## Newton's Errors (papers by Gopi)

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### Re: Newton's Errors (papers by Gopi)

agroposo wrote:I didn't presume that the word series as used by Gopi meant a sum of elements, because nowhere in his paper he is summing the higher order forces, but after re-reading Gopi's paper, I've come to the conclusion that he is using the term series to indicate a set, as when he says in the paper's abstract "an infinite series of higher order rotational forces", meaning that the force F and its derivatives F', F'', F''', F(4), F(5), ..., constitute a set. If we consider all the derivatives, then we have an infinite set.

I am glad that agroposo caught the meaning as intended. I couldn't have put it that well myself.

agroposo wrote:If you're postulating that there are "infinite higher order forces", necessary to account for circular and elliptical motion, what would happen if at some point in the sequence, let's say n, the derivative F(n) is zero? Then all the subsequent derivatives would be zero, and your postulate will be contradicted.

1. I am not postulating it, I am deriving it. That is a big difference, as the method is the same as how velocity and acceleration are traditionally derived for circular motion, with the difference being that I see no logical reason to stop the derivative process at acceleration. If you can take the first and second derivatives, then you can take all of them, since they are all non-zero.

2. If F(n)=0, as suggested above, then that means that some Rw^n = 0. This implies that either R = 0 or w = 0, i.e. either the radius or the angular velocity has to go to zero. In that case you no longer have circular motion, so there is nothing to contradict. Not only the subsequent derivatives, but the preceding derivatives will vanish as well -- a peculiarity of circular motion that is unlike linear motion. It pulls the ground out from the entirety of the circular motion we are starting with.

Where Newton stopped was at the second derivative, acceleration, so that it could then be fit with Galileo's theory. Using geometry to stop the derivatives process is not simplification, it is plain wrong. You cannot chop an infinite series by fiat because it is convenient. If Newton has to be given his due, it will have to be in his derivation of the calculus, and the several mathematical techniques he applied in other places in the Principia.

hoi.polloi wrote: My guess is that Gopi accidentally mixed prosaic language with math language, therefore failing to communicate his idea in established understandings/agreements.

I admit I may have done a good bit of that. It is only with the three papers attached that I have done my best to keep the terminology strictly mathematical and peer-reviewable, so please do not take the wording I am using on the forum to be the literal mathematical phrase as used in the literature. I am only trying to get the meaning across here by trying to phrase it in different ways.
Gopi
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### Re: Newton's Errors (papers by Gopi)

If you don't mind, Gopi, some clarification on how you are using derivatives.

The number of centripetal forces (F, F (4), F (8), F (12)… etc.) are equal to the number of centrifugal
forces (F’’, F (6), F (10), F (14)… etc.)

When taking successive derivatives of theta in angular velocity we hit zero quickly. For example, using a theta say, like 3t^3 + 5t +3, after taking the 4th derivative we are at zero. So how can one compare infinite sets of derivative when in actuality there are only a few derivatives before we hit zero?
Kham
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### Re: Newton's Errors (papers by Gopi)

Or why not compare the limits of the centripetal and centrifugal force derivatives instead?

Sorry, I'm still thinking through your work, nice job by the way.
Kham
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### Re: Newton's Errors (papers by Gopi)

Kham wrote:When taking successive derivatives of theta in angular velocity we hit zero quickly. For example, using a theta say, like 3t^3 + 5t +3, after taking the 4th derivative we are at zero. So how can one compare infinite sets of derivative when in actuality there are only a few derivatives before we hit zero?

Very important question... it is as you say, of course, IF the series can be written as a set of finite terms that you give above.

However, in simple circular motion, there are sine and cosine series involved, both of which contain infinite number of terms. That is simply a property of the circular functions.

For example: sin (wt) = wt -(wt)^3/(3!) + (wt)^5/(5!) ... so on and on.

If you wish to see more on these functions, see the first part of: https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-07-dynamics-fall-2009/lecture-notes/MIT16_07F09_Lec05.pdf

Now you have asked why I don't sum the centrifugal and centripetal series. It is because the summation is of different derivatives, and they cannot be added together directly. For example, I cannot say that a term T= position + velocity + acceleration, because they are quantities having different dimensions, namely x, x/t and x/t^2 respectively.
Gopi
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### Re: Newton's Errors (papers by Gopi)

We probably dare not add the notion that these infinite circles are, in fact, very very slowly expanding spirals. No?
hoi.polloi

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### Re: Newton's Errors (papers by Gopi)

If you think about the athletic sport of hammer throwing. The athlete gets the steel ball('the hammer') moving with energy outwards by spinning himself, which causes a centrifugal force on the hammer. Why the athlete spinning with the hammer at a wider radius than most of his weight causes a centrifugal acceleration I do not know.

The inverse is true also, once the hammer gets out to its 'orbit', the athlete must apply an acceleration in the opposing direction so that the hammer doesn't fly off. So by gripping the handle of the hammer and applying a pulling force towards himself, the athlete creates a centripetal force on the hammer. Thus causing the hammer to remain at the same radius while spinning around.

What my engineering friends tell me is that if the athlete stopped spinning himself, thus stopped creating a centrifugal force on the hammer, but continued to grip and apply a centripetal force.. they say the hammer would continue to orbit around the athlete in perpetuity, as the centripetal force of him pulling the hammer towards him, would be balanced by the hammer 'falling' away from him. Which their theory is backed up by many textbooks and 4 centuries of work by physicists & astronomers, and the work of several generations of space engineering experts.
aa5
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### Re: Newton's Errors (papers by Gopi)

aa5 wrote:What my engineering friends tell me is that if the athlete stopped spinning himself, thus stopped creating a centrifugal force on the hammer, but continued to grip and apply a centripetal force.. they say the hammer would continue to orbit around the athlete in perpetuity, as the centripetal force of him pulling the hammer towards him, would be balanced by the hammer 'falling' away from him.

I think anyone can picture what will happen if the athlete stops spinning. Hammer throwing doesn´t seem to be a very felicitous analogy to what you are trying to explain.
aa5 wrote:...several generations of space engineering experts.

I suppose that would include von Braun. By the way, what exactly is space engineering?
Flabbergasted
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### Re: Newton's Errors (papers by Gopi)

hoi.polloi wrote:We probably dare not add the notion that these infinite circles are, in fact, very very slowly expanding spirals. No?

Yes, that would make it even more complicated. When even the simple circle has to be expressed with a whole retinue of terms, you can only imagine what would happen with further complications. The moon's motion is a prime example of the types of complications possible.

aa5 wrote:What my engineering friends tell me is that if the athlete stopped spinning himself, thus stopped creating a centrifugal force on the hammer, but continued to grip and apply a centripetal force.

Exactly, and all the engineering friends stop the analysis short at "force". For four centuries we have not updated the force model, and it needs to be updated because there is not just a force involved, but a whole series higher order forces that are the higher derivatives of force. Rotational motion is impossible to reproduce with a simple "gravitational force".
Gopi
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### Re: Newton's Errors (papers by Gopi)

Gopi » 01 Jun 2017, 19:38 wrote:For four centuries we have not updated the force model, and it needs to be updated because there is not just a force involved, but a whole series higher order forces that are the higher derivatives of force. Rotational motion is impossible to reproduce with a simple "gravitational force".

It would be nice to know if you have come up with a solution of the new model needed, in terms of equations.
agraposo
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### Re: Newton's Errors (papers by Gopi)

Flabbergasted » June 1st, 2017, 4:13 am wrote:
aa5 wrote:What my engineering friends tell me is that if the athlete stopped spinning himself, thus stopped creating a centrifugal force on the hammer, but continued to grip and apply a centripetal force.. they say the hammer would continue to orbit around the athlete in perpetuity, as the centripetal force of him pulling the hammer towards him, would be balanced by the hammer 'falling' away from him.

I think anyone can picture what will happen if the athlete stops spinning. Hammer throwing doesn´t seem to be a very felicitous analogy to what you are trying to explain.
aa5 wrote:...several generations of space engineering experts.

I suppose that would include von Braun. By the way, what exactly is space engineering?

What happens when I push this on my engineering friends who have all taken modern physics classes is they get really irrational and emotionally block out further debate on the subject. Two guys even went to the trouble of getting out their college physics text books that show me how the centripetal force of gravity on the space station is balanced by the space station 'falling' away from the Earth. With the mathematics that allegedly 'prove' it. I agree with them that this is exactly what the textbooks say, but I do not agree with the textbook, which to many in engineering is heresy.

I don't know what space engineering is either, and I just invented it, but even in my backwater city we have university programs in physics and astronomy that teach these theories. And I should add government research jobs, where people go even deeper into these types of theories, coming up with even more brilliant ideas, that build on this kind of prior work.
aa5
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### Re: Newton's Errors (papers by Gopi)

Gopi » June 1st, 2017, 9:38 am wrote:
aa5 wrote:What my engineering friends tell me is that if the athlete stopped spinning himself, thus stopped creating a centrifugal force on the hammer, but continued to grip and apply a centripetal force.

Exactly, and all the engineering friends stop the analysis short at "force". For four centuries we have not updated the force model, and it needs to be updated because there is not just a force involved, but a whole series higher order forces that are the higher derivatives of force. Rotational motion is impossible to reproduce with a simple "gravitational force".

For the higher order forces, are you talking about changes in the rate of acceleration?
aa5
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### Re: Newton's Errors (papers by Gopi)

aa5 wrote:For the higher order forces, are you talking about changes in the rate of acceleration?

Yes, rate of change of acceleration, rate of change of rate of change of acceleration, and so on.

aa5 wrote:With the mathematics that allegedly 'prove' it.

Yep, that will be the most common mind-block, especially when you show that mathematics does NOT prove it.

I am curious, aa5, did you actually show these papers to some University folks?

agroposo wrote:It would be nice to know if you have come up with a solution of the new model needed, in terms of equations.

Yes, the work is in progress, but I think the new approach cannot use equations because of the inherent mathematical limitation. For instance, it is not possible to write down the value of "pi" exactly, no matter how many years or mega-computers you use, since pi is a continued non-repeating decimal. One therefore cannot write an equation like this: pi = 3.14, unless it is meant as an approximation.

Since the entirety of the force equations are built on circular functions, if we don't take the artificially simplified solution of Newton, we are thrown into a similar conundrum. We would need an infinite number of equations in the same way that "pi" requires infinite number of digits to represent.

I will share more when I have something clearer, since that is an entirely new topic in itself. For the time being, I wanted to focus on cleaning out the detritus.
Gopi
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### Re: Newton's Errors (papers by Gopi)

Say when the Moon is getting pushed away from the Earth with a force 'x', then later we see the Moon being pulled towards the Earth with a force 'y'.

Therefore at some time period that is between when we took the snapshots of x and y, there had to be a change in the rate of acceleration. (this force defined as the Moon's travelling between its Perigee at ~365,000 Km and its Apogee at ~405,000 Km.)

Another step is that the Moon's velocity in its circular motion around the Earth, may not be constant. Like it may be losing speed and gaining speed, depending on where it is relative to the Earth in its orbit. In one complete orbit of the Earth these changes in speed would cancel each other out.

I haven't shown my friends your papers yet. I have a feeling they would just dismiss them anyway because it doesn't match what they had to memorize in school.
aa5
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