ...

If the maths of an abstraction is applied correctly, how would it contain an error? There would only be an error there if they bundled in an assertion that the method used represents the actual physical mechanism.

Note that it requires you to treat the Earth and moon in isolation so as to avoid complications, and that it requires them to be at a constant distance apart.

And YOU should note that moon and earth are basically "at a constant distance apart.” …Relatively very small changes don´t affect significantly to the “bottom” line. In their model, that is not an arbitrary decision to “avoid complications” whatsoever !!

The point I was making is that it doesn't deal with elliptical orbits. It may be that the method needs no modification to deal with elliptical orbits, but that's something I was hoping you would be able to spell out with your expertise in applying this abstraction. You're the one backing it, so you should know how it's done. When I ask you where the centripetal force is supposed to be taken from, I want a clear answer from you so that I can program it in the knowledge that I'm doing it the way you want it to be done rather than having to read through many pages of junk and trying to guess what you mean. I was expecting you to say that it should be applied from the barycentre, and if you had met that expectation, I would have written the code days ago. You don't appear to want to say it comes from the barycentre though because that would have the moon's gravity apply to the Earth from within the Earth rather than from the moon, and that would reveal just how ridiculous an abstraction you're pushing here. So, naturally enough, you sow confusion instead and try to avoid giving a clear answer, going off on a bizarre diversion involving centres of curvature. If I took you at your word on that and wrote code to apply the centripetal force from a series of centres of curvature, it would generate a mess and I'd have wasted a lot of time. As the curve straightens, for example, the centre of curvature moves further and further away, leading to it straightening further and driving the centre of curvature further away still - that process would never stop, so the curve would never tighten again. (That's actually why I know not to waste any time programming it that way as it wouldn't even be an interesting experiment.)

Scientists are busy with their work and don't need to be interrupted over trivia. If anyone has been misled by that page, that will come out in places like this forum and they can be shown the errors. If they are rational, they will recognise the errors and learn. If they are not rational, they will fail to recognise the errors and will appeal to authority instead.

Only some of those scientists are too busy to answer, and not always. In fact, in some of their sites they clearly invite people to ask questions. They usually work in a team, and there is always somebody with enough time to answer, unless your question were too absurd !!

In that case, you should be able to put to them the situations where I say their method fails and see if they are capable of recognising that their mechanism is broken.

And, do you really think people can learn better in forums like ours (by the way, with members “king” like you), than discussing directly with eminent scientists ??

It takes the pressure off scientists if people discuss things on science forums first instead of bothering scientists directly, but it also gives opportunities for many people to learn things at the same time without them all bothering the same scientist with the same series of questions.

(And don't pay any attention to the silly descriptions that the forum software uses to encourage people to post more. It merely reflects the number of posts someone's made, and a high score can be an indication of mental health issues, or an indication that the person engages in a lot of chatting in threads where a lot of posts are single sentences.)

If you were trusting reason, you'd recognise that their explanation doesn't work for all the reasons that have been pointed out to you in this thread, such as centrifugal force not being able to lift material at opposite sides of the Earth with one lot caused by the Earth following a curve with the sun on its inside while at the same time it follows a curve with the moon on its inside (while the sun and moon are to opposite sides of the Earth)

Once again, you twist my words …

I'm not twisting your meaning. Either your mechanism uses centrifugal force to lift water at those two locations or it doesn't. If it's only doing it at one of those locations, then it isn't doing it at the other, but your explanation would have to work in both directions, in one case treating the sun and Earth as a system and in the other case treating the Earth and moon as a system. The mechanism then contradicts itself unless you have a way to recognise that it is wrong for one of the two cases. If you recognise that its wrong for one of them, which one's wrong? Given that the sun's gravitational pull on the Earth massively out-guns the moon's, the centrifugal force mechanism for the bulge on the sun-side of the Earth must be wrong, and that means your mechanism does not apply to the Earth-moon system. It's been disqualified.

I would never "recognise that their explanation doesn't work … “ for what you say, because I (and neither them), as I explained on #411:
"I never said centrifugal force is the unique cause of any bulge (as you and L.R. sometimes say I claim), let alone I used terms such as "the centrifugal bulge", as one of you recently did ...

The point is that it isn't any part of the cause of the bulge. Centrifugal force only ever exists in the special case of reactive centrifugal force, and that doesn't occur in cases where the centripetal force is gravity - as I've told you before, it's a different category of centripetal force. (The two cases really should have different names to prevent people like you being misled by them.)

They would neither "change position on it very quickly because he'd think it through", nor "see the places where it fails”, because, at least in the case above, YOU are the one who are unable to grasp what clearly explained to you …

On the contrary, my dear fellow, it is you who is consistently failing to understand the vast bulk of what's been discussed here. Judging by the quality of his writing though, your NOAA scientist has a good mind which I think will rapidly recognise the error he's made when you point it out to him. All you need to do is show him some of the cases where his method breaks, and ask him if perhaps differential gravity might be a better explanation as it works in all cases.

No wonder. As we all have seen, you are unable of understanding correctly dictionary definitions of even basic concepts of Physics and Maths.

Hardly - there are some that I don't actually know, but I can pick them up quickly if I need them. What keeps happening here though is that I don't realise that you mean what you say because what you say is just too bonkers to think it possible that you mean that, and yet it turns out that you do.

then you could put the problems to him and ask him how his mechanism applies in the cases where it most clearly fails.

Last paragraphs apply here too.

In what way? You aren't going to put those questions to him because I don't understand things that have no relevance to the questions I've suggested you should put to him? Are you scared to ask him because you don't know what you'll do if he replies to tell you that he got it wrong?

Put the case to him where the Earth is directly between the moon and Sun with centrifugal force lifting water at two opposite sides and ask him how that's possible.

Time and again, you alter “our” words … Neither any of them, nor myself, have ever said:
"... with centrifugal force (alone) lifting water at two opposite sides”,
and it would be another of YOUR absurdities to "ask him how that's possible” ...

Then convert it into your own wording. The problem doesn't magically disappear just because you don't like my wording of it. If your centrifugal force doesn't lift water, what the heck is it doing in the mechanism?

[rmolnav]

Just one thing, for now ...

Quote
Quote from: David Cooper on 01/11/2018 22:49:47
If you were trusting reason, you'd recognise that their explanation doesn't work for all the reasons that have been pointed out to you in this thread, such as centrifugal force not being able to lift material at opposite sides of the Earth with one lot caused by the Earth following a curve with the sun on its inside while at the same time it follows a curve with the moon on its inside (while the sun and moon are to opposite sides of the Earth)
Once again, you twist my words …

I'm not twisting your meaning. Either your mechanism uses centrifugal force to lift water at those two locations or it doesn't.] If it's only doing it at one of those locations, then it isn't doing it at the other, but your explanation would have to work in both directions[/i;
 in one case treating the sun and Earth as a system and in the other case treating the Earth and moon as a system. The mechanism then contradicts itself unless you have a way to recognise that it is wrong for one of the two cases. If you recognise that its wrong for one of them, which one's wrong? Given that the sun's gravitational pull on the Earth massively out-guns the moon's, the centrifugal force mechanism for the bulge on the sun-side of the Earth must be wrong, and that means your mechanism does not apply to the Earth-moon system. It's been disqualified.

And you claim to be specialist on Logics ??
Either you are quite the opposite, or you, time and again, lie making others think I claim just "centrifugal force (to) lift(s) water at those two locations”, something I´ve never, ever said !!
In more than a way I´ve explained that:
 

Each bulge is the result of four nature physical "features": two of them gravity-related (caused by moon and sun), and two inertia-related (centrifugal forces inherent in earth´s "dance" with moon and its revolving around the sun) ...
... if applied to the "sunwards" bulge with the scenario sun -> earth´s CM -> barycenter -> moon (full or almost),
1) Sun exerts its stronger pull there.
2) The revolving of earth-moon couple around the sun makes inertia manifest itself as a centrifugal  force, logically in the sense sun -> earth´s closest side, what actually opposes to sun´s pull, but with a weaker  strength ...
3) In its "turn", earth´s revolving around the barycenter similarly makes inertia manifest itself as a centrifugal force, this time in the sense moon -> barycenter- > earth´s CM -> sun, that is, contributing to the formation of the bulge on mentioned area.
4) Moon also exerts its pull there, in the sense opposite to effect 3), but smaller.
THE ADDITION OF ALL THOSE FORCES (NOT ANY CENTRIFUGAL FORCE ALONE) is the total force exerted on the water there (apart from own weight) …

… and on the rest of the planet. In a similar way the other spring bulge could be explained.
WHAT SAID DOESN´T MEAN EARTH IS FOLLOWING TWO DIFFERENT ELLIPTICAL ORBITS SIMULTANEOUSLY WHATSOEVER ... But a "rational" dynamical analysis of earth complex movement requires to break it down into two different “components”, caused by dynamical effects related to TWO DIFFERENT celestial objects …

And if, as you also claim, it is my way of explaining things what misleads you, just read as it is explained on:
http://www.newenglandphysics.org/other/French_Tides.pdf
"… the production of ocean tides is basically the CONSEQUENCE of the gravitational action of the moon - and, to a lesser extent, the sun …The analysis of the phenomenon is, however, considerably helped by introducing the concept of INERTIAL FORCES as developed in the present chapter.
… With respect to the CM of the earth-moon system … the earth´s center of mass has an acceleration of magnitude Ac … every point in the earth receives this same acceleration from the moon´s attraction.
… for a particle at the earth´s center, the CENTRIFUGAL FORCE and the moon´s gravitational attraction are equal and opposite. If, however, we consider a particle on the earth´s surface at the nearest point to the moon …, the gravitational force on it is greater than the CENTRIFUGAL FORCE by an amount that we shall call Fo …
… the tide-producing force on a particle of mass m at the farthest from the moon … is equal to -Fo …”

or on:
 https://tidesandcurrents.noaa.gov/restles3.html
“… At point A in Fig. 2, approximately 4,000 miles nearer to the moon than is point C, the force produced by the moon's gravitational pull is considerably larger than the gravitational force at C due to the moon. The smaller lunar gravitational force at C just balances the centrifugal force at C. Since the centrifugal force at A is equal to that at C, the greater gravitational force at A must also be larger than the centrifugal force there. The net tide-producing force at A obtained by taking the difference between the gravitational and centrifugal forces is in favor of the gravitational component - or outward toward the moon. The tide-raising force at point A is indicated in Fig. 2 by the double arrow extending vertically from the earth's surface toward the moon. The resulting tide produced on the side of the earth toward the moon is know as the direct tide.
At point B, on the opposite side of the earth from the moon and about 4,000 miles farther away from the moon than is point C, the moon's gravitational force is considerably less than at point C. At point C, the centrifugal force is in balance with a gravitational force which is greater than at B. The centrifugal force at B is the same as that at C. Since gravitational force is less at B than at C, it follows that the centrifugal force exerted at B must be greater than the gravitational force exerted by the moon at B. The resultant tide-producing force at this point is, therefore, directed away from the earth's center and opposite to the position of the moon. This force is indicated by the double-shafted arrow at point B. The tide produced in this location halfway around the earth from the sublunar point, coincidentally with the direct tide, is know as the opposite tide”-

or on:
https://tidesandcurrents.noaa.gov/publications/Tidal_Analysis_and_Predictions.pdf
"… Although the moon appears to orbit around the Earth, the Earth and moon both actually revolve
around a common point, which, because the Earth is 82 times more massive than the moon, is inside the Earth, but not at the Earth’s center (see Figure 2.. At the center of the Earth there is a balance between gravitational attraction (trying to pull the Earth and moon together) and centrifugal force (trying to push the Earth and moon apart as they revolve around that common point).
At a location on the Earth’s surface closest to the moon, the gravitational attraction of the moon is greater than the centrifugal force of the Earth (moving around the center of the revolving Earth-moon system).
On the opposite side of the Earth, facing away from the moon, the centrifugal force is greater than
the moon’s gravitational attraction.
In a hypothetical ocean covering the whole Earth with no continents there will be two tidal bulges resulting from these imbalances of gravitational and centrifugal forces, one facing the moon (where the gravitational force is greater than the centrifugal force) and one facing away from the moon (where the centrifugal force is greater than the gravitational force) “.

Where “on earth” do you find any of us is saying “same cause” (a centrifugal force)  “lifts” water simultaneously at two opposite sites, that would be absurd, and "therefore" our mechanism is "broken" ??

 

[David Cooper]

And you claim to be specialist on Logics ??
Either you are quite the opposite, or you, time and again, lie making others think I claim just "centrifugal force (to) lift(s) water at those two locations”, something I´ve never, ever said !!

If you're using centrifugal force at all as part of your mechanism (and you are), then your mechanism fails completely in the three body system. If you treat the Earth and moon as a complete system, your mechanism gives centrifugal force a role in lifting water at the far side of the Earth from the moon. If you treat the Earth and sun as a complete system, your mechanism gives centrifugal force a role in lifting water at the far side of the Earth from the sun. If you treat all three as a system, you can make a choice about whether the rotation round the moon or sun is generating centrifugal force, but for your mechanism to be correct, it really has to apply to both at the same time, so you have centrifugal force lifting material at opposite sides of the Earth. That is an impossibility though, so you really have to choose either the sun or moon as the thing that's flinging the Earth about in such a way as to produce centrifugal force on one side of it only, and having your mechanism work for one choice while it is then ruled out for the other automatically disproves your mechanism through contradiction.

WHAT SAID DOESN´T MEAN EARTH IS FOLLOWING TWO DIFFERENT ELLIPTICAL ORBITS SIMULTANEOUSLY WHATSOEVER ... But a "rational" dynamical analysis of earth complex movement requires to break it down into two different “components”, caused by dynamical effects related to TWO DIFFERENT celestial objects …

As I said, you choose one and reject the other, which means you're using your mechanism for one thing and overriding it for the other. That is being inconsistent.

"The analysis of the phenomenon is, however, considerably helped by introducing the concept of INERTIAL FORCES as developed in the present chapter."

The analysis is substantially hindered by using that approach.

"… With respect to the CM of the earth-moon system … the earth´s center of mass has an acceleration of magnitude Ac … every point in the earth receives this same acceleration from the moon´s attraction."

That bit's wrong. The acceleration from the moon's attraction is different depending on distance between moon's CM and the point in question. Almost of that difference is then hidden by forces transmitted by the Earth as a whole to each point on the Earth to keep it together as a single entity, but a tiny amount of difference remains, leading to material lifting a little. In addition, the reduction of force is greater across the near side, so the point of average force is not the CE.

… for a particle at the earth´s center, the CENTRIFUGAL FORCE and the moon´s gravitational attraction are equal and opposite. If, however, we consider a particle on the earth´s surface at the nearest point to the moon …, the gravitational force on it is greater than the CENTRIFUGAL FORCE by an amount that we shall call Fo …
… the tide-producing force on a particle of mass m at the farthest from the moon … is equal to -Fo …”

Great, until you bring the sun into play as well and put it at the opposite side, at which point the "centrifugal" force is centrifugal in name only and is revealed to be an incorrect description.

(snip the quotes)

Where “on earth” do you find any of us is saying “same cause” (a centrifugal force)  “lifts” water simultaneously at two opposite sites, that would be absurd, and "therefore" our mechanism is "broken" ??

You don't say it. What we're dealing with here is a logical extension taking it into a 3-body system. I'm taking your mechanism and showing that if you apply it one way, you imagine there to be centrifugal force lifting water on one side of the Earth, while if you apply it the other way, you imagine there to be centrifugal force lifting water on the other side of the Earth. For your mechanism to be valid, it has to be correct when applied both ways, and that necessarily means that you must have centrifugal force lifting water on opposite sides of the Earth at the same time. If you want to choose one direction in which you decide you don't want to apply your mechanism (either the sun's pull on the Earth or the moon's), then you are disowning your own mechanism for that direction, and that means your mechanism is a dud. But I don't expect you to understand this point because you have no idea how to apply reason to anything.

There is no equivalent problem for differential gravity which simply accounts for the facts without difficulty (and in a much simpler way) in all scenarios, and that's because it reflects the actual physics instead of your warped mathematical abstraction.

[rmolnav]

What we're dealing with here is a logical extension taking it into a 3-body system. I'm taking your mechanism and showing that if you apply it one way, you imagine there to be centrifugal force lifting water on one side of the Earth, while if you apply it the other way, you imagine there to be centrifugal force lifting water on the other side of the Earth. For your mechanism to be valid, it has to be correct when applied both ways, and that necessarily means that you must have centrifugal force lifting water on opposite sides of the Earth at the same time. If you want to choose one direction in which you decide you don't want to apply your mechanism (either the sun's pull on the Earth or the moon's), then you are disowning your own mechanism for that direction, and that means your mechanism is a dud. But I don't expect you to understand this point because you have no idea how to apply reason to anything.

It is YOU who are actually taking what YOU call "my mechanism"..., YOU who are imagining I apply it in certain ways ...
All that stuff is a false (or erroneous at least) picture of reality, because, similarly to when I said:

It´s not a question of how I "want to apply the force.", it is a question of a "rational" analysis of facts

YOU are erroneously referring to a supposed "mechanism" of mine, because what i´ve always done is just to analyze dynamically THE REAL SCENARIO, especially what relative to main forces to be considered: gravity, internal stresses ... and inertial forces such as centrifugal force.
It seems YOU are trying to simulate a certain mechanism which is not actually "mine", and due to YOUR lack of basic education on Physics and Maths, YOU are looking for the points where inertial forces should be "applied" from (I wonder what for), and YOU time and again kind of mix up causes and effects !!
Therefore, any problem you can find in that "endeavour" is only YOURS !
And, by the way, you are also wrong when saying:

Quote
"… With respect to the CM of the earth-moon system … the earth´s center of mass has an acceleration of magnitude Ac … every point in the earth receives this same acceleration from the moon´s attraction."
That bit's wrong. The acceleration from the moon's attraction is different depending on distance between moon's CM and the point in question.

What in bold is quite right ... What is actually wrong is what in italics, because YOU mix up to basically different concepts: acceleration and force !!
The acceleration of the whole earth (with total mass M), its center of mass included, due to moon´s total gravitational force F is  F/M, according to Newton´s 2nd Motion Law, whatever the distribution of "local" pull forces and/or earth density, and whatever internal stresses !!

[David Cooper]

It is YOU who are actually taking what YOU call "my mechanism"..., YOU who are imagining I apply it in certain ways ...

You have no option other than to apply it in certain ways, and when you do it properly (i.e. for both the Earth-moon and sun-Earth systems at the same time), it contradicts itself.

All that stuff is a false (or erroneous at least) picture of reality, because, similarly to when I said:

It´s not a question of how I "want to apply the force.", it is a question of a "rational" analysis of facts

YOU are erroneously referring to a supposed "mechanism" of mine, because what i´ve always done is just to analyze dynamically THE REAL SCENARIO, especially what relative to main forces to be considered: gravity, internal stresses ... and inertial forces such as centrifugal force.

When are you ever going to understand that centrifugal force doesn't exist? It's an artefact of an abstraction using rotating frames. You aren't dealing with the real scenario, but a warped abstraction which produces the appearance of a force that doesn't exist.

It seems YOU are trying to simulate a certain mechanism which is not actually "mine", and due to YOUR lack of basic education on Physics and Maths, YOU are looking for the points where inertial forces should be "applied" from (I wonder what for), and YOU time and again kind of mix up causes and effects !!

Make up your mind whether you're using centrifugal force or not. You have it being applied from the barycentre, but now you don't want to apply it at all, while at the same time asserting that it has a key role. You are horribly mixed up.

Therefore, any problem you can find in that "endeavour" is only YOURS !

You are denying the real mechanism and proposing instead a mixture of a method involving a rotating frame combined with a denial of what you're doing. All you can do now is try to paint as confused an image as possible of your method in order to hide how ridiculous it is.

And, by the way, you are also wrong when saying:

Quote
"… With respect to the CM of the earth-moon system … the earth´s center of mass has an acceleration of magnitude Ac … every point in the earth receives this same acceleration from the moon´s attraction."
That bit's wrong. The acceleration from the moon's attraction is different depending on distance between moon's CM and the point in question.

What in bold is quite right ... What is actually wrong is what in italics, because YOU mix up to basically different concepts: acceleration and force !!

You removed the following sentence:-

"Almost of that difference is then hidden by forces transmitted by the Earth as a whole to each point on the Earth to keep it together as a single entity, but a tiny amount of difference remains, leading to material lifting a little."

Perhaps you didn't understand what it was getting at because you're such a shallow thinker. Do you not understand that if the acceleration is identical for every particle, no material can lift? That lifting movement reveals a different speed of travel while it's rising, and that's supported by a differing amount of acceleration. Study the first half of the sentence (the one that you cut) up to the comma and note that I wasn't talking about the difference in attraction force - most of that difference is hidden by forces transmitted through the Earth which almost completely equal out the acceleration, but not quite. Some acceleration difference has to remain to enable material to lift. You don't look that deep though, so you miss important little details. You're also desperately looking for things to attack instead of clarifying your method, which is clearly something you have no intention of doing - you don't want people to see it being simulated because it would show just how warped an abstraction it is, so you're filling page after page with endless diversion tactics instead of providing answers.

[rmolnav]

Make up your mind whether you're using centrifugal force or not. You have it being applied from the barycentre, but now you don't want to apply it at all, while at the same time asserting that it has a key role. You are horribly mixed up.

I´m afraid it is actually YOU who "are horribly mixed up"...
When you say "... whether you're using centrifugal force or not", what exactly do you suppose I should "use" centrifugal force for (obviously, keeping in mind I consider centrifugal force does exist) ?

Do you not understand that if the acceleration is identical for every particle, no material can lift? That lifting movement reveals a different speed of travel while it's rising, and that's supported by a differing amount of acceleration. Study the first half of the sentence (the one that you cut) up to the comma and note that I wasn't talking about the difference in attraction force - most of that difference is hidden by forces transmitted through the Earth which almost completely equal out the acceleration, but not quite. Some acceleration difference has to remain to enable material to lift.

What an absurd and misleading way of analyzing facts !! No scientist would talk that way, because you are mixing up different realms and concepts.
On the one hand, when dealing with whole planets, the center of mass is both an astronomical term and a geological one. We don´t have to be equally accurate at both realms. What would be an accuracy completely superfluous in astronomy, in some aspects of geology would be necessary. 
On the other hand, what you consider kind of "residual" accelerations ("Some acceleration difference has to remain to enable material to lift"), has nothing to do with earth dynamics. It is not the "famous" case of three "free" balls whatsoever...
Moon´s pull gradient causes internal stresses, and those cause deformations, bigger or smaller depending on both pull gradient and considered material elasticity, but not on its mass (involved in accelerations) ... To consider those deformations as "some acceleration difference" shows how confusion there is inside your head !!
On "another hand", as in/on farther hemisphere deformations are in opposite sense than in/on closer hemisphere, they asymptotically tend to null towards the center of mass . It is not just at the CM, but within a relatively not small area at both sides of the CM, where those deformations can be considered null (as the so called "tidal forces").
Or, when giving the results of your simulations, your numbers are accurate to the trillionth of the used units ?? 

[David Cooper]

I´m afraid it is actually YOU who "are horribly mixed up"...
When you say "... whether you're using centrifugal force or not", what exactly do you suppose I should "use" centrifugal force for (obviously, keeping in mind I consider centrifugal force does exist) ?

The whole point is that it doesn't exist, but you're treating it as a force, and as soon as you do that, you have to fiddle the opposing force to cancel it out. If you are applying the centripetal force from the CG of the other body rather than the barycentre, then the centrifugal force must be zero.

What an absurd and misleading way of analyzing facts !! No scientist would talk that way, because you are mixing up different realms and concepts.

On the contrary - any competent scientist would agree with me that the material cannot change separation without a difference in acceleration - if the acceleration is identical for all the particles, the separations are fixed and material cannot lift at all. I'm discussing a tiny difference, but it has to be there.

On the other hand, what you consider kind of "residual" accelerations ("Some acceleration difference has to remain to enable material to lift"), has nothing to do with earth dynamics. It is not the "famous" case of three "free" balls whatsoever...

No acceleration difference would mean no lift at all and no tides.

Moon´s pull gradient causes internal stresses, and those cause deformations, bigger or smaller depending on both pull gradient and considered material elasticity, but not on its mass (involved in accelerations) ... To consider those deformations as "some acceleration difference" shows how confusion there is inside your head !!

I was referring to material (e.g. water) lifting a tiny amount at the surface due to the reduced pressure. It doesn't matter how infinitesimal the lift is - if you don't have any at all, you eliminate the tides, and that infinitesimal lift requires a difference in acceleration to change it. Reject that if you like, but you are rejecting physics. (It would of course be no surprise at this stage that you reject physics.)

Or, when giving the results of your simulations, your numbers are accurate to the trillionth of the used units ??

How much accuracy do you need? It shows the forces clearly enough without having to worry even about thousandths. (It doesn't attempt to show acceleration differences, but that could be done if anyone wants to do the necessary research and add a lot of code to calculate them. There will be differences though.)