[Le Repteux]

As a reaction the passenger´s shoulder pushed outwards on the glass, with a real force equal but opposite to centripetal one, until it broke

It's the glass that pushes inwards on the shoulder, so the shoulder resists to the force, and the glass breaks. Whether the force is direct or centripetal, bodies behave the same when the are accelerated: they resist, and they nevertheless accelerate in the direction of the force, not in the opposed direction. The word centrifugal contains the suffix fugal, that derives from the french word fugue, which means run away, and there is simply no run away when a body resists to a force. We're actually orbiting around one another so close and so fast that tidal bulges are beginning to grow on us. We should shut off the force before we get dislocated! :0)

[rmolnav]

The word centrifugal contains the suffix fugal, that derives from the french word fugue, which means run away, and there is simply no run away when a body resists to a force.

Come on !
I´m Spanish, and know the origins of "fugal", actually from latin ...
But I said :
"... that outwards force has a name: centrifugal force, as I said, in the broad sense of the term" (mainly not to mislead people, because many dictionaries define "centrifugal force", in quite a restrictive sense, as a ficticious force, linked to the concept of non-inertial force).
But for the adjective "centrifugal" you can find, e.g. on Oxford English Dictionary:
"Physics
Moving or tending to move away from a centre.
The opposite of centripetal”
It is precisely when the circular movements are more kind of avoided when we actually have bigger centrifugal forces !!
By the way, as an “example sentence” they include:
"Einstein warmed to the idea that the gravitational field of the rest of the Universe might explain centrifugal and other inertial forces resulting from acceleration.’ ...
though I dare say that is a too far fetched idea ...

[rmolnav]

MY ULTIMATE GO ? (5th part)

Before trying and convey my stand on non-inertial frames issue, let us go back to the drawing board, as if we didn´t have any education on dynamics …
Same image with Earth (E) on upper part, and vertically below the Moon (M).
Let us suppose we only know how they move, with kind of the mind of a “smart” child.
And then we learn that (as David Cooper said many times), if Earth and Moon tangential speeds somehow became null, they would begin to accelerate straightly towards each other, because of gravitational mutual attraction …
If just stopping their circular movements, they get “free” to accelerate towards each other … THOSE CIRCULAR MOVEMENTS ARE WHAT, WHEN EXISTING, WERE SOMEHOW COUNTERING THOSE STRAIGHT ACCELERATIONS NOW THEY HAVE GOT !!  No other logical possibility for a “clean” child mind …
How come? Let us see …
Curiously, with a rotating (so called "non-inertial”) frame of reference, same thing happens, but let us say “virtually” …
As the frame of reference rotates with E and M, E and M don´t "rotate" anymore
relatively to that frame of reference … Centripetal forces are not required whatsoever, and gravitational pull would make them fall onto each other … But that´s far from reality …
Then physicists go on: "How can we do “real” maths with that “artificial” (the adjective is mine ...) reference system ? … We have to apply a “fictitious” force, which we´ll call centrifugal force". That way WE GET BACK TO THE REAL SCENARIO … as far as dynamics is concerned.
Well, that force is certainly “fictitious”, because it has been introduced by us to work with that non-inertial frame of reference … But that means that the real circular movements, not actually needing the addition of any “artificial” force, somehow produce an inertial effect that keeps E and M without falling straightly onto each other !! To me (and not only me), that is a REAL centrifugal force !!
In case B (# 362), as E and M were moving horizontally at same speed, Moon´s pull was able not only to bend E´s trajectory, but also to accelerate E straightly towards M with its full strength, quite a “free” acceleration. That “freedom” was made possible by the movement of the moon towards the left, with same horizontal speed as E.
The real case is dynamically quite the opposite: the movement of M in opposition to E´s speed, and with speeds which make them to revolve/rotate around the barycenter, makes impossible the decrease of E-M distance, and even any proper orbiting of E around M. It gives us a “rotating” scenario, where all forces have basically same direction as the line between centers of mass, and where the angular position doesn´t matter much (as far as Earth-Moon dynamics is concerned), as long as we accept centrifugal forces keep the separation constant …
After all, if Earth and Moon were the only celestial objects in the universe, to talk about angular position of the system would have no sense at all …
But, still, they would have to keep rotating.  That way inherent inertial force, the centrifugal force, would keep them without following straightly onto each other !! 
Therefore, as I´ve said many times, I find quite correct what a NOAA scientist told me:
"... to provide a basic description of the forces which create the tides.  It's intended audience were the grade school children and adults of that time.  It used terminology of science and forces which were common in the 1950s.  Such as centrifugal force.  Centrifugal force was always an "imaginary force" (not a real / measurable force).  But that type of description made the concepts easier to understand and explain.  That  description and use of centrifugal force continued to be common practice until the 1970-80's.  At that point, the terminology shifted and the textbooks used in grade schools were changed to use a more modern terminology and description of this "effect" being a result of inertia rather than an "imaginary force”.
Initially I didn´t fully grasp his point ... But later I did.
The problem is that many books, dictionaries included, keep following models with ideas which are several decades out of date …

   

[Le Repteux]

It gives us a “rotating” scenario, where all forces have basically same direction as the line between centers of mass, and where the angular position doesn't matter much (as far as Earth-Moon dynamics is concerned), as long as we accept centrifugal forces keep the separation constant …
After all, if Earth and Moon were the only celestial objects in the universe, to talk about angular position of the system would have no sense at all …

Reference frames were invented to account for inertial motion, not rotation. In a merry go round, we know we are rotating because of the force, and we also know we are orbiting because of the tides. Rotation and orbiting motion are not relative motions since we know we are moving. We can use a Sagnac interferometer to measure our orbital speed, so even if the earth and the moon were alone in the universe, we could know we are moving. That's mainly why I decided to attribute mass and motion to light, and to make simulations based on the absolute direction and speed of light. If I had to make a simulation of orbital motion, I wouldn't use equations based on an instantaneous force like David did, I would use photons that take time to transfer the information, and doppler effect and aberration produced at the source and at the observer as the only available information, apart from the photon's force weakening with distance of course. This way, no need for an external reference to know that the system is moving, and it is the light exchanged between the particles that drives it.

[David Cooper]

For any new readers of this thread who may only have read the start and end of it, the correct answer does not involve centrifugal or centripetal force.

The sun's pull on the Earth dictates the direction the Earth moves in much more strongly than the moon's pull, out-gunning it to the point that when the Earth is in between the Sun and moon, the moon is on the outside of the curved path that the Earth is following through space and not on the inside of it, so any imagined role for centrifugal force throwing water up on the sun-side of the Earth is revealed to be a fantasy, and the sun isn't responsible for lifting most of the water on that side either. If water was being thrown upwards by centrifugal force, it would be towards the moon at such times, but there is no such effect (other than from the Earth's rotation which raises the sea all the way round, most strongly at the equator).

The real answer is simply straight-line differential gravity, mostly from the moon. The moon's and sun's gravity decreases over distance, but it falls in strength most strongly over distance with greater proximity to the source, which is why the moon has a greater effect on the tides than the sun even though the sun's pull on the Earth is much stronger - the moon's effect on our tides is greater because the moon is so close to us, leading to its pull reducing more quickly over distance from one side of the Earth to the other, whereas the sun's so far away that its pull is much closer to an even pull across the planet.

The Earth simply moves where the combined pull of moon, sun, Juptier, etc. forces it to go, and the water of the sea has a slightly different amount of force acting on it due to differential gravity. The water nearest the moon is always pulled a bit more strongly towards the moon, and the water furthest from the moon is always pulled less strongly by it, so whenever the Earth is being pulled towards the moon (e.g. when the moon is between the sun and Earth), the water nearest the moon will try to move more quickly towards the moon than the Earth as a whole and the water furthest from the moon will try to move less quickly in that direction, whereas if the Earth is being pulled away from the moon (e.g. when the Earth is between the sun and moon), the water furthest from the moon will be pulled away most strongly (because it's held back the least by the moon's gravity) while the water nearest the moon will be held back most strongly by the moon.

The effect of these forces is that the pressure on the sea nearest to and furthest from the moon reduces a bit and the water tries to rise a tiny amount - it doesn't rise much directly because there isn't enough time for water to rush in from elsewhere to pile up there, so the actual tidal bulges that we see are a secondary effect built up by resonance responding to the input of the tidal forces. The tidal forces from the sun are smaller because the sun's gravity reduces less over distance where we are (it is spreading out less by the time it reaches us). When the tidal forces from the sun are aligned with the moon's, we get the biggest combined force and higher tides. When the tidal forces from the sun are acting at 90 degrees to those from the moon, we get lower tides, but note that the water is still being lifted slightly by the sun's tidal forces on the sides nearest and furthest from it, so it doesn't actually subtract from the moon's tidal forces, but merely masks their strength. This is why it's important to realise that the tides that we see are a secondary effect (through resonance) and not direct lifting of water into bulges.

Until the topic is locked, I'll repost this every page or two just to make sure that no one is misled by authoritative nonsense.

[Le Repteux]

But, still, they would have to keep rotating.  That way inherent inertial force, the centrifugal force, would keep them without falling straightly onto each other !! 

It is their speed with regard to one another that keeps them from falling, and speed is not a force, only a motion.

[rmolnav]

Reference frames were invented to account for inertial motion, not rotation

Well, I´m afraid your background can´t help me help understand what you actually mean ...
"Rotation" requires acceleration (centripetal) ... Therefore inertial phenomena appears !
I´m not expert on the history of the concept, but if e.g. you visit:
 NON-INERTIAL FRAMES - Oxford Physics - University of Oxfordhttps://users.physics.ox.ac.uk/~harnew/lectures/lecture12-mechanics-handout.pdf
you can see as an example:
"Mass rotating in a circle
In the inertial frame
Centripetal acceleration provided by tension in the string: T=mrω2
􏰀In the non-inertial frame
The block is at rest and its acceleration is zero
In NIF need Ffictitious = mrω2 (centrifugal force) to balance the tension in the string".
And what I say about NIF and its usual use comes from that FACT ...
(those certainly very common ideas)

[Le Repteux]

mrω2 (centrifugal force) to balance the tension in the string".

In your example with the earth and the moon alone in the universe, if a centrifugal force was needed to keep them orbiting, cutting the centripetal one would throw the moon directly outwards, and it is not what we observe when we let go a stone out of a slingshot. The stone moves directly away from the location where it was released, not from the direction the centripetal force was coming from.

[rmolnav]

But, still, they would have to keep rotating.  That way inherent inertial force, the centrifugal force, would keep them without falling straightly onto each other !! 

It is their speed with regard to one another that keeps them from falling, and speed is not a force, only a motion.

Again, ONLY SPEED wouldn´t keep them from falling ...
Gravitational pull (centripetal force) don´t let them to keep constant their speed vectors (as they would "like" to, because of inertia phenomenon) ... Their tendency to follow straight makes an inertial force appear as a reaction, equal but opposite to the gravitational pull: the centrifugal force.
And that is what I explained on #382 ... But you, perhaps reading it without sufficiently open mind, I´m afraid can´t understand ... (apart from agreeing or not agreeing with what proposed ...)

[Le Repteux]

Again, ONLY SPEED wouldn´t keep them from falling ...

Of course it does. What is actually preventing our ideas from falling towards one another is the different direction and speed they had when we met. They are not voluntarily trying to pull on their own side, they just follow the way they were already following, and what links them keeps them orbiting.

[Colin2B]

Reference frames were invented to account for inertial motion, not rotation.

LOL, so you are going to rewrite history? 
Galileo first used reference frames (although he didn’t call them that) to explain why he supported Copernicus in his idea that the earth orbits the sun. The observer on earth in the rotating frame sees the sun orbit the earth, the distant observer sees the earth orbit the sun.

In a merry go round, we know we are rotating

It doesn’t matter whether we know or not, the issue is which frame do we calculate from.
Take a pilot travelling at, say 200mph on a collision course with another plane at 300mph. The pilot knows the 2 aircraft are moving relative to the ground but the mental calculations to avoid collision are made in the reference frame that assumes s/he is at rest and computes the trajectory of the other plane relative to that.
A ships radar uses the same ship centred frame with all other targets moving relative to that centre.
All celestial navigation tables assume a static earth at the centre of the celestial sphere.
These POVs are extremely useful, and when using centrifugal force we are doing no more or less than calculating from one of these frames. It doesn’t confuse unless you start mixing frames, which is what you have been doing.
You quote a merry go round. Take 2 observers, one on the ground, one on the merry go round. The rotating one sits in the centre, attached to the centre is a spring and on the end a weight (no friction etc). The ground observer - not really inertial, but good enough - sees the weight trying to travel in a straight line and the spring pulling it into a curve. The rotating observer from that rest frame sees the playground rotating around the merry go round, the spring is in tension and in order to account for it uses a centrifugal force to balance the tension in the spring. Of course the rotating observer knows they are rotating, that’s not the point, it is where you are making the calculations from that determines what method you use.

The real answer is simply straight-line differential gravity, mostly from the moon. The moon's and sun's gravity decreases over distance, but it falls in strength most strongly
over distance with greater proximity to the source.

I would agree with this from an inertial frame. I would need to look through your detail to see whether I would agree with your methodology, but in principle using gravitational potential is a valid way of working this out.
But neither have I been through the detail of @rmolnav  so I wouldn’t say whether I agree  with him.
My main concern in joining this discussion is that @Le Repteux  is muddying the waters confusing frames and introducing photons and quantum movement.

Until the topic is locked, I'll repost this every page or two just to make sure that no one is misled by authoritative nonsense.

Don’t do that, someone will only delete them as we don’t encourage repeat posts. We’ll have to decide what to do with this topic.

[rmolnav]

Some of you will remember that not long ago I mentioned:
Sources of Misconceptions in Astronomy, by Neil F. Comins (University of Maine).
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 ..."
Well, months ago I saw a NFC youtube video where an interactive event is recorded, closely related to what above, because it is about how earth would be without the moon, and he corrects many misconceptions of the audience.
It is not specifically about tides and their causes, but logically NFC (the audience too) refers to the issue.
He asks the audience many questions, and that and audience´s answers make the video too long ... That´s why I haven´t mentioned it here before.
I recently saw it again, and with the purpose of writing down the time location of what about our discussion on causes of tides (gravitational difference? ... centrifugal forces? ... both?).
Though he uses the term "outward force" instead of the controversial "centrifugal force", he clearly says the same I´m saying since long ago (and other scientists as previously mentioned from NOAA) ...
And he even clearly replies "NO" when somebody from the audience suggests (as antipodal bulge and tide cause) "gravitational difference" (without adding anything more) is the cause.
You can see it, and listen to, app. starting on 15:40. Title of the youtube video:
What if the Moon Didn't Exist? — Neil F. Comins 
Could that so experienced expert be completely wrong on the issue ??
Well, theoretically he could ... But, as I said in relation to the NOAA scientist similarly very, very expert on tides, the odds of he being wrong would be, I guess, smaller than 1:1000 !!

[Le Repteux]

Galileo first used reference frames (although he didn’t call them that) to explain why he supported Copernicus in his idea that the earth orbits the sun. The observer on earth in the rotating frame sees the sun orbit the earth, the distant observer sees the earth orbit the sun.

In this case, we discovered which observer was moving faster, whereas in the case of inertial motion, we can tell without knowing how much they were accelerated in their respective direction.

The rotating observer from that rest frame sees the playground rotating around the merry go round, the spring is in tension and in order to account for it uses a centrifugal force to balance the tension in the spring.

I would explain to him that the force pulling on him is only due to him pulling the weight towards him instead of letting it go, and I would also add that he would better call his pulling centripetal since he actually is at the center of the rotation.

Of course the rotating observer knows they are rotating, that’s not the point, it is where you are making the calculations from that determines what method you use.

Calculations made from the wrong viewpoint leads to epicycles, so it is a lot better to know which viewpoint is right before making them.

[Le Repteux]

Though he uses the term "outward force" instead of the controversial "centrifugal force",

If it was an outward force, a rotating ball would move directly outward when we let it go, and it doesn't: it moves at right angle to the outward direction.

[David Cooper]

I would need to look through your detail to see whether I would agree with your methodology, but in principle using gravitational potential is a valid way of working this out.

All you have to do to see who's right is look to see which way the Earth is actually moving when it's between the moon and sun. It's following a curve, and the sun is on the inside of that curve, which means that any role for centrifugal force would be driving a tidal "bulge" on the side nearest the moon rather than on the daylight side. You can do the maths really simply by working out where the Earth would have to be for the moon's and sun's pull to be equal - that would make the Earth move in a straight line, and that would happen if the Earth was orbiting out near Saturn's orbit. Put the Earth in any orbit nearer the sun than that and its path will necessarily curve with the sun on the inside of the curve rather than the moon. This neatly disproves rmolnav's explanation: the "bulge" on the daylight side cannot be attributed to centrifugal force at all, and most of the "bulge" on the night side can't be attributed to it either because most of that is caused by the moon's differential gravity pulling it up. The case is closed and the thread should be locked to prevent the right answer being buried under a ton of junk. I have no problem with rmolnav having the last word before the thread's locked, but the right answer needs to be on the last page where it can be found easily.

[rmolnav]

Though he uses the term "outward force" instead of the controversial "centrifugal force",

If it was an outward force, a rotating ball would move directly outward when we let it go, and it doesn't: it moves at right angle to the outward direction.

Sorry, but you don´t deserve the time and effort Colin2B and myself are "wasting" discussing with you ...
You clearly IGNORE basic laws of the SCIENCE called DYNAMICS, and with your layman mind dare think you know better than anybody else, eminent physicists included ...
What in bold is UTTERLY WRONG !!
The ball "would move directly outward" if ONLY that "outward" force were acting on it ... (1st and 2nd Newton´s Motion Laws).
But on the "rotating ball" mentioned by you, an "inward" force has to be acting, the centripetal force (inherent in any not straight movement). Otherwise there would be no "rotation" at all ...
And there is also an initial speed vector (do you know what a "vector" is ?), that is being "forced" to continuously change direction towards the center of curvature ...
Leaving aside the issue of reference frames, the phenomenon called INERTIA manifests itself as a force equal but opposite to the centripetal force (the one which causes the centripetal acceleration that changes the direction of the linear speed vector): an OUTWARD force.
Therefore, in the radial direction, TWO opposite forces act on the ball, and the ball goes neither directly outward, nor directly inward: it goes on with its tangential speed, that continuously changes direction, that is, it just "rotates" ...
Neil F. Comins uses a quite correct word ... He knows much, much better than you !!
By the way, have you watched the video?
If so, have you notice none of the audience, after NFC explanations, replies saying they don´t agree ??   
 

[Le Repteux]

Leaving aside the issue of reference frames, the phenomenon called INERTIA manifests itself as a force equal but opposite to the centripetal force (the one which causes the centripetal acceleration that changes the direction of the linear speed vector): an OUTWARD force.

Inertia opposes the direction of acceleration, and acceleration is caused by a direct force, in such a way that if we let go an important weight while we are rotating it around us, we start moving directly away from it, which is not the case of the weight since it goes on moving in the same direction it was moving when we let it go. Inertia only resists an acceleration, whereas a force gives some.

[Colin2B]

If it was an outward force, a rotating ball would move directly outward when we let it go, and it doesn't: it moves at right angle to the outward direction.

Only in the inertial frame. Again you are mixing and confusing frames.
From the rotating frame the ball initially moves radially outwards then begins to curve away from the direction of rotation.
You are passenger in a car driving round a curve. Do you feel a force pushing you on a tangent to that curve ie forwards relative to the car, or do you feel a force pushing you perpendicular to the tangent ie towards the side of the car?. Think before you answer.

Galileo first used reference frames (although he didn’t call them that) to explain why he supported Copernicus in his idea that the earth orbits the sun. The observer on earth in the rotating frame sees the sun orbit the earth, the distant observer sees the earth orbit the sun.

In this case, we discovered which observer was moving faster, whereas in the case of inertial motion, we can tell without knowing how much they were accelerated in their respective direction.

It doesn’t matter. We are not looking at root causes here, just what motions and forces are seen by the observer. The question is asked whether the @rmolnav  model using centrifugal force can adequately describe the tide raising force from the rotating frame. You are diverting that discussion due to your lack of understanding of basic dynamics.

The rotating observer from that rest frame sees the playground rotating around the merry go round, the spring is in tension and in order to account for it uses a centrifugal force to balance the tension in the spring.

I would explain to him that the force pulling on him is only due to him pulling the weight towards him instead of letting it go, and I would also add that he would better call his pulling centripetal since he actually is at the center of the rotation.

He’s not puling on the spring, it is attached to the roundabout axis, and this observer does call the spring tension centripetal. The question is what does he call the force stretching the spring, and in his frame he calls it centrifugal.

Of course the rotating observer knows they are rotating, that’s not the point, it is where you are making the calculations from that determines what method you use.

Calculations made from the wrong viewpoint leads to epicycles, so it is a lot better to know which viewpoint is right before making them.

Calculations do not lead to epicycles, incorrect interpretation does. There are many situations were it is important to calculate retrograde motion relative to earth, but it is not necessary to attribute it to epicycles.
There is no ‘right’ viewpoint, just inappropriate viewpoints for a certain application. If we want to look at the orbit of the moon around the earth and particularly, for example,  it’s apisidal precession, then we really ought not to choose a heliocentric frame, one of the earth centred frames would be better even though the heliocentric gives a more accurate view of the motion within the solar system.

As I said, we are not talking about root causes, just what is observed from a particular frame. If you can’t understand that you really need to leave this discussion.

[rmolnav]

All you have to do to see who's right is look to see which way the Earth is actually moving when it's between the moon and sun. It's following a curve, and the sun is on the inside of that curve, which means that any role for centrifugal force would be driving a tidal "bulge" on the side nearest the moon rather than on the daylight side. You can do the maths really simply by working out where the Earth would have to be for the moon's and sun's pull to be equal ... This neatly disproves rmolnav's explanation: the "bulge" on the daylight side cannot be attributed to centrifugal force at all, and most of the "bulge" on the night side can't be attributed to it either because most of that is caused by the moon's differential gravity pulling it up.

How "on earth" do you dare tackle the dynamics of the whole sun-earth-moon system simultaneously, when even grasping only the dynamics of  earth-moon system, as we are seeing, is so tricky ??
Previously, in some of the cases when I said I was discussing only that last system, you even replied "so am I" ... But now, with no better arguments, just "observing" what you think are the real movements of the three celestial objects (you need no other information, as you also said), you deduce what in italics ... If you were a guy really well educated on Dynamics, or in Astronomy, the odds of being right could be not insignificant. But with the background you have shown here, quite flawed conclusions are unavoidable ... And, as so frequently, you are utterly wrong !!
Sun-related tidal effects are similar to moon-related tidal effects. We can even say there are two sun-related bulges, but being smaller than moon´s, they are not directly visible ... They, added to moon-related bulges, manifest themselves making the total tide intensity oscillate with changes in relative locations of moon and sun ...
If we analyze them separately, when with FULL MOON we have:
1) On the one hand sun´s pull is maximum AT LOCAL NOON SIDE. Sun-related centrifugal force at that area, as "outwards" at that time is towards earth´s CM, would actually make sea water level decrease, but less than opposite sun´s pull effect: THAT WOUD GIVE US ONE OF THE SUN-RELATED BULGES.
And on the other hand, at mentioned area moon-related bulge also builds, because moon´s pull there is smaller than moon-related centrifugal force: ONE OF THE MOON-RELATED BULGES.
Both bulges ADD UP, and we have spring high tide at that area, some time after noon due to the gap caused by fast earth daily spinning ...
2) Sun´s pull is minimum AT LOCAL MIDNIGHT SIDE, and being towards earth CM it would actually make sea water level decrease, but less than "outward" (from earth CM) sun-related centrifugal force: THE OTHER SUN-RELATED BULGE.
And, in its turn, at mentioned area moon-related bulge also builds, because moon´s pull there is bigger than opposite sense moon-related centrifugal force (not forgetting that earth "revolves" around earth-moon barycenter): THE OTHER MOON RELATED BULGE.
Both bulges ADD UP, and we also have spring high tide at that area, some time after midnight, equally due to the gap caused by fast earth daily spinning ...
Rather tricky, isn´t it ? ... But much simpler than trying and analyzing both "differently-rooted" phenomena together !!

(Sorry in case of any lapse ... There are so many details ...)

[Le Repteux]

Again you are mixing and confusing frames.

I don't think I am. I knew what the observer at the center of rotation was seeing, but I also knew which one was moving faster because I knew which one was suffering a force, so I didn't need to change reference frames. If I had, it would only have been to show how it worked, or to show that I knew. When we are rotating, we know we are, and if an observer at rest says that, from his viewpoint, we are not, then we can change places with him so that he can feel the force, which would then be a good reason to change reference frames in this case.

From the rotating frame the ball initially moves radially outwards then begins to curve away from the direction of rotation.

Theoretically, the ball never moves directly outwards since the rotation never stops, it starts making epicycles as soon as it is no more held, and if such a complicated motion happened in my simulations, I would immediately know I am wrong, because I know that bodies don't make epicycles when they are on inertial motion.

It doesn’t matter. We are not looking at root causes here, just what motions and forces are seen by the observer. The question is asked whether the @rmolnav  model using centrifugal force can adequately describe the tide raising force from the rotating frame. You are diverting that discussion due to your lack of understanding of basic dynamics.

I'm simply using my own viewpoint like everybody does, which is incidentally the same as David's one, but I'm also trying to understand what Rmolnav doesn't seem to understand, and I also use my own background to do that. No need for me to suspect that he doesn't know the basics, I consider that he does and I push the reasoning further. If it is true that differential gravitation explains it all, then adding an outward pull is only adding epicycles to the explanation. When we accelerate a body, it certainly does as if it was pulling the other way, but do we call this force centrifugal?

He’s not puling on the spring, it is attached to the roundabout axis, and this observer does call the spring tension centripetal. The question is what does he call the force stretching the spring, and in his frame he calls it centrifugal.

What he observes is the same force we feel when we accelerate a body, and we don't call it centrifugal. If that observer knows what inertia is about, he also knows he is rotating since he knows that the acceleration doesn't come from his location, and if he doesn't, then I'm afraid that using the reference frame principle won't help him to learn it. He will never be able to know what inertia is about without stepping out of his merry go round and beginning to accelerate things. Since the advent of the Sagnac interferometer, we all know that rotational motion is absolute, so why go on tinkering with the reference frame principle? It only confuses the readers.

As I said, we are not talking about root causes, just what is observed from a particular frame.

If the rotating observer had a Sagnac interferometer, he would know he is rotating, and he could deduce what inertia is about. The other way around would be to go to the edge of the merry go round, and to throw balls perpendicularly to the force. He would then discover that there is a direction and a speed at which it doesn't move away from the platform, and that the platform seems to be rotating around a center. If he is brilliant, he will deduce that the force needed to accelerate the ball tangentially is of the same kind than the force on the spring, and he will know he is rotating. On the contrary, there is no way to know that we are on inertial motion, and one of the ways to illustrate it is to use the reference frame principle, which is simply about not knowing which one of the observers is moving. If we knew, we wouldn't need the reference frame principle to explain the result. In the Twins paradox for instance, we know which one has accelerated, so we know which one will be younger at the end without using reference frames. By the way, here is a simulation I made with light clocks instead of twins that shows the way they slow down. It uses the absolute speed of light as the only reference, and I couldn't have built it without choosing the screen as the frame in which light moves at the same speed in any direction. Nothing tells the moving clock that it is moving, light simply takes more time to make its round trip and it simply registers more time than the one at rest. In this case, changing reference frames would mean moving the clock that was at rest at the speed of light without accelerating it so that it stays at rest with regard to light, and consider that the other clock is at rest even if it accelerates at more than the speed of light and if light doesn't take the same time going right than going left between the mirrors. Do you really think it would help the readers to understand why the moving clock slows down?