[Le Repteux]

Since the very first instant (an infinitesimal fraction of time), mentioned acceleration vector changes the object speed, though logically only an infinitesimal amount of change ...

If nothing is faster than light, then nothing changes instantly, thus when we apply a force on a body, it necessarily takes a while before it changes speed or direction. If bodies could move instantly, we wouldn't have the time to feel any force, and they would go from one point to the other without going through the transitional ones. Now, if bodies can absolutely not change speed or direction instantly, it is straightforward to deduce that this may be the cause for their resistance to change, and I don't feel I'm misleading people while suggesting that. You may not be tempted to discuss that point, but others might be interested. On the other hand, if you could just admit that possibility for a while, I think you may understand more easily what I'm saying about rotational motion.

[rmolnav]

Since the very first instant (an infinitesimal fraction of time), mentioned acceleration vector changes the object speed, though logically only an infinitesimal amount of change ...

If nothing is faster than light, then nothing changes instantly, thus when we apply a force on a body, it necessarily takes a while before it changes speed or direction. If bodies could move instantly, we wouldn't have the time to feel any force, and they would go from one point to the other without going through the transitional ones. Now, if bodies can absolutely not change speed or direction instantly, it is straightforward to deduce that this may be the cause for their resistance to change, and I don't feel I'm misleading people while suggesting that. You may not be tempted to discuss that point, but others might be interested. On the other hand, if you could just admit that possibility for a while, I think you may understand more easily what I'm saying about rotational motion.

Sorry, but if you have NO IDEA of what the maths of infinitesimal values of variable and functions are, as clearly your comments show, this is not the place for me to try and explain that too ...

[rmolnav]

MY ULTIMATE GO ?
Once again I´m going to try and convey a core idea of my stand, now in a “fresh” way …
It will have three parts. I´ll post them neither on same post, nor on three different ones, but on two posts … (that way readers will have more time to “ruminate” what proposed).

A) Not to need to include a figure, please kindly IMAGINE one with two celestial objects on same “vertical” line (on your screen).
Let us imagine the lower one (M) on a fix location, and the upper one (E) moving “horizontally” from right to left, and let us consider M´s gravity starts to pull downwards E just when reaching M´s vertical (remember, M is considered somehow on a fix location).
If within certain game of relation between masses, distance and speed of E, E will start “orbiting” around M.
M´s gravity, acting as centripetal force, changes E´s speed vector direction, but it is not “able” to change its size. A “free fall” to many, but rather a “partially free fall” to me, because E´s inertia avoids a direct straight line fall.

B) Let us now imagine M, at the very moment E gets at M´s vertical, starts moving also from right to left, with same velocity as E.
Being now M´s pull on E always vertical, E will fall towards M, following a parabolic line.
Now M´s pull is able not only to bend E´s speed vector, but also to increase its vertical speed with an acceleration proportional to M´s pull … same way as if neither of them had an initial horizontal speed …
That´s what I consider is a “fully free” fall ...
And now we should not say E is orbiting “around” M, because it will fall onto it !!
 

[Le Repteux]

Sorry, but if you have NO IDEA of what the maths of infinitesimal values of variable and functions are, as clearly your comments show, this is not the place for me to try and explain that too ...

To study a relativistic phenomenon, we need Relativity math, but even then, math won't help us if our theory is wrong, so since I find my motion simulations interesting, for the moment, I prefer to think that our theory on motion is wrong. By the way, in my simulations, the particles do move while making very smal steps. They progress by steps whose length is .01 times the steps of the photons, which are only 1 pixel long on the screen. I could have used a lot smaller steps, but it would have slowed down the simulation too much. There is no way to move anything on a screen without using steps, and I can't see how nature could avoid that.

[rmolnav]

MY ULTIMATE GO ? (2nd part)

C) Let us now suppose that, when E reaches M´s vertical with its initial “horizontal" speed, apart from starting M´s gravitational pull, M somehow is given an initial speed parallel to E´s, not to the left as in case B but to the right … And not just as big as E´s (as in case B) but much, much bigger (see below how much).
If with the correct values for masses, M-E distance, and initial speeds, we would have our real case, E being the Earth and M the Moon …
We know the result is that E, instead of orbiting around M as in case A, and somehow opposite to what in case B (when E got “fully free” to fall directly onto M), now E is “forced” to bend its trajectory much more, because M´s location is changing in a sense opposite to E´s speed … E and M revolves/rotates around their common center of mass. E´s trajectory curvature is much, much bigger than when orbiting around M (case A).
For similar (but kind of opposite) reasons to case B, it is erroneous to consider E “orbits” around M, and to say that E is in a “free fall” … In cased A we had a “partially free" fall, and in B a “fully free” fall … But now I consider we have no free fall at all, because initial speeds and mutual pulls are causing a kind of dance of the couple, keeping their separation actually constant …
With this and last post I´ve already delivered what “promised”: a fresh explanation of one of the main roots of my stand …
But I´ll leave for another post the elaboration of main consequences of that, as far as I can understand ...   

[Le Repteux]

Let us now suppose that, when E reaches M´s vertical with its initial “horizontal" speed, apart from starting M´s gravitational pull, M somehow is given an initial speed parallel to E´s, not to the left as in case B but to the right …

Notice that when the pulling begins, the motion is straight. If it was already curved, no force would be needed to curve it. A force that curves a trajectory needs to be applied to a straight trajectory, so since we don't observe such a motion at our scale, atoms are probably going straight line for a while when we apply a force on them. They probably change their direction, and then go on straight line, and change their direction again, and go straight line, indefinitely. That's probably the main reason for their quantified energy. Their quantified light is probably linked to their quantified motion. They probably move by steps to accommodate individually each photon that strikes them, and it is probably while they are executing a step that they emit a photon. That would produce straight steps, and each of them would have a specific speed and a specific direction. In the case of a curved motion, the steps would have a constant length in the direction which is perpendicular to the force, and their length in the direction of the force would depend on its intensity. This way, there can be no outward force during an orbital motion, only inward. Nothing forces a body to go straight line, it moves all by itself.

[Colin2B]

Notice that when the pulling begins, the motion is straight. If it was already curved, no force would be needed to curve it. A force that curves a trajectory needs to be applied to a straight trajectory, so since we don't observe such a motion at our scale, atoms are probably going straight line for a while when we apply a force on them.

The gravitational force is continuous, it doesn’t switch on and off so the object does not have the option of travelling in a straight line even for a fraction of time. In order to keep an object’s orbit (curved path) the gravitational force has to be continuous otherwise it would fly off at a tangent, it will not keep a curved path without that force.

That's probably the main reason for their quantified energy. Their quantified light is probably linked to their quantified motion. They probably move by steps to accommodate individually each photon that strikes them, and it is probably while they are executing a step that they emit a photon.

‘Quantified light’ has nothing to do with quantified motion. The energy of a photon is quantised because the electron, when bound to an atom, can only release or absorb energy in quanta. It’s worth noting that a free electron is not so constrained and can take on any energy value.

Let’s try and keep this thread on real physics rather than made up ideas.

[rmolnav]

MY ULTIMATE GO ? (3rd part)

To diminish the risk of misinterpretations, before delivering the conclusions I referred to on 2nd part, I´ll repeat here the "breakdown" of earth complex movement into its simpler (and more easily graspable) components ...
Earth´s movement (as a whole) is basically the addition of three simple, but quite different, movements:
1) Earth-moon common center of mass orbits the sun (once a year). Both celestial objects, as a "couple", are kind of linked to that CM (called barycenter), and move with it.
 That movement, and sun´s pull, originates what I call sun-related tidal effects (sea tides included).
For the sake of simplicity, I usually disregard that movement, when analyzing main component of tides: moon-related tides.
2) The "couple", as I said yesterday on 2nd part, revolves/rotates around the barycenter (once every some 28 days).
That is the movement I always refer to (unless clearly said the contrary), discussing and analyzing it as if only that movement were happening ... Moon´s pull, and dynamical effects originated by that movement´s features, causes two opposite bulges that continuously change position, logically with same periodicity of some 28 days (relative to the rest of the universe).
Details of the singularity that earth revolves (instead of rotating like the moon) are explained on #328, with a "handy" analogy ...
3) Earth also has its daily spinning, which, apart from causing the permanent equatorial bulge (by the way, thanks to huge centrifugal forces inherent to such fast circular movement), makes us to perceive the period of the movement of the pair of bulges as if it were once a day, instead of once every some 28 days.
Some time ago I posted the link of a youtube video relative to that:
"I suggest anybody interested to have a look at :

where it´s clearly seen that daily movement of the bulges is only apparent, that they are almost still and it is the solid part of our planet (though also the bulk of ocean waters due to friction) what is actually spinning …
The formation of the bulges is a rather slow process (some 28 days the complete cycle) … Nothing to do with all those daily local whirlpools, due to the much faster Earth spin, and with any other local singularity"
 
   

[Le Repteux]

by the way, thanks to huge centrifugal forces inherent to such fast circular movement

There is no more centrifugal force in the case of the equatorial bulge than in the case of the tidal ones. Both forces are due to massive bodies refusing to change their speed or their direction. They resist whether we pull them tangentially or perpendicularly to the motion they already have. They resist as if they were at rest. There is no centrifugal force when a car accelerates, it only resists to accelerate. If it stops accelerating, it only moves in the direction it is already moving, not in the other. The same thing is happening in the case of bodies on circular motion: no centrifugal force is exerted by them.

[Le Repteux]

The gravitational force is continuous, it doesn’t switch on and off so the object does not have the option of traveling in a straight line even for a fraction of time.

Gravitation looks continuous at our scale like any force, but considering that the atoms exhibit a randomness behavior when they are observed separately, it may very well be discontinuous at theirs. In other words, the constant forces or motions that we observe at our scale may very well be issued from a statistical phenomenon at theirs, and if it is the case, they could be free to move in whatever direction they chose for a while providing they chose the right one more often. In my simulations on motion, I have no other option than to move my particles by steps, and I also move them in the direction of the force, but in reality, I could move them statistically and I would get the same result after a while. If we could nudge an individual atom for so short a time that it wouldn't have time to exhibit a statistical answer, I think it might very well not take the direction or the speed we expect it to take.

‘Quantified light’ has nothing to do with quantified motion. The energy of a photon is quantised because the electron, when bound to an atom, can only release or absorb energy in quanta. It’s worth noting that a free electron is not so constrained and can take on any energy value.

I wasn't talking about unbounded bodies either: to me, gravitation is a kind of bonding. To follow a curved trajectory, a body has to suffer acceleration, and it is precisely during acceleration that I suspect the particles to behave statistically.

Let’s try and keep this thread on real physics rather than made up ideas.

What I'm suggesting doesn't seem to contradict the observations, but tell me if you see any and I'll stop arguing. I'm not suggesting to change the physics, but to use it to make another step further. In fact, I use what I had to figure out to build my simulations to convince Rmolnav that the equatorial bulge and the tidal ones are equivalent. I'm not really expecting him to change his mind though, just to take a closer look at what the particles might be doing during motion.

[Colin2B]

What I'm suggesting doesn't seem to contradict the observations, but tell me if you see any and I'll stop arguing. I'm not suggesting to change the physics, but to use it to make another step further.

It's OK to take the physics a (specualtive) step further, but not in this section.
It is worth setting up a new theory to discuss.
While we see quantum effects for energy, there is no evidence that that energy varies as the particle moves ie no stop start or quantised motion.
If you want to discuss it, let's do it elsewhere, here it just causes confusion amongst the readers.

[Le Repteux]

It's OK to take the physics a (speculative) step further, but not in this section.

What about the tides then? Aren't we speculating about the composition of the force? The way Rmolnav explains them, a centrifugal force is needed, whereas no centrifugal force is present when no orbital rotation is involved and the tidal bulges are still present.

[rmolnav]

MY ULTIMATE GO ? (4th part)

As said on 2nd part, I consider that rather than talking about “free fall” within a given gravitational field, it is more realistic to consider earth-moon interactions as if they were parts of an unique extended object, with no massive parts apart from where both celestial objects actually are, and rotating/revolving about their common center of mass, maintaining the distance between them due to their dynamic equilibrium.
An ice skating couple can spin like a single dancer, because they are linked usually through their hands … If one of them had a pony-tail, when spinning, instead of hanging vertically, the pony-tail would move upwards, against its own weight … Clearly due to centrifugal force.
The same would happen whatever the way they were linked to each other. If it were a kind of mutual “gravitational” pull sufficient not to need their hands (as earth-moon case), and they had suitable initial "tangential" speeds, the pony-tail would also “feel” that inertial force (why wouldn´t it?) … It would react to the TOTAL force acting DIRECTLY ON IT (WHATEVER the pull on other parts of the dancer, what the pony-tail “ignores" …), and raise where centrifugal force prevailed.
Earth particles react to those inertial forces in a similar way to what quite clearly explained for the diminishing of our weight on the equator, and causes the equatorial bulge (though the author prefers not to mention the adjective “centrifugal” … ):
“"The figure shows the force vectors W and mg, which are the only forces acting on the man. The vector F is their sum. W is directed along the radius of the Earth. Being the radial component of the net force (it is the net force in this case), its size is a = v2/R (the centripetal force). Now compare these two cases. On the non-rotating Earth the man's weight was of size mg. Remember, the weight of an object is the force required to support it, i.e., the force exerted upward by the weighing scale. With the Earth rotating, that force (man´s weight) is smaller than before. The contact force between the man's feet and the scale is reduced. But all other such stress forces are reduced as well, within the man, within the scale's springs, within the body of the Earth itself. This causes a slight decompression of these materials, a relaxation of the spring in the scales. In fact, the entire body of the earth expands slightly and the man and scale move outward from the axis of rotation slightly, until forces come into balance with the requirements of rotational stability at the new radius. This is the reason for the equatorial bulge of the Earth due to its own axial rotation"
https://www.lockhaven.edu/~dsimanek/scenario/centrip.htm
That´s why the NASA scientists I´ve referred to many times say:
"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)”
I DO KNOW many people (physicists included) will say: "But you are using a non-inertial frame of reference, where centrifugal forces are “added” by us, in order to keep Newton´s Motion Laws valid. But those forces are “fictitious”, they don´t actually exist" … (or something similar).
This post is already rather long. I´ll leave my refuting of what usually is deduced from that question of frames of reference for another post.

[rmolnav]

There is no centrifugal force when a car accelerates, it only resists to accelerate. If it stops accelerating, it only moves in the direction it is already moving, not in the other. The same thing is happening in the case of bodies on circular motion: no centrifugal force is exerted by them.

Without sufficient imagination to think there can be manifestations of inertia different than what we are kind of used to, it´s impossible to properly grasp the concept of centrifugal force, and therefore tides ...
If a car accelerates in a straight line, LOGICALLY there cannot be any "centri***al" force, because there is no "center" at all !! Inertia manifests itself "trying" not to let the velocity of the passengers increase, and they somehow "feel" pushed backwards (relatively to the car). But if they had inflatable cushions between their backs and seat´s backs, and the acceleration were sufficiently big compared to the strength of the cushions, these could explode. And for them to blow up two opposite forces are required ... They backward one exerted by the passengers on the seat backs is clearly an inertial force (though not "centrifugal" whatsoever !!).
But if, e.g., one of the passenger shoulder were leaning on a side window glass not sufficiently strong, and the car were turning to the other side when going very fast, the window could get broken ...
Inertia certainly just tries to keep constant the passenger´s speed vector (similarly to the above mentioned straight-line case), but now the window is "forcing" the passenger to turn (centripetal force), and as an "inertial" reaction (3rd Newton´s Motion Law) the passenger pushes outwards on the window and brakes it (centrifugal force).   
I´ve said it many times: inertia manifests itself in different ways, depending on the type of individual forces exerted on the considered object, and especially on the type and degree of "freedom" to move the object actually has !!

[Le Repteux]

now the window is "forcing" the passenger to turn (centripetal force), and as an "inertial" reaction (3rd Newton´s Motion Law) the passenger pushes outwards on the window and brakes it (centrifugal force).

It is not a centrifugal force, but a relative or apparent centrifugal motion that results from the car changing direction and the passenger being forced to follow it. If the passenger was free to move, he would follow a straight line while the car would be moving away from him: in this case, motion is still relative but the driver knows it is the car that moves away because he suffers a force, and the passenger knows it too because he doesn't suffer a force while the car is still moving away.

[Colin2B]

It is not a centrifugal force, but a relative or apparent centrifugal motion that results from the car changing direction and the passenger being forced to follow it. If the passenger was free to move, he would follow a straight line while the car would be moving away from him: in this case, motion is still relative but the driver knows it is the car that moves away because he suffers a force, and the passenger knows it too because he doesn't suffer a force while the car is still moving away.

You have to be careful not to mix frames, which is something many people get confused over.
From the inertial frame the car is being forced in a circle by friction with the road and the driver/passengers are trying to travel in a straight line, but again centripetal forces pull them into a curve.
From the rotating frame the driver and passengers feel centrifugal force throwing them radially outwards and they are restrained by a reactive centripetal  force - either friction from the seats or force from the side of the car.
Both views are valid, just don’t mix frames or everyone gets confused.

The radial motion experienced by the observer in the rotating frame can easily be seen by plotting the locus of the tangential motion relative to the observer on the rotating curve. If you’re not sure what I mean I could try and draw it for you.

[Le Repteux]

Both views are valid, just don’t mix frames or everyone gets confused.

I didn't mix frames, I simply didn't use the wording. A reference frame is a viewpoint experimented by an observer, so comparing the viewpoints of the two observers like I did is like comparing the two reference frames. If there is no mistake, there is no need to use the reference frame wording for people to understand what is going on. Knowing that one of the two observers is accelerating is enough for them to know that it is the one that is moving away. When acceleration is involved, adding the reference frame principle to the explanations confuses them. There are tons of pages written about the twins paradox on the forums that try to use the reference frame wording without being able to stop the questioning, whereas the questioning immediately stops if we simply say that the accelerating twin is the one that moves away. There is no reason to change reference frames either if we know an observer is accelerating, and if no observer is accelerating, then there is simply no need to use the reference frame principle since there is no use to the observations made by either of the observers anyway, except if they need to meet, and then they can use doppler effect and aberration to know their relative speed and direction. Changing reference frames only helps us to illustrate up to what point inertial motion can be relative, not to know which one of the observers is getting younger or older.

[rmolnav]

From the rotating frame the driver and passengers feel centrifugal force throwing them radially outwards and they are restrained by a reactive centripetal  force - either friction from the seats or force from the side of the car.

Though I´m much "closer" to what you say than to what said by L.R., please kindly note that, if the window glass breaks, an outward quite real force (centrifugal force, in the broad sense of the term) has to exist, whatever the reference system !!
To me the whole issue of reference systems is generally misunderstood and wrongly used.
Locations, speeds, and accelerations can be easily handled using different reference systems: it is just a question of deducting vectors.
But real forces (apart from exclusively "inertial" forces), as far as I can understand, either exist or not, no matter which reference system we use, or from where we observe reality !!

[Le Repteux]

if the window glass breaks, an outward quite real force (centrifugal force, in the broad sense of the term) has to exist, whatever the reference system !!

If the window breaks, it is still the car that will be moving away from the passenger, not the inverse. The passenger will simply be moving in the same direction the car was moving when the window broke.

[rmolnav]

if the window glass breaks, an outward quite real force (centrifugal force, in the broad sense of the term) has to exist, whatever the reference system !!

If the window breaks, it is still the car that will be moving away from the passenger, not the inverse. The passenger will simply be moving in the same direction the car was moving when the window broke.

You insist in speaking in a kind of layman language, without taking into consideration what I already told you: in physics science, "motion" is not a variable ... What "motion" units would you use when calculating real variables of physics science such as momentum, energy, etc ?
And "motion" can´t be what directly causes the breaking of the window glass ... Inertial forces originated by movements, only if not completely "free", can break (or just deform) things !!
The passenger was TRYING to move "in the same direction the car was moving". But the solidity of the window "forced" him to turn with the car for some short time (centripetal force). 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 (the window frame was also pushing the glass inwards ...).
And that outwards force has a name: centrifugal force, as I said, in the broad sense of the term.
If you only have layman ideas about physical phenomena, you had better learning something of the science called "physics", especially "dynamics" ... I´m sure there are many sites on the internet where that won´t be difficult.
But let me suggest you something: keep an open mind if you do that ...