[David Cooper]

WRONG! You talk about " add the perpendicular movement", and "When the perpendicular movement is removed" ... How do you "imagine" those actions could actually be realized ??

In the case of a ball on the end of a string (let's have this floating in space and going round a pole with huge masses on either end), a bat can be used to start it going round and to stop it moving. In the case of a ball orbiting an asteroid, a bat can be used to stop the orbital movement, and to start it again if there isn't too long a delay before doing this (because it will fall towards the asteroid).

Why do you find it so hard to think up a practical experiment of this kind to illustrate what you somehow imagine to be an impossibility? It took me about five seconds of thinking time to construct those two examples. But you shouldn't even be asking me to realise them when we're dealing with principles which still apply in the case of a moon going round a planet where we can't make a bat big enough to do the same job - the impossibility of making an adequate bat for that does not negate the principle. Stop shouting "WRONG" at people and sort out your incorrect position instead of assuming it's not you that's got it wrong.

Because you don´t even mention Newton´s Motion Laws I referred to, that ALWAYS must be accomplished, as far as movement is concerned ...

Newtons laws are on my side. Relativity (all versions) are on my side too. I don't need to drag names in to boost a rock-solid argument.

When the line is “slack” as you say, its end is supposedly still. And at a certain moment there is a physical transference of momentum (or kinetic energy, if you prefer) between the two “objects” in contact: the ball and the string hook.
As I´ve said several times, the hook and string end ONLY can be put in motion with an external force, because the ball cannot directly “deliver” any type of energy or momentum as if it were a kind of commodity …

The ball is floating in space and the string is slack. I hit the ball in a direction perpendicular to the string. The ball tries to move in a straight line and pulls on the string, and that pull generates the centripetal force in the string. The reactive centrifugal force in this case isn't so much reactive as a causitive force, but relativity blurs the difference in any case. We don't need to care, because these forces result from the ball moving as a result of being hit by the bat. That is all that matters - we are comparing this with the ball sitting near the asteroid (and falling towards it) which, if we hit it with the bat to produce an orbit for it, that hit did not generate or trigger into existence in any way shape or form the gravitational force that is coming from the asteroid. That force was already acting. These are the facts, and no amount of dissecting the components of the action will reverse these facts. The case is closed.

Do you know better than Newton...

If Newton agrees with you, tell him to join the forum and to state which side he's on.

Also WRONG.

Someone's sold you a faulty dictionary. The word you should be using is "right".

Let us imagine moon´s gravity were constant across the earth, maintaining moon´s total pull, and therefore actual distances and moon-earth “dancing” …

An evenly applied force where each atom of the Earth is pulled equally. Lovely.

The “tendency” of earth revolving particles (both solid and water) not to change their velocity vectors (INERTIA) would cause two “tidal” bulges, but BOTH in the sense opposite to the moon (opposite to the centripetal force, that is, always parallel to line earth C.M. - barycenter - moon C.M.).

An evenly applied force of this kind would move the whole Earth without producing any bulges on it whatsoever. That's why we don't get tidal bulges from the strongest pull on us which comes from the galaxy - its pull is stronger than the sun's and the sun's is stronger than the moon's, but it is so evenly applied that we see no effects on the Earth's shape.

As I´ve said on "Why do we have two high tides a day?" thread many times, those centrifugal inertial "effects", added to what caused directly by the varying gravitational moon´s pull (inversely proportional to the square of the distance), is what causes the real tidal bulges !!

Stop using the word centrifugal. It's misleading. All we have is different parts of the Earth being pulled towards the moon with different strengths, leading to some trying to move faster than others and the whole thing attempting to elongate. One bulge is from the material being pulled towards the moon most strongly, while the other bulge is from the material being pulled least strongly lagging behind. That is it. It works in a straight line system with no orbit exactly as it does in an equivalent system with an orbit - the orbit is irrelevant.

Remember what Einstein thought:

If Einstein agrees with you, tell him to join the forum and to state which side he's on.

Do you know better than Einstein ??

If he disagrees with me on this, then yes, but I don't think he will. Bring him here and let's find out.

Or do you think that gravitational pull, acting as centripetal force (by the way, your "grey" area ...) doesn´t cause centripetal acceleration, and subsequently neither centrifugal forces nor other inertial "effects" are present ??
If so, please kindly give all of us your "reasons", instead of just saying "your imagined centrifugal effects don't exist in the gravity case"[/b]

You've had my reasons and they prove the case in multiple ways. You do not have any centrifugal force building any bulges anywhere at all in these gravity cases, and you don't even have it building any bulges in cases with a string because even when there is reactive centrifugal force in play, it's pulling the wrong way, limiting the amount of bulge rather than driving the bulge.

[rmolnav]

Since long ago, time and time again, I´ve seen it is useless to discuss with you, at least on dynamics, because you kind of feel 100 % sure of something ONLY if it is what you think you see in nature, forgetting that in milliseconds many things can happen, impossible for our eyes to see ...
When I once asked you for references supporting some of your ideas, you yourself said (thread "Why do we have two high tides a day", #184):
"I am always more interested in actual science than error-ridden authorities. I haven't seen anyone in science support my position (primarily because I haven't looked for that) - what I'm saying is based 100% on what I see when I look directly at the physics involved in this !!!”.
No wonder now, after me saying what quoted below, instead of giving us any alternative scientific explanation (with formulas "converting" physical variables and functions into others, as far as "movement" and forces are concerned):

the hook and string end ONLY can be put in motion with an external force, because the ball cannot directly “deliver” any type of energy or momentum as if it were a kind of commodity …
In an initial instant ∂t, if we consider m the average of moved mass of hook and string end, f=ma (1st Newton´s Motion Law).
That force ONLY can be exerted by the ball, and it “comes” from its energy. But for that transformation to happen, part of the ball´s energy has to be transferred to the hook, what happens via impulse I, according to the relation:
I = f ∂t = m ∂v,
Over same instant dif.t, the momentum of the ball decreases also in that amount (the speed inversely to ball´s mass).
From that it can be deduced that same force f, but opposite, is being exerted by the hook on the ball (3rd Newton´s Motion Law). But, though apparently the “primary” force is exerted by the ball on the hook (by the "movement" as you say), that´s not so. Without an initial reduction of the ball´s velocity, part of its momentum couldn´t have been transferred to the hook. And that ball´s momentum reduction requires the force exerted by the hook on the ball initiate the transference of momentum. 

you now just say:

Newtons laws are on my side

and try to explain us the experiment imagined by you, apparently supporting your stand, in a quite "layman" way ...
Newton stated that the direct cause of movement (acceleration that initiates a movement, or modifies its velocity vector), is ALWAYS a force (external to the object). He also considered a force can directly be caused by another force (as inertial reaction), but he never said what you say, e.g. that a movement can "generate" (?) a force, let alone what you said on mentioned #184:
"If a force is generated by rotation, that is clearly centripetal force - a force that comes into play because of the rotation ...” !!!
You seem to want to change Physics science, at least Dynamics, because I also gave you references such as:
"- Univ. of Ohio ( "phisics.ohio-state.edu”, "Dynamics of Uniform Circular Motion" (Chapter 5, 5.3 Centripetal Force).
- Univ. of Louisville (Centripetal Force - Physics 298 - Department of Physics and Astronomy, www.physics.louisville.edu/cldavis/phys298/notes/centripetal.html 
- Several Physics academies, mentioned on my post # 413.
- Merriam Webster dictionary (“movement”, “to move”, “force”…)
- Oxford dictionary (“centripetal force”) 
among others",
but you keep stuck to your ideas ...
Either you explain them "scientifically", not just telling us what you "see" in nature, or in experiments imagined by you in five seconds (!!):

Why do you find it so hard to think up a practical experiment of this kind to illustrate what you somehow imagine to be an impossibility? It took me about five seconds of thinking time to construct those two examples

or, sorry, your ideas can´t be taken seriously ...
If you did some real experiment in a lab, with modern hardware (at least a camera able to take thousands of pictures in a second), and appropriate software, the results would shed light on the issue, and you could see who is right and who is wrong ...
 

[David Cooper]

Since long ago, time and time again, I´ve seen it is useless to discuss with you, at least on dynamics, because you kind of feel 100 % sure of something ONLY if it is what you think you see in nature, forgetting that in milliseconds many things can happen, impossible for our eyes to see ...

You can chop a dog into as many components as you like, but you will never be able to prove it's a cat. It remains a dog.

No wonder now, after me saying what quoted below, instead of giving us any alternative scientific explanation (with formulas "converting" physical variables and functions into others, as far as "movement" and forces are concerned):

I'm not going to waste my time dissecting a dog to prove it's a dog to someone who's adamant that it's a cat.

Newton stated that the direct cause of movement (acceleration that initiates a movement, or modifies its velocity vector), is ALWAYS a force (external to the object). He also considered a force can directly be caused by another force (as inertial reaction), but he never said what you say, e.g. that a movement can "generate" (?) a force, let alone what you said on mentioned #184:
"If a force is generated by rotation, that is clearly centripetal force - a force that comes into play because of the rotation ...” !!!

I can't help it if you can't find the right thing to quote from Newton or if he never spelt out what is happening in a case like this one. If a force can only be caused by another force, two objects that are moving towards each other will be unable to produce any impact forces when they collide because you demand that a force can only be caused by a force.
 

You seem to want to change Physics science, at least Dynamics, because I also gave you references such as:
...
but you keep stuck to your ideas ...

I'm sticking to ideas that are right, whereas all you're doing is looking for anything you can take out of context to support your errors (or anything you can find where a scientist has made the same errors).

Either you explain them "scientifically", not just telling us what you "see" in nature, or in experiments imagined by you in five seconds (!!):

Why do you find it so hard to think up a practical experiment of this kind to illustrate what you somehow imagine to be an impossibility? It took me about five seconds of thinking time to construct those two examples

or, sorry, your ideas can´t be taken seriously ...

Oh, sure they can't - it would be impossible for a ball to orbit an asteroid because we've never put a ball in orbit round an asteroid, and because we've never done it, it must be impossible to stop it going round the asteroid by hitting it with a bat. That's essentially your argument. I say it can be done though. Science gives us universal principles which allow us to predict how things will behave, and in this case it gives us every confidence that if we were to put a ball in orbit round an asteroid (which isn't even very far from something we have already done with space probes visiting asteroids), it would go round the asteroid and could be stopped by hitting it with a bat, whereupon it would accelerated down onto the asteroid because the gravitational force is still being applied to it in full.

If you did some real experiment in a lab, with modern hardware (at least a camera able to take thousands of pictures in a second), and appropriate software, the results would shed light on the issue, and you could see who is right and who is wrong ...

You want to do the experiment in a lab with a ball orbiting an asteroid? I hope you've got an antigravity machine to stop the Earth's gravity wrecking the experiment. How have you managed to shackle your thinking abilities in such an extreme way that you can't imagine the interactions between simple things like a bat hitting a ball?

The other case was a ball on a string, which again I had to ask you to do in space to stop you obsessing about the Earth's gravity interfering when the ball's stopped by the bat. The ball is stopped and the string goes slack. Do it on the Earth and it doesn't go slack for long because gravity pulls the ball downwards - we're then dealing with a mixed gravity and string case instead of looking at a pure string case, which is what you ought to be capable of considering. In the pure string case though where we aren't messing it up with gravity, when the bat stops the ball, the string goes slack.

But you don't want to consider this case because it hasn't been done in space, and therefore my description must be bad science, just like the bad science which people relied on when sending people to the moon by calculating what would happen and then acting on the assumption that the laws of nature wouldn't let them down. It worked, and my thought experiments will work for real too if they're ever tried. If anyone thinks they won't, please name yourself in a reply so that we can see how many people have the same beliefs as rmolnav.

[rmolnav]

You can chop a dog into as many components as you like, but you will never be able to prove it's a cat. It remains a dog.

Right !

I'm not going to waste my time dissecting a dog to prove it's a dog to someone who's adamant that it's a cat.

WRONG ... because what I "dissected" was TIME, a second into milliseconds, and never said those milliseconds are not TIME any more ...
And however good vision you might have, you would´t notice physical, real things that happen in milliseconds !!
You initially see and object moving, afterwards you see forces that didn´t exist before ... and you conclude thinking something as if you were a child (or a non-educated adult): the movement is what "generates" the forces ...
And you dare say Logics is your speciality !!
Sorry, but as I´ve said many times, it´s useless to discuss with you ... If I have done it for so long, it has been for the sake of any other reader who could be interested.
 

You want to do the experiment in a lab with a ball orbiting an asteroid?

What an absurd way of misunderstanding my words !! I said:
"If you did SOME real experiment in a lab ... "[/quote]
and, logically, I referred to the pole-string-ball case, or something similar.
With suitably placed gauging devices, ultra high-speed camera, and appropriate software, we could see forces building up ("reacting" to other previous "action" force interchanged between the two objects in contact), but ALWAYS starting with an initial force exerted by the string ...
If that initial force didn´t exist at all, nothing could start braking the moving object, what is absolutely necessary for any transference of momentum !!
Remember:

the hook and string end ONLY can be put in motion with an external force, because the ball cannot directly “deliver” any type of energy or momentum as if it were a kind of commodity …
In an initial instant ∂t, if we consider m the average of moved mass of hook and string end, f=ma (1st Newton´s Motion Law).
That force ONLY can be exerted by the ball, and it “comes” from its energy. But for that transformation to happen, part of the ball´s energy has to be transferred to the hook, what happens via impulse I, according to the relation:
I = f ∂t = m ∂v,
Over same instant dif.t, the momentum of the ball decreases also in that amount (the speed inversely to ball´s mass).
From that it can be deduced that same force f, but opposite, is being exerted by the hook on the ball (3rd Newton´s Motion Law). But, though apparently the “primary” force is exerted by the ball on the hook (by the "movement" as you say), that´s not so. Without an initial reduction of the ball´s velocity, part of its momentum couldn´t have been transferred to the hook. And that ball´s momentum reduction requires the force exerted by the hook on the ball initiate the transference of momentum. 

That fully agrees with Newton´s Motion Laws ...
You consider movement can also directly "cause" forces, and once you even said there is a "symmetry" ... Could you please give us Motion Laws "symmetric" to Newton´s, which could allow us explain the case (with affected physical variables, functions and formulas, not just "literature" ? 

[David Cooper]

WRONG ... because what I "dissected" was TIME, a second into milliseconds, and never said those milliseconds are not TIME any more ...

The dog is the big picture in which stopping the ball moving causes the centripetal and reactive centrifugal force in the string to disappear and where starting the ball moving again (perpendicular to the string) causes those forces to reappear. The dog is the big picture in which when you stop the ball in the gravity case, the asteroid  continues to apply its gravitational pull on it in full.

The cat is an alternative picture in which stopping the ball moving doesn't cause the centripetal and reactive centrifugal force in the string to disappear and where starting the ball moving again (perpendicular to the string) doesn't cause those forces to reappear. The cat is incompatible with the universe.

Dissecting the dog will never turn it into a cat.

And however good vision you might have, you would´t notice physical, real things that happen in milliseconds !!

I'm not missing any momentary cat. It's always a dog.

You initially see and object moving, afterwards you see forces that didn´t exist before ... and you conclude thinking something as if you were a child (or a non-educated adult): the movement is what "generates" the forces ...
And you dare say Logics is your speciality !!

No, my conclusion is the kind that a scientist comes up with. Yours is a complete inversion of science.

Sorry, but as I´ve said many times, it´s useless to discuss with you ... If I have done it for so long, it has been for the sake of any other reader who could be interested.

You have gone on doing it because you still can't see that you're wrong. It is certainly interesting to watch you and wonder how you manage to go on being so wrong though.

What an absurd way of misunderstanding my words !! I said:
"If you did SOME real experiment in a lab ... "

And in doing so, you deny the validity of the fully sound thought experiments which you're trying to discredit on the basis that they haven't been done for real in a lab.

and, logically, I referred to the pole-string-ball case, or something similar.
With suitably placed gauging devices, ultra high-speed camera, and appropriate software, we could see forces building up ("reacting" to other previous "action" force interchanged between the two objects in contact),

There is no disagreement here about the forces building up over time and the possibility of cutting the dog into tiny slices to see that play out, but it doesn't turn it into a cat.

but ALWAYS starting with an initial force exerted by the string ...
If that initial force didn´t exist at all, nothing could start braking the moving object, what is absolutely necessary for any transference of momentum !!

How does it start with an initial force exerted by the string? The first force is applied to the string by the ball as the ball tries to follow a path that would require the string to lengthen if no force was to be generated.The perpendicular movement of the ball ceases to be perpendicular to the string after a moment of movement because the other end of the string and the ball aren't co-moving. This means the movement of the ball is now in a direction that applies a force to the string - its movement generates that force. We're dissecting the dog here and it is not turning into a cat. If it was a cat, we would magically start with a force springing out of nothing in the string, and that force would then cause the ball to move perpendicular to the string. But we are most certainly not dealing with a cat.

But, though apparently the “primary” force is exerted by the ball on the hook (by the "movement" as you say), that´s not so. Without an initial reduction of the ball´s velocity, part of its momentum couldn´t have been transferred to the hook. And that ball´s momentum reduction requires the force exerted by the hook on the ball initiate the transference of momentum.

There is room to argue about which force acts first to drive the other, but these rival forces are centripetal and reactive centrifugal forces. Relativity allows you to have them both play an equal role (i.e. to be equally first), but it also allows either one to drive the other. None of that is of any importance to our discussion though - it remains the dissection of a dog. What drives the generation of BOTH of those forces is the movement of the ball relative to the thing at the opposite end of the string, and we can call that thing at the other end of the string an anchor (on the basis that the string is anchored to something). When they are not moving relative to each other, there is no force in the string. When we start moving the ball relative to the anchor and perpendicular to the string, or if we start moving the anchor relative to the ball and perpendicular to the string, that generates the two forces in the string as soon as the movement ceases to be perpendicular. This is not a moggy. In the moggy, you want to have the forces act in the string first, and then you want either the ball or anchor to start moving as a result, but that is bonkers science. Real science works the other way round - the perpendicular movement of ball or anchor (or both) generates the forces in the string (and if we dissect the dog a little, this happens because the movement relative to the string doesn't remaining perpendicular until the forces are generated in the string to force the movement to remain perpendicular).

Woof!

[rmolnav]

A lot of "literature" on last post, but no scientific explanation of how on earth movement of an object can "cause" and a force on another ...
If there is a symmetry as D.C. says, it should be possible to have "motion --> force" laws, kind of symmetric to "force --> motion" Newton´s Laws.I haven´t seen them anywhere, I asked D.C. for them, but business as usual ...
Leaving aside the tricky case pole-string-object, I´ll go back to a gravitational scenario, to have yet another go.
Remembering the “famous” case of the three balls, let us make it simpler and consider just two, in straight line with a much more massive object exerting gravitational pull on them (for the sake of simplicity, let us consider negligible the gravitational pull between the two balls).
On each ball  ONLY the gravitational pull at its location is exerted, and they, completely free to move, are being accelerated, back one less because the pull is smaller there. That makes them separate more and more.
Inertial “resistance” to accelerate (tendency to keep their velocity constant), proportional to mass and actually given acceleration, is just “overcome” by gravity pull, and they accelerate “without any problem” …
We could “refer" the movement of one of them relatively to the other (non-inertial reference system), and say back one accelerates “backwards”, though only relatively to the other … I would understand even the use of the term “differential acceleration” …
But the term “differential gravity” would be absurd, because the “difference” between the two real pulls is not a force actually exerted anywhere, it is something only exists in our minds, as I´ve said many times. When, e.g., at the beginning of a competition, a bike accelerates more than another, we can say there is a  “differential acceleration”, that can be directly observed and even measured. But the terms “differential thrust” of the engines, and the thrust of one "relatively" to the other, would have no sense at all ...
But if mentioned balls are stuck together, they aren´t free to move: they are somehow “forced” to accelerate the same, despite the different gravitational pulls exerted on them …
Forward ball is being accelerated less than what gravity there would cause if it were “independent” to move … Inertial resistance to accelerate is smaller than actual gravitational pull … A “spare” forward force remains acting on it.
The opposite happens to backward ball: it is being accelerated more than what gravity there would cause if the ball were completely free to move … Inertial resistance to accelerate is bigger than actual gravitational pull … A “spare” backward inertial force acts on it.
Those two opposite forces, directly exerted on the balls (by the way, not the case of anything like the so called “differential gravity”), stretch the two-part "object", a clear “tidal” effect, using the adjective in its broad sense.
It would be utterly absurd to think mentioned backward force could be called “centrifugal force”, because in that one-dimension scenario there isn´t a proper “center”. The same could be said about the term “centripetal force”.
But if the two balls also had an initial velocity perpendicular to the straight line going from them to the object causing the gravity, resulting movement would be a curved one, and mentioned stretch would also happen, exactly for the same reasons ...
In that case of circular (or at least curved) movement, both centripetal and centrifugal force terms are the correct ones used in Physics, though “centrifugal” one certainly not by everybody ...
And please kindly note that closer ball is forcing (pulling) further one to experience an acceleration additional to the one directly caused by gravity, in that case by “contact”, same way as in the string case the hook pulls inwards (centripetally) the rotating, “hooked” object.
And, again, when gravitational pull exerts the FUNCTION of centripetal force, logically it doesn´t change the ESSENCE of it ...
And, also logically, if tangential velocity is somehow reduced to null, that FUNCTION disappears, because we are in a different scenario, the one-dimension exposed above ("centripetal" adjective should be substituted by "forward", and "centrifugal" by "backward").
And the fact that gravity remains even if the "perpendicular" movement is somehow removed doesn´t mean that to call its previously existing FUNCTION as centripetal is erroneous, as D.C. has as kind of "life motive" ... (no wonder D.C. says "centripetal force" concept is a "grey area").
If with initial "perpendicular" movement, the gravity would be somehow switched off, the balls would continue its straight path ... That means gravitational pull (or at least a part of it), when existing, is what causes the curved movement, though initial "tangential" speed, logically again, is a necessary condition.

[David Cooper]

A lot of "literature" on last post, but no scientific explanation of how on earth movement of an object can "cause" and a force on another ...

Apart from the scientific explanation I provided (which you simply ignore).

If there is a symmetry as D.C. says, it should be possible to have "motion --> force" laws, kind of symmetric to "force --> motion" Newton´s Laws.I haven´t seen them anywhere, I asked D.C. for them, but business as usual ...

Imagine that you are drifting in deep space and that you have a ball on a long coiled string with the other end tied onto you. You throw the ball away from yourself, the string is pulled out by the ball, and when it reaches its full length, a strong tension force is suddenly generated in it. If the movement of the ball (relative to you) isn't responsible for generating that tension force, what is? Magic? I say that the movement generates the force (once the movement is resisted by the string). If there is no movement in a case like this, there will never be a force in the string.

When you run a reversible event backwards, the causation reverses too. If I drop a weight on a spring it may cause the spring to compress. The spring may then rebound and fling the weight off it. The movement of the weight causes the spring to compress and a force to be generated which halts the weight while energy is stored in the spring. The spring then releases that energy back and generates a force which accelerates the weight upwards, this force causing weight to move again. Every step in that process is governed by a rule that future parts of the action do not cause parts in their past, but that the causation operates from past to future. Perhaps this was so obvious that Newton didn't think it worth mentioning, but you can be sure that he fully understood it to be the case.

But the term “differential gravity” would be absurd, because the “difference” between the two real pulls is not a force actually exerted anywhere, it is something only exists in our minds, as I´ve said many times.

There is a pull on each ball, and a difference between the strength of those pulls. It is not something that merely exists in the mind (unless we're applying a theory of gravity in which it is not a force).

But the terms “differential thrust” of the engines, and the thrust of one "relatively" to the other, would have no sense at all ...

What's the problem with that? If they're putting out different amounts of thrust, that description sounds fully apt.

But if mentioned balls are stuck together, they aren´t free to move: they are somehow “forced” to accelerate the same, despite the different gravitational pulls exerted on them …

...which means that the different pulls on each will generate tension forces which resist the stretching.

The opposite happens to backward ball: it is being accelerated more than what gravity there would cause if the ball were completely free to move … Inertial resistance to accelerate is bigger than actual gravitational pull … A “spare” backward inertial force acts on it.

The only forces acting on it are gravity, pulling it towards the massive object, and the tension force from the ball nearer to the massive object. There is no force pulling the further out ball outwards. The only force pulling outwards is the tension force acting on the inner ball, and that is resisting the stretch.

Those two opposite forces, directly exerted on the balls (by the way, not the case of anything like the so called “differential gravity”), stretch the two-part "object", a clear “tidal” effect, using the adjective in its broad sense.

The actual forces in the object are trying to arrest that stretch; not drive it.

It would be utterly absurd to think mentioned backward force could be called “centrifugal force”, because in that one-dimension scenario there isn´t a proper “center”. The same could be said about the term “centripetal force”.
But if the two balls also had an initial velocity perpendicular to the straight line going from them to the object causing the gravity, resulting movement would be a curved one, and mentioned stretch would also happen, exactly for the same reasons ...

The stretch is caused solely by the nearer ball being pulled more strongly towards the massive object than the other ball. That is what is applying the stretch. The other forces that are generated in the object are both opposing that stretch. The perpendicular movement makes no difference to the forces in play, as you can tell when you apply relativity to this.

In that case of circular (or at least curved) movement, both centripetal and centrifugal force terms are the correct ones used in Physics, though “centrifugal” one certainly not by everybody ...

You need to see past the official correctness of the usage of terms to the actual causes and effects, and to the actual forces that are involved and their actual roles. The only cases where we've found any real force that can legitimately have "centrifugal" used as part of part of its name has that force act in the wrong direction to drive the generation of bulges.

And please kindly note that closer ball is forcing (pulling) further one to experience an acceleration additional to the one directly caused by gravity, in that case by “contact”, same way as in the string case the hook pulls inwards (centripetally) the rotating, “hooked” object.

Yes, kindly note that it is pulling in such a way as to suppress the forming of a bulge, as is the force opposing it.

And, again, when gravitational pull exerts the FUNCTION of centripetal force, logically it doesn´t change the ESSENCE of it ...

When there is no orbit, the force is the same strength at a given distance as when there is no orbital movement. The force is simply gravitational pull. Playing games where you call it centripetal in some cases and not in others illustrates that they are mere games, but even when you play those games, there are no centrifugal forces anywhere building bulges. The only real centrifugal force is reactive centrifugal force, and it always acts to suppress bulges.

And, also logically, if tangential velocity is somehow reduced to null, that FUNCTION disappears, because we are in a different scenario, the one-dimension exposed above ("centripetal" adjective should be substituted by "forward", and "centrifugal" by "backward").

The "forward" force is pulling on the outer ball while the "backward" force is pulling on the inner ball, so these forces are pulling the balls towards each other. They are not friends of your argument at all.

And the fact that gravity remains even if the "perpendicular" movement is somehow removed doesn´t mean that to call its previously existing FUNCTION as centripetal is erroneous, as D.C. has as kind of "life motive" ... (no wonder D.C. says "centripetal force" concept is a "grey area").

It's a grey area because we have two radically different cases. With the string, we have a centripetal force (and reactive centrifugal force opposing it) which ceases to exist when the orbital motion is removed, so there is deeper, more fundamental name for it. In the gravity case though, there is a deeper, more fundamental name for it, and that is gravity, and removing the orbital movement also shows that the correct name for the force is gravity because it remains in play when the word centripetal disappears from it without any loss of the force. That tells you what the force really is.

You could argue that the force in the string is an acceleration force both in cases where there's a acceleration in a straight line and where there's orbital motion, and thereby claim that there is no force that's fundamentally a centripetal force in that case either because it's actually an acceleration force, and then you could argue that gravity is an acceleration force too, so the word centripetal is equally valid in both cases. You haven't argued that, but I've just done that work for you. Does it help your case though? No. The only reason this line of thought has been followed at all was to try to get through to you that in gravity cases there is no centrifugal force opposing the gravity, which makes it different from the string case in which there's a reactive centripetal force opposing the centripetal force. You scored a significant point though when you pointed out that forces like those in string are in play within a ball even in the gravity case, but those forces oppose the stretching rather than driving it, and it turns out that the reactive centrifugal force in the string case opposes the stretching too. There is never a centrifugal force of any kind feeding into the formation of a tidal bulge or any equivalent bulge on a distorted ball on the end of a string.

You seek to find centrifugal forces that help to build bulges, but they always do the opposite. The only real centrifugal force is a reactive centrifugal force which tries to pull things outwards that are further in (such as the outer ball pulling the inner ball), thereby suppressing the formation of bulges. Reactive centrifugal force thus helps to pull the inner tidal bulge down, and that's an outward pull away from the source of the gravitational pull from the other body, so this is a case of a real centrifugal force pulling something outwards, but it isn't outwards in relation to the body where this pull is acting - it's an inward pull locally.

[rmolnav]

I haven´t replied last D.C. post so far to give other possible readers time to read it quietly.
I hope some have already done , and seen at least some of its persistent errors …
Now I´m going to refer to some of them, all at the very root of D.C.´s “grey” flawed stand.

A) You only refer to Newton when saying:

... a rule that future parts of the action do not cause parts in their past, but that the causation operates from past to future. Perhaps this was so obvious that Newton didn't think it worth mentioning, but you can be sure that he fully understood it to be the case

But I´ve never said Newton didn´t mention that ... ("causation operates from past to future") ... What Newton never said, as far as I know, is that movements, by themselves, can cause forces. He delivered his Motion Rules, stating forces cause accelerations. Therefore, they are absolutely necessary, both to initiate a movement, or to change its velocity vector …
“Your” artificial pole-string-object case and similar cases are far-fetched and uncommon, but natural collisions aren´t rare at all … How could Newton “forget" to analyze what (according to you) happens in those cases, that motion cause forces, and somehow include the results in his Motion Laws ?? Impossible to me.     
As I´ve already said, neither momentum nor kinetic energy are a kind of commodity, directly transferable when a collision or similar cases (such as when the string gets tight). An "exchage currency" is necessary, and it is called impulse. To start that “transference”, in an infinitesimal amount of time the momentum of the moving object HAS TO BE REDUCED by an external force, according to:
∂I = F∂t = ma∂t = m∂v.
That force, depending on each particular case, might be an initial latent force, a string own weight component, static friction, initial material resistance to deformations, etc.
The fact that it is not clearly visible to our eyes doesn´t mean it doesn´t exist … Otherwise the moving object would keep constant its velocity vector (Newton´s 1st Motion Law), and no transference of any momentum could occur !! 
 As a REACTION to that force (Newton´s 3rd Motion Law), the moving object starts exerting an equal but opposite force on the “obstacle” (string or initially still object). And a “chain” of mutual actions and reactions, in milliseconds, massively raise those opposite forces exerted on each other, what  changes velocities …

B) Many other ther errors are basically same error repeated many times !!:
B1)

The only forces acting on it are gravity, pulling it towards the massive object, and the tension force from the ball nearer to the massive object. There is no force pulling the further out ball outwards. The only force pulling outwards is the tension force acting on the inner ball, and that is resisting the stretch.

I´m afraid you haven´t fully grasped what a stretching actually is ... The "pairs" of opposite internal forces which "resist" the stretch logically are inwards (relative to the object, or the two stuck balls in our case). But that´s a clear evidence that some other forces are pulling outwards on both balls, and causing the stretch !!
In the two-ball case, one of the forces is gravitational pull on "forward" ball. The other is not so clearly visible when with only two "objects". But if we imagin "behind" ball cut into transverse slices, every slice is being pulled back by its neighbor, and each one is being stretched by its two next-door neighbors, what works in the sense of forming the further bulge …
Logically what you say also happens: through each section between two contiguous slices, they are pulling each other in the sense of “resisting” the stretch … But that is a kind of “the other side of the coin” !!
B2)

Quote
Those two opposite forces, directly exerted on the balls (by the way, not the case of anything like the so called “differential gravity”), stretch the two-part "object", a clear “tidal” effect, using the adjective in its broad sense.
The actual forces in the object are trying to arrest that stretch; not drive it.

Same comment on B1) applies.
B3)

Quote
But if mentioned balls are stuck together, they aren´t free to move: they are somehow “forced” to accelerate the same, despite the different gravitational pulls exerted on them …
...which means that the different pulls on each will generate tension forces which resist the stretching.

... which means that the different pulls on each (two pulls, each one applied on different locations - not a "differential pull" applied we don´t know where), together with the fact that those pulls don´t match with actual accelerations (what brings up inertial forces),  will stretch the whole.
Regarding material reactions, comment on B1) also applies.
B4)

The stretch is caused solely by the nearer ball being pulled more strongly towards the massive object than the other ball. That is what is applying the stretch. The other forces that are generated in the object are both opposing that stretch

Same comment on B1) applies.
There are some more paragraphs we could comment on similarly ...
C5)

The perpendicular movement makes no difference to the forces in play

.
A movement, even if not "perpendicular", certainly doesn´t directly affect forces … The opposite happens (Newton´s Motion Laws).
But that curved movement has both a velocity ("perpendicular") to forces in play, and also an acceleration, in line with forces in play ...
And you stubbornly (and blindly) keep saying things such as:

In the gravity case though, there is a deeper, more fundamental name for it, and that is gravity, and removing the orbital movement also shows that the correct name for the force is gravity because it remains in play when the word centripetal disappears from it without any loss of the force. That tells you what the force really is.

As far as I can remember, trying to make you see your Logics (and Physics) error, I´ve brought up two analogies so far:
- Donald Trump is "more deeply and fundamentally" a man, a human being ... Do you think we shouldn´t say he is also the President of USA, as if his FUNCTION didn´t exist ??
- The same with an airplane pilot, which also is "more deeply and fundamentally” a human being (ESSENCE), but when flying FUNCTIONS as a pilot.
But to no avail ...
If a moving object follows a curved path (whatever the causes), in an infinitesimal period of time ∂t its velocity vector v changes to v + ∂v ... That infinitesimal increase of velocity vector ∂v divided by the time ∂t is, BY DEFINITION, the acceleration vector of the movement at that point and instant ...
That acceleration HAS TO BE CAUSED by a force (Newton´s 1st Motion Law), exactly F = ma (Newton´s 2nd Motion Law).
For the sake of simplicity, let us suppose the size of the velocity vector keeps constant. In that case acceleration and causing force are perpendicular to the curved trajectory, and, also BY DEFINITION, they get the adjective CENTRIPETAL.
And the force exerting that FUNCTION of "bending" the trajectory, among several other ESSENCIALY different forces, can perfectly be gravity ...
If you don´t change some of your "chips", in particular if you stubbornly keep not accepting that centripetal character (FUNCTION) and its gravitational ESSENCE are quite compatible, you will keep drawing erroneous conclusions (by the way, the same will happen if you keep thinking Newton forgot to deliver "motion --> force" laws)  !!
We could even call that force, during the period mentioned function exists, "gravi-centripetal force" …
And, keeping “centripetal force” in your “grey area” that way, logically makes impossible for you even to just "imagine" the possibility that a CENTRIFUGAL force, (an inertial force requiring the existence of centripetal acceleration and forces), could exist in those cases !!

[David Cooper]

I haven´t replied last D.C. post so far to give other possible readers time to read it quietly.
I hope some have already done , and seen at least some of its persistent errors …
Now I´m going to refer to some of them, all at the very root of D.C.´s “grey” flawed stand.

And that's where I've stopped reading your post. I doubt anyone is reading it any more and I don't see why I should keep wasting more and more time doing so either. If anyone ever does read the rest of your latest post though and thinks there's something worthwhile in it, perhaps they can comment to alert others to the miracle.