Talk:Centrifugal force/Archive 4

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Centrifugal Force does not exist

I learned that in the first month of high school physics. The length and scientific precision of this article suggests the veracity of this falsehood. This article should explain where the misconception comes from, why it is incorrect, and then point readers to the centripetal force page.

The scope of this article extends beyond the first month of high school physics. What high school physics teachers should say is "The centrifugal force does not exist in an inertial frame of reference". But then they would have to explain what a non-inertial frame of reference is, and that is usually saved for the university courses. --PeR 09:02, 11 January 2007 (UTC)

Centrifugal repulsion exists radially between any two objects that possess mutual tangential motion. That is an indisputable fact. It manifests itself if we try to restrain it. Maxwell used centrifugal force in the hydrodynamics of part I of his 1861 paper 'On Physical Lines of Force' in order to account for electromagnetic and ferromagnetic repulsion. He also used it to account for diamagnetic attraction and repulsion in what was effectively the Archimedes' Principle of magnetism.

I was also taught at university that centrifugal force does not exist. This false teaching is based on the simplistic argument that when we release an object that is being constrained to move in a circle, it will fly off at a tangent and not radially. In actual fact, it flies off both tangentially and radially. There can be no doubt that centrifugal force is a very real force but that it has been dropped out of modern physics. The Coriolis Force is also a real force that manifests itself in electromagnetism as F = qvXB. David Tombe 4th February 2007 ( 20:40, 3 February 2007 (UTC))

Actually, the object will fly off at a tangent. The velocity vector of the object MUST be tangential to the circle (if it's not, the object isn't traveling in a circle anymore). When you cut the centripital force there are no more forces left acting on the object. Thus it maintains its current velocity, which at the time of release was tangental to the orbit.
Let's assume for a moment the existance of a centrifugal force, acting on an object rotating with constant speed. For simplicities sake, the object is rotating in outer space, so all other forces (frictional, gravitational, etc.) are negligibly small. The centrifugal force must point in the direct opposite direction of the centripital force. If it didn't, there would be a component that was parallel to the velocity, and it would cause the object to change speed. That obviously can't happen, since our stipulation was that the object is orbiting with constant speed.
Now, examine the system at the moment of "release". The centripital force is perpendicular to the direction of movement (because it always is). The centrifugal force would also be perpendicular to the direction of motion, but pointing the opposite way. If the centrifugal force was real, it would not cause the object to travel in a radial path. It would in fact make the object travel in a radial path.
The most commmon use of a "centrifugal force" is for doing math while IN a rotating (IE, non-inertial) reference frame. However, even then it's rare that a physicist will use a "centrifugal" force, because generally doing so will produce incorrect results. —The preceding unsigned comment was added by (talk) 12:20, 12 February 2007 (UTC).

If you don't mind, can I just quote you here. You say,

If the centrifugal force was real, it would not cause the object to travel in a radial path. It would in fact make the object travel in a radial path.

I agree that if the centrifugal force is real, it would cause the object to travel in a radial path. So I don't know what your quote means. Can you please clarify? It also seems that you can't see centrifugal force outside of the limited context of circular motion. David Tombe 12th February 2007 ( 13:32, 12 February 2007 (UTC))

Maxwell on Real Centrifugal Force

The reason that I deleted your insertion

"It should be noted however that when proposing this 'hydrodynamic' description (that was built upon in work published in the seminal papers 'On Faraday's Lines of Force' and 'On Physical Lines of Force') Maxwell was not intending the fluid to be thought of as real:[1] -


- It is not even a hypothetical fluid which is introduced to explain actual - phenomena. It is merely a collection of imaginary properties which may be - employed for establishing certain theorems in pure mathematics in a way - more intelligible to many minds and more applicable to physical problems - than that in which algebraic symbols alone are used.



was because the web link for Maxwell's 1861 paper 'On Physical Lines of Force' was made available for anybody to read. Anybody reading part I of this paper would know that Maxwell believed absolutely in the reality of the fluid aethereal medium. To say otherwise is a total misrepresentation of the truth. You then finished with a quote but didn't tell us who made the quote.

Maxwell was quite clear on the fact that a sea of aethereal vortices exists and that these vortices must be surrounded by electrical particles. If these vortices aren't real, and yet they explain the mechanics of magnetism, then what are they? Why would they be any less real than the elements of the periodic table? David Tombe 7th February 2007 ( 18:34, 7 February 2007 (UTC))

I went further than that and removed the entire section. To the best of my comprehension it tried to argue that the fact that Maxwell had an ether-dynamic interpretation of electrodynamics somehow implies that one must consider centrifugal force a fundamental force (except that it muddled the concept further by speaking about "real" forces, a word with a host of varying possible meanings) – a conclusion that mainstream physics unanimously rejects. In order for an argument otherwise to be relevant Wikipedia material, the very least we can accept is a solid citation showing that such an argument has been made in a respected peer-reviewed professional journal. (I might add that the major schism among editors of this article appears to be whether the "reactive" or the "fictitious" meaning of "centrifugal" is the most important, but neither of the camps would accept either of the concepts as describing a fundamental force). Henning Makholm 22:40, 7 February 2007 (UTC)
Oops, I misread the conclusion of the deleted section; one of the negations must have slipped me. My apologies for misrepresenting it. I still think that the section was confusing, of doubtful relevance and definitely out of place as early in the article as I found it, so I'll not self-revert – but if it were to be rewritten with a clearer emphasis about what the story can tell us about the centrifugal force concept and less emphasis on what Maxwell personally believed (or didn't) about the physical nature of the electromagnetic field, I might not be opposed to having it appear later in the article, after the basic concepts have been well presented. (This is not meant to contradict the WP:NOR policy, so proper sourcing would still be necessary). Henning Makholm 22:58, 7 February 2007 (UTC)

Maxwell's 1861 paper is highly relevant regarding the topic of centrifugal force. The original archive paper has been provided in the form of a pdf web link. The paper consists of four parts. Part I is the relevant hydrodynamical part.

Maxwell operates on the basis that space is pervaded by a sea of tiny aethereal whirlpools. Maxwell does the mathematics for such a sea of whirlpools, and at equation (5) he arrives at an expression for some of the important aspects of magnetism. Central to this hydrodynamical analysis is the fact that centrifugal repulsion force acts between spinning objects.

Anybody who has ever studied polar coordinates, knows that any two objects with a mutual tangential velocity will have a mutual radial repulsion which takes on the mathematical form of the centrifugal force. Maxwell uses this concept to show that ferromagnetic repulsion, electromagnetic repulsion, as well as diamagnetic repulsion and paramagnetic attraction can all be explained by focused centrifugal force in the equatorial plane of his sea of whirlpools.

Unless you are a logical positivist, this ought to be conclusive evidence that centrifugal force is real and that the sea of aethereal vortices is also real.

The 1861 paper is there to be read by anybody who can then make up their own mind.

The reason that I deleted the extra insertion was because whoever made the insertion made it look as if it was part of the original article, and it had the effect of undoing the point. Whoever made that insertion was trying to have us all believe that Maxwell did not actually believe that the sea of whirlpools was real. The insertion was completely untrue and the matter can be easily checked out simply by reading the preamble of part I of Maxwell's 1861 paper. Had the person making the insertion simply stated that they themselves didn't consider Maxwell's sea of vortices to be real then that would have been a different matter. But they tried to put across the idea that Maxwell didn't believe it.

Maxwell did believe it and he went to considerable pains to give a mechanical explanation of magnetism using the concept.

But the key point as regards the principle topic 'Centrifugal Force' is that centrifugal force can explain magnetic repulsion. That is an indisputable fact. David Tombe 8th February 2007 ( 05:43, 8 February 2007 (UTC))

Two points. I did reference my quote as being from 'On Faraday's lines of Force' by Maxwell himself, Maxwell also refers the reader to this paper in 'On Physical Lines of Force'. Secondly Maxwell dropped this mechanical explanation in favour of a field description in 'A Dynamical Theory of the Electromagnetic Field' (A move towards Field descriptions is his real legacy), so I wonder how much he did believe it? What he did or did not believe is not for us to say, I was just illustrating that the point wasn't as clear cut as made out.

It doesn't surprise me that the quote was actually from the 1855 paper "On Faraday's Lines of Force". In the 1861 paper "On Physical lines of Force", Maxwell does indeed refer to this 1855 paper and the fact that the mechanical illustrations in it were designed to assist the imagination and not to accont for phenomena. He immediately goes on to say that he now proposes to examine magnetism from a mechanical point of view.

So what you have done is to take a quote from an 1855 paper about an imaginary phenomenon, and apply that quote as if it were referring to a real phenomenon in another 1861 paper. You basically tried to undermine the reality of centrifugal force in Maxwell's 1861 paper by using an 1855 quote totally out of context.

On your other point, it's true that Maxwell didn't continue with the vortex sea in his later papers. That doesn't mean that he had dropped the idea. He actually gives his reasons towards the end of the 1861 paper, and those reasons were to do with the fact that he couldn't get a focused picture of how the idle wheels would actually relate to the vortices. He made it clear that his proposition was not the focused picture, but that it was almost certainly heading in the dircetion of the focused picture.

In his 1864 paper, he began to concentrate exclusively on a dynamical approach and he avoided any mention of the vortex sea. He did nevertheless state his unequivocal belief that a dielectric medium existed for the purposes of electric and magnetic phenomena, and he held this belief until his death.

We shouldn't discount the hydrodynamics used by Maxwell in his 1861 paper, and which involved centrifugal force and also lead to the Coriolis force, simply on the grounds of a quote about another matter in an 1855 paper, or because Maxwell didn't progress with his vortex cell model. 2/13/07 ( 10:57, 13 February 2007 (UTC))

Regarding: "If these vortices aren't real, and yet they explain the mechanics of magnetism, then what are they? Why would they be any less real than the elements of the periodic table?", that is an interesting point. The atomic model of a nucleus and electron shells, which the gives the arrangement of the periodic table it's logic, is just a model which fits the observables. One shouldn't really think of a particle orbiting a center - except that it's a handy tool for describing the situation (just as Maxwell's vortices). The reality of actually what these things are is not necessarily the same as the model used to describe them.

I still think all this Maxwell stuff is an interesting afterthought on the topic of Centrifugal Force, it really should be relegated to the bottom of the article - most people will be looking for other information on this page.

Richard Allen 13:29, 9 February 2007 (UTC)

I would have no objections to it being relegated to further down the article. But there is a group of people who are dedicated to this article and who have been insisting on deleting it completely. It's like as if there exists a fictititious brigade that wants to view everything as being fictitious. They would rather talk about artificial circular motion in a rotating frame of reference and the accompanying fictitious centripetal, fictitious centrifugal and fictitious Coriolis forces, rather than talk about situations in which centrifugal force is very real.

You mentioned that even the orbital model of atoms does not necessarily represent reality. Maybe it is not an exact picture. Maxwell acknowledged that his vortex cells were almost certainly not an exact picture. But anybody who reads his 1861 paper would know that there must exist something that is roughly in that likeness. It is too extreme an option to merely abandon it and replace it with pure vacuum. We have clear evidence for swirling dynamical space and not only for real centifugal force, but also for real Coriolis force.

Some of you even believed that my name was fictitious. It's time that alot of you snapped out of this unhealthy cult of fictitiousism. So this time, I'll sign out as a fictitious anon. 2/13/07 ( 11:19, 13 February 2007 (UTC))

Fictitious Centrifugal Force

Every fictitious centrifugal force as viewed from a rotating frame of reference will correspond to a real centrifugal force. Mutual radial repulsion due to tangential velocity is an absolute fact, dependent only on the existence of a real frame of reference to give meaning to the tangential velocity.

This is in contrast to fictitious Coriolis force. Fictitious Coriolis force is truly fictitious and it occurs only in a rotating frame of reference.

The difference between fictitious centrifugal force and fictitious Coriolis force arises from the fact that centrifugal force is a radial deflection due to a tangential motion, whereas Coriolis force is a tangential deflection due to a radial motion. As such, a rotating frame of reference masks the cause of a real centrifugal force but leads to an apparent Coriolis force.

In order to obtain a real Coriolis force we would need to have curled space. According to Maxwell's sea of molecular vortices, we ought to have curled space leading to a real Coriolis force. This is almost certainly the origins of the electromagnetic F = qvXB force, where B is related to the vorticity. David Tombe, 9th February 2007 ( 10:36, 9 February 2007 (UTC))

David - You are totally mistaken about the nature of centrifugal force. There is no radial repulsion at work, only inertia. The "force" the is felt by a object undergoing a forced rotation is actually a centripetal (or inwards directed) acceleration. So while it feels like you are being pushed outwards, in fact you are being accelerated inwards. Only inertia is needed to explain your wanting to go "outwards" in the accelerated frame of reference of the rotating object.
I hope that you find this explanation helpful. However, I must in any case kindly ask you to stop introducing misconceptions into Wikipedia. You may mean well, but in fact you are disrupting this encyclopedia. Please research your topic and be sure that you know what you are taking about before editing in Wikipedia in the future. --EMS | Talk 16:09, 9 February 2007 (UTC)

Centripetal force is not relevant in this discussion. Centripetal force is only a 'requirement' force needed to accelerate an object in a circle. Centrifugal force is not specifically related to circular motion. Centrifugal force exists radially between any two objects in the universe that have got a mutual tangential velocity. I don't understand why you have such difficulty seeing this simple fact.

In conjunction with the radially attractive force of gravity, centrifugal force leads to either elliptical motion, circular motion, parabolic motion, or hyperbolic motion depending on initial parameters.

You misrepresented me above. I made it quite clear that we only feel centrifugal force when it is restrained, just as in the case of gravity. Ie. we feel the reaction surface that is pushing against it. I wasn't getting confused with centripetal force at all.

You are completely wrong when you say that inertia is what causes the tendency to move outwards. The tendency to move outwards is a fundamental fact of the geometry of space which occurs when two objects possess mutual tangential velocity.

If you think that the tendency to move outwards is caused by inertia, can you please tell me exactly what inertia is and how it causes this tendency to move outwards. I might then ask how inertia causes an object to vear to one side in the case of the sister Coriolis force.

It strikes me that alot of the contributors to this article need to do an applied maths course in orbital mechanics.

And yes, I was meaning well. I was trying to simplify the article for you because it appears to have been written by people who's qualifications are limited to having swung a bucket of water over their heads.

Centrifugal force is always real. A rotating frame of reference cannot create a centrifugal force fictitiously that then proceeds to bump somebody against the inside of their car door. David Tombe 9th February 2007 ( 17:28, 9 February 2007 (UTC))

  • The centrifugal force is ficticious - all kinds of reliable sources will confirm this, and none will not. Not only that, but WP:V allows us to include uncontraversial stuff that anyone can verify - grapes are a fruit doesn't require sourcing, neither does the Centrifugal force is ficticious. Beyond which, other factual errors (like requiring two objects to have a centrifugal force, when a single object will experience it (try rotating a bucket of water) cast unsourced assertions into serious doubt. WilyD 18:11, 9 February 2007 (UTC)
The point is that this is an article in the wikipedia, and hence is subject to the wikipedia's policies. There's no notable point of view that you have been able to quote David to support these additions, and thus it cannot stay in this article, whether it is right or wrong.WolfKeeper 18:19, 9 February 2007 (UTC)
I agree with WilyD and Wolfkeeper. You have to make a case for your viewpoint, and show that it is held by others and not just yourself. Wikipedia is dedicated to documeenting human knowledge. It therefore makes no different if you are right of wrong (although I have no qualms about saying that you are totally wrong). Instead what matters are 1) your disagreement with commonly held scientific opinion, and 2) a total lack of any evidence that it is held by a notable group of people. --EMS | Talk 19:45, 9 February 2007 (UTC)
Since you ask, it's because of what the phrase ficticious force is used to mean in physics. If you care to assail my credentials, I'll remind you that authority and training don't count, only reliable sources do. That said, I have an honours Bachelor of Physics from here and I'm currently a Ph.D. student in astronomy/astrophysics here. So please attack my arguments rather than my credentials. WilyD 03:23, 11 February 2007 (UTC)

What evidence do you need to show that two objects with mutual tangential motion possess a mutual radial repulsion? It is a self evident geometrical fact. It is basic undergraduate level applied mathematics. Take a position vector and differentiate it twice with respect to time. You will arrive at a general acceleration vector that is split into two components. The radial component contains a direct component and a centrifugal component. The centrifugal component is equal to the velocity squared divided by the distance. Then there is the tangential component that is divided into the Coriolis acceleration and the angular acceleration.

This is not controversial theory. I'm sorry to see that WilyD felt it necessary to mention the bucket of water. This tends to confirm exactly what I said above. Have any of you guys taken an applied maths course in vector algebra or orbital mechanics, or are your qualifications limited to having swung a bucket of water over your heads?

Why is it that a very simple topic such as centrifugal force always has to be studied in conjunction with rotating frames of reference? Why do we have to go into that hall of mirrors? It opens up endless permutations. We could talk about the fictitious effects on a real motion as viewed from a rotating frame of reference, or we could talk about the fictitious effects on a fictitious motion due to viewing the object from a rotating frame of reference. We could talk about a fictitious circular motion being caused by a fictitious centripetal force which is itself caused by a fictitious outward centrifugal force in tandem with a fictitious inward Coriolis force that is twice as strong. But why bother?

We can sit and debate whether the man is flung against the inside of the car door, or whether the car door comes against the man.

The reason that I simplified the article was because it was an incoherent confusion of real centrifugal force and fictitious centrifugal force.

I really don't know what makes WilyD so sure that centrifugal force is never real. I would suggest to WilyD that before he goes around censoring left right and centre, that he should think long and hard about that bucket of water that he mentioned. The water above his head defies downward gravity. I don't see anything fictitious about that. The question only remains to quantify this effect. It is clearly an exclusive product of the fact that the water has got tangential motion relative to the fulcrum. There is no need to introduce inertia. It is a purely kinematical fact.

Have any of you censors ever actually studied planetary orbital theory? The haste with which you deleted my references to hyperbolic, parabolic, and elliptical motion suggests to me that you all possess a fear of the unknown. David Tombe 10th February 2007 ( 03:03, 10 February 2007 (UTC))

David Tombe wrote above:
Take a position vector and differentiate it twice with respect to time. You will arrive at a general acceleration vector that is split into two components. ... a direct component and a centrifugal component.
I strongly advise taking that same position vector but expressing it in Cartesian coordinates instead of polar coordinates. In that case you will end up with second derivatives of zero! The truth is that your "general acceleration vector" arises from the geodesic equations for the polar coordinate system. Inertial motion, which is the local extension of a path through space and time in the same direction at each event in the particle's path, naturally occurs along geodesic paths. If the Cartesian coordinate system is being used in Newtonian physics, this is tanatmount to the particle continuing "in the same direction" as originally stated by Newton. However, if other coordiante systems are used, then the matter of what the geodesics are has to be taken into account. In the process of doing so, your "real centrifugal force" just plain vanishes.
As for the motion of the planets, you need to learn about Newton's theory of gravity, which is an inward directed force (effectively a certripetal force) that keeps the planets in orbit. Beyond that, please realize that applied math is all fine and dandy, but only if you apply it properly. --EMS | Talk 04:44, 10 February 2007 (UTC)

Yes, Newton's inverse square law force is an inwardly directed radial force. In the special case of a circular orbit, Newton's inverse square law force does indeed act as the centripetal force.

Now have you ever looked at the general situation for elliptical, parabolic, and hyperbolic orbits? The method is to consider the total forces involved. The tangential components of the general acceleration vector vanish because of Kepler's law of areal velocity (ie. zero curl). This leaves us with only the two radial components, ie. the Newtonian inverse square law force inwards, and a centrifugal force outwards. The centrifugal force is equal to the tangential speed squared, divided by the distance between the two planets. We are left with a complicated differential equation of which the solution is either an ellipse, a parabola, or a hyperbola, depending on initial parameters.

If the gravitational force is very weak compared to the centrifugal force, then we will have hyperbolic motion. If the gravitational force is negligible, then that hyperbola effectively becomes a straight line.

It is this straight line solution that we see around us all the time. Every two objects with mutual tangential velocity will possess a mutual radial repulsion. In our everyday cartesian/Euclidian view of things, this will show up as straight line motion. However, if we adopt the broader spherical universal vision, then those straight lines will actually be highly eccentric hyperbolae.

At the end of the day, the radial expansion between two objects moving tangentially is a reality irrespective of whatever coordinate system we use. It is the cause of pressure in a gas.

Let's now, for the sake of argument, enter into your rotating frame of reference, which according to the experts is the home of fictitious centrifugal force, and the only centrifugal force. Let's look at a centrifuge. The centrifuge throws objects to the edge and it even accords with Archimedes' Principle. That is a very real effect. The tangential motion that causes this effect is masked out by the rotation of the centrifuge, and hence from the perspective of the centrifuge, it becomes obvious that we now have a radially outward force. Mathematically, this centrifugal force is built into the transformation equations.

But that is no reason to deem the force as 'fictitious'. That radial motion is a reality no matter what frame of reference we look at it from. As soon as the centrifuge begins to spin, a tangential motion is set up between the particles and the fulcrum, and a radially outward acceleration occurs.

Not so with the Coriolis force. It is only fictitious. This is because the circular motion of the rotating frame of reference actually yields a tangential effect, whereas the radial effect of the centrifugal force has to be there anyway. The rotating frame of reference cannot create a radial effect.

I would have liked to have been able to talk about situations where the Coriolis force becomes real, but sadly it seems that that would be a forbidden topic because it involves concepts, such as curled dynamic liquid space, that have not been considered by the ruling physics party. David Tombe 10th February 2007 ( 06:40, 10 February 2007 (UTC))

I'm enclosing a Wikipedia link [1] on 'Orbital theory'. If we scroll down to the section entitled "Analysis of orbital motion" and look at the first equation, we will see that the last term on the right hand side is the centrifugal force. This is the general equation for orbits in a gravitational field and we can clearly see that centrifugal force is involved as a real effect.

Yet I am being accused of breaching Wikipedia policy by using unorthodox ideas. The accusations are being made by people who clearly haven't got the first clue about orbital theory. WilyD is going around arrogantly censoring everything that I write and claiming it to be pseudoscientific blabber. WilyD storms in claiming that all sources will confirm that centrifugal force is fictitious. Yes, a physics department might confirm it, but an applied maths department might not. It is clearly a contentious issue that hasn't been resolved. It ill becomes WilyD to assume that it has already been resolved in favour of 'fictitious only'.

This 'Orbital Theory' web link confirms what I have been saying all along. There is another school of thought which knows that centrifugal force is real. The right hand doesn't know what the left hand is up to. If anybody is in doubt, then please show me a differential equation that leads to conic section orbits, but doesn't involve the centrifugal force.

It is time that WilyD was told to stop the vandalism. David Tombe 10th February 2007 ( 07:46, 10 February 2007 (UTC)).

As far as I can see, there is only one vandal here, namely the anon who calls himself "David Tombe". Henning Makholm 14:22, 10 February 2007 (UTC)
Also, please note that you currently seem to be in violation of the three-revert rule. Continuing in this fashion is rather likely to get you blocked. Henning Makholm 14:32, 10 February 2007 (UTC)
Sigh. WP:AN/3RR it is, then. Henning Makholm 16:13, 10 February 2007 (UTC)

Count Iblis and Henning Makholm. You panic at the sight of the words ellipse, parabola, and hyperbola. You obviously haven't got a clue about planetary orbital theory. The centrifugal force is one of the input components of the differential equation which leads to these conic solutions. Why not begin by looking at the Wikipedia article on 'Orbital Theory'. [2]. Or look at equation (15) in this St. Andrew's University web link [3] David Tombe 10th February 2007 ( 14:43, 10 February 2007 (UTC))


Hi Edward. I was reading a little bit about your background and I see that General Relativity is your speciality. This means that you would be well into debates on topics like inertia and the equivalence between gravitational mass and inertial mass. At the moment however, I would prefer to concentrate on the issue regarding whether or not inertia is actual relevant in centrifugal force, irrespective of what inertia actually is, or how it could be relevant.

I can already see that you are influenced by the Newtonian concept that a body continues in a straight line unless acted upon by a force. I certainly don't disagree with this fact.

However I don't adopt the Newtonian concept that this motion is explained by inertia. I adopt an attitude more akin to that of Einstein, but without the special relativity. I see space itself as determining the motion of particles. Just like Boscovich, I believe that it can all be explained kinematically without any involvement of force or inertial mass. However, I'm satisfied enough with Newton's definition of force and mass but I don't think that they are necessary when analyzing planetary orbital motion.

From what I can see, mutual tangential speed leads to radial repulsion and that is a geometrical fact. Inertia doesn't come into it. David Tombe 10th February 2007 ( 06:59, 10 February 2007 (UTC))

You have just established in totally unmistakable terms that your work is orginal research!!! I don't promote my original research in the Wikipedia article space, and I am not about to let you do so either. --EMS | Talk 03:33, 11 February 2007 (UTC)

No I haven't done anything of the sort. It is not original research. Centrifugal force is a reality in orbital theory. Take it away and the planets will go down. That is clear from equation (15) in the citation. My comments and views on inertia are a side issue to the core point. Your problem is that you probably never did an orbital theory course. The left hand in the science world doesn't know what the right hand is doing. You have been conditioned into believing that centrifugal force is only fictitious and so you don't want to look at equation (15). David Tombe 11th February 2007 ( 08:09, 11 February 2007 (UTC))

Edit War

An edit war has been declared so I will not revert again for the meantime. I wish however to draw attention to one of the first paragraphs in the original edit. I will quote it here,

"A real or "reactive" centrifugal force occurs in reaction to a centripetal acceleration acting on a mass. This centrifugal force is equal in magnitude to the centripetal force, directed away from the center of rotation, and is exerted by the rotating object upon the object which imposes the centripetal acceleration. Although this sense was used by Isaac Newton,[1] it is only occasionally used in modern discussions.[2][3][4][5] "

This is an appalling inaccuracy. It implies that centrifugal force is only something that occurs in conjunction with centripetal force, and that it is confined to circular motion situations.

I have tried to explain that centrifugal force has got a much wider application and that it acts in planetary orbital theory to yield, parabolic, elliptical, and hyperbolic orbits. This raw fact appears not to have been to the liking of the guardians of this article. Am I to conclude that you are all at best physicists who have never done the orbital mechanics courses in applied mathematics?

The original article was very schoolboyish. I would hope that you would all go away and study the differential equation for a planetary orbit and take note of the presence of a very real centrifugal force. David Tombe 10th February 2007 ( 15:32, 10 February 2007 (UTC))

If you look at the archives, you'll find that the many of us do consider the notion of "reactive" centrifugal force to be spurious, useless and misleading. However, eventually the proponents of that meaning eventually dug out sources that undeniably show that the term "centrifugal force" sometimes is used in the sense of the reaction to a centripetal force. It would be a disservice to our readers not to tell them that the term is sometimes used with this meaning.
On the other hand, your repeated additions are completely bogus. There is no centrifugal force involved in orbital dynamics, when done in a rectilinear intertial coordinate system as reasonable people do. One gets perfect agreement with conic-section orbits (and nearly perfect agreement with reality, up to general-relativistic effects) by not including any centrifugal force. Your ramblings are too incoherent for me to be sure, but I suspect that you're taking higher derivatives in a polar coordinate system, which is not valid without adding in some scary terms involving Christoffel symbols. Henning Makholm 15:52, 10 February 2007 (UTC)

Henning Makholm. Now you are really showing yourself up in your true colours. You are talking total rubbish in order to try and cover up some basic truths about orbital dynamics. Centrifugal force is in the differential equation, end of story. I've shown you two citations, but really I shouldn't have had to bother. Christoffel symbols don't come into it. There is no need to introduce irrelevencies to cloud the issue and make it appear more complicated than it is.

You are totally out of order and I hope somebody else brings this subject up sooner or later. You are stamping on the truth and I don't know what your motive is. I solved the planetary orbital equation many times so don't try to pull the wool over my eyes that it doesn't contain the centrifugal force. Just click on those links that I gave you and see it right now. Equation (15) right here [4] David Tombe 10th February 2007 ( 16:35, 10 February 2007 (UTC))

The page to which you continue linking does not even contain the word "centrifugal", and the formula you keep pointing to does not contain any forces at all. (Where it comes from is mystrerious - the author appears to pull it out of a hat with no comments except that it is "analogous" to something that might be found in a dynamics textbook). The closest it comes to speaking about forces is that it contains a second derivative of the radial distance, which has the dimension of an acceleration, but is not in fact one, precisely because it is a higher derivative by coordinates in a non-rectilinear coordinate system. And even if it were a true acceleration (which it isn't), the introduction to the page explicitly states that it is about doing orbital dynamics without speaking about mass at all, and thus also without speaking about forces. Henning Makholm 17:14, 10 February 2007 (UTC)
Hello David, Thank you for stopping the revert war. Disputes like this are easier to work out on talk pages. Equation (15) on the page you cite does indeed contain a centrifugal force term. This is because the equation applies to a rotating frame of reference. (The radius vector r changes direction in time.) However, the text that you put into the article seemed to say that there is a centrifugal force in an inertial frame of reference. This is why people have been reverting your edits. Best regards, PeR 17:30, 10 February 2007 (UTC)

Hi Henning, in the particular example at equation (15), they are using polar coordinates in an inertial frame of reference. The radial effect is a reality no matter what frame of reference we use.

I am fully aware of that branch of applied maths that deals with rotating frames of reference and we are all agreed that rotating frames of reference create fictitious effects. But I can assure you that orbital theory has got absolutely nothing to do with rotating frames of reference. The differential equation (15) contains two components. (1) Newton's gravity downwards, and (2) Centrifugal force upwards. Without the latter component there could be no planetary orbits. Are you trying to say that the centrifugal term is fictitious?

Look at it another way. If you think that just because the radial vector is rotating that this makes the centrifugal force fictitious, then you are overlooking the fact that the radial vector is also rotating for the inward Newtonian inverse square law component. Does that make the downward gravity fictitious too? David Tombe 11th February 2007 ( 06:16, 11 February 2007 (UTC))

I think that you all need to see the "Inertia" section above. David is saying right off of the bat that he is disregarding Newton's laws! This is not a mistaken edtior as we originally thought, but instead an independent researcher who has his own personal view of things and no sense that his believing in what he writes does not make it right. This also is one of those people who thinks that Wikipedia is here to spread the "truth" instead of to document human knowledge.
I advise semi-protecting this article if David should try to edit it again. As he lacks a stable IP address, the only way to block him is via semi-protection for the duration of the block. In the meantime, it is my opinion that further discussion is useless. --EMS | Talk 03:51, 11 February 2007 (UTC)

First of all I ought to make it quite clear that I agree totally with Newton's laws of motion. The statement above which said "David is saying right off the bat that he is disregarding Newton's laws!" is a downright lie. At any rate, even if I was disregarding Newton's laws would that be a reason to disregard what I am saying? The ruling physics party who you all protect have long since moved on from Newton. So apart from it being a lie, what was your point?

I could easily delete this kind of misrepresentation, but I wouldn't want to stoop to that cheap level of deleting everything that doesn't take my fancy. It seems that the author above is so concerned that I might continue to press the case for real centrifugal force that he is advocating that the article become semi-protected.

Let's go over the main points again. This edit war began in the Coriolis force section. Having studied Maxwell's 1861 paper 'On Physical Lines of Force' I saw how he used centrifugal force to account for ferromagnetic and electromagnetic repulsion, as well as diamagnetic repulsion and paramagnetic attraction (Archimedes' Principle). I deduced from his paper that not only was centrifugal force real, but that real Coriolis force is also involved in magnetism.

I put forward the case for real Coriolis force in magnetism but it instantly resulted in an edit war. I backed down on that for the reason that whether I like it or not, the concept was indeed original research, and as such it was contrary to Wikipedia policy.

However, the same elements that were deleting me on the Coriolis force issue continued to delete me on the centrifugal force issue. The difference now is that real centrifugal force is not original research. It is built into planetary orbital theory. Take the centrifugal force out of the planetary orbital equation and the planets will not stay up. Henning Makholm has tried to wriggle out of this by suggesting that the centrifugal force term in equation (15) is in a rotating frame of reference. It is not. Polar coordinates are not the same thing as rotating frames of reference. Think it all through very carefully before locking your article up in its current amateur format. David Tombe 11th February 2007 ( 06:37, 11 February 2007 (UTC))

Polar coordinates is the same thing as a rotating frame of reference. In a stationary frame, the coordinate axes (for example and ) do not change direction. In polar coordinates, the axes and change direction when changes. The equations of motion for an object that is not affected by any force is:
There appears to be a centrifugal acceleration term in the first equation, but this is not due to any actual force. As I said, these equations represent inertial motion. The equivalent to the above in Cartesian coordinates is:
For a longer explanation, see section 3.4 of this textbook on celestial mechanics.
Best regards, --PeR 08:20, 11 February 2007 (UTC)

I'm going to quote you here. You say "There appears to be a centrifugal acceleration term in the first equation, but this is not due to any actual force."

This quote represents your utter delusion. If the force is in the equation, then it represents a real force if it has any effect.

But much more importantly, if you think the fact that the radial vector rotates renders the centrifugal force fictitious, then it should do the same to the inward Newtonian inverse square law force. They both operate in the radial direction. Therefore they are either both real or they are both fictititious.

You can't have it both ways, and you know fine well that gravity is real. The force of gravity and the centrifugal force both operate together in the planetary orbital equation and they operate inside the same radial component. You cannot arbitrarily say that one of these two forces is fictitious and that the other is real. Radial repulsion is a reality. It is independent of whatever frame of reference we use. Tangential motion leads to radial repulsion. It doesn't matter that the radial vector is rotating. It still has a real effect and it causes gas pressure.

Do you seriously believe that the whole picture is going to change if you view it from cartesian coordinates? For a start, cartesian coordinates are hardly suitable for analyzing the radial force of gravity, so why bother at all? If you do it in cartesian coordinates, there still has to be a Newtonian gravitation component acting towards a fixed point. There will equally be a convective component acting in the opposite direction to the inward gravity. You cannot eliminate centrifugal force just by switching to cartesian coordinates. If something moves in an ellipse, then it moves in an ellipse irrespective of whatever coordinate system we use to describe it. If that ellipse involves an inward gravitational force to the fulcrum, then it must also involve an outward centrifugal force away from the fulcrum. Polar coordinates are the system most suited for this geometry. But because the centrifugal force is so transparent in polar coordinates, you are trying to pull the wool over my eyes and exhort me to look at it all in the much more complicated cartesian coordinate system. And you believe that if I were to read the book which you referred me to that I would be made to believe that cartesian coordinates could make the outward radial acceleration vanish?

And you even performed a conjuring trick! You used the general acceleration equation in polar coordinates without the inclusion of Newton's law of gravity and told me that it equals zero acceleration in the cartesian frame. Absolutely true. You then went even further and referred me to a big thick book just in case I was in any doubt. But your transformation had got nothing to do with the interplay of centrifugal force and Newtonian gravity within a radial differential equation. David Tombe 11th february 2007 ( 09:51, 11 February 2007 (UTC))

Yes, I do believe that if you were to read that textbook you might understand what we are trying to tell you. If that is not the case, then I don't think there is anything that I can say here that will help. Sorry. --PeR 10:04, 11 February 2007 (UTC)

Our lines obviously crossed and you missed my latest insertion. Am I to read the textbook to convince myself that the general acceleration equation in polar coordinates in the absence of gravity is equal to zero acceleration in cartesian coordinates? I'm already convinced. But that is not the scenario that we are talking about. We are talking about the interplay between inward gravity and outward centrifugal force both contained within the rotating radial component.

Once it gets to the stage of trying to fob people off with big thick books it is usually a sign that they have no argument. It is a classical ploy of a cornered academic. David Tombe 11th February 2007 ( 10:28, 11 February 2007 (UTC))

Please don't delete text that somebody has responded to, even if you wrote it yourself. It is against the talk page guidelines, and it makes it appear as if I responded to something which you didn't say. You can strike out your earlier remarks, while leaving them visible, so that it is possible to follow the conversation. I have restored your comment in that way above. --PeR 10:41, 11 February 2007 (UTC)
Referring to textbooks is the standard way of resolving disputes on Wikipedia. The articles here reflect what is said in the textbooks, not necessarily what is true. If you don't like it, then this may not be the place for you. --PeR 10:50, 11 February 2007 (UTC)

Now we are into sophism. You referred me to a texbook in order to convince myself that the general acceleration equation in polar coordinates, in the absence of a gravitational force, is equal to zero acceleration in the cartesian frame. That fact is absolutely true. I was not disputing that fact, but it is not the scenario that we are debating. We are debating the interplay between centrifugal force and gravitational force. They both occur in the radial direction. The radial vector is rotating, but that can hardly make the centrifugal force fictitious and yet leave the gravitational force real.

You have ducked this issue. You have used the classic decoy ploy of referring me to a textbook for an irrelevancy. You are even continuing now by coming out with 'de jure' phrases such as that texbooks are a way of solving disputes. You are being presumptious that any textbook exists which contradicts what I am saying. Show me the textbook and the exact page number that says that the centrifugal force radially outwards is fictititious because the radial vector is rotating, but that the radially inward gravitational force is real even though the radial vector is rotating. David Tombe 11th February 2007 ( 11:16, 11 February 2007 (UTC))

I'm not going to discuss the "issue" anymore. I don't think there is anything that I can say here that will help. Regarding the burden of proof, it is the other way round. If you want to introduce a novel idea into an article then you must provide a reference supporting your insertion. --PeR 11:38, 11 February 2007 (UTC)

No you can't go away at this stage of the argument. We were steadily homing into the conclusion. At first you guys were trying to deny that the centrifugal force appears in the planetary orbital equation. I then had to provide citations.

You have now accepted that the centrifugal force is present in the orbital equation. We know that it acts radially outwards, just as the Newtonian inverse square law component acts radially inwards. The allegation has now been made that the centrifugal force is fictitious because the radial vector is rotating. How come this same logic is not applied to Newton's law of gravity? Newton's law of gravity speaks of a radially inward force. For a tangentially moving object, that radial direction is rotating. Does that make gravity fictitious? Of course not. So why should the same line of reasoning make centrifugal force fictitious?

Can you not see the picture clearly when we home in on two particles with mutual tangential velocity? There will be a radial expansion. It doesn't matter if that radial vector is rotating. The expansion is a reality, and we live in a spherical universe. That expansion accounts for pressure in kinetic theory of gases.

Your concept of fictitious centrifugal force is very much mistaken. If centrifugal force is only an artifact of a rotating frame of reference, then how can it throw somebody against the inside door of a car? How can it invoke Archimedes' Principle in a centrifuge? Artifacts don't have such real effects.

It is of course possible to have a purely fictitious centrifugal force. A particle that is stationary in an inertial frame of reference will have an artificial circular motion in a rotating frame of reference. This artificial circular motion will have a fictitious centripetal force comprised of a fictitious centrifugal force outwards, and a fictitious Coriolis force inwards. (as you know, the Coriolis force is 2vω = 2r(ω^2)= 2 X the centrifugal force. Hence the fictitious centripetal force inwards is equal in magnitude to the fictitious centrifugal force outwards. But we really don't need to go into this hall of mirrors).

In standard rotating frame of reference theory, we obtain an inbuilt centrifugal force that applies to objects that are stationary within the rotating frame. These objects get flung out radially to the edge. But this is a real effect. It is not an artifact. The expansion of their radial vector from the fulcrum is due to a very real tangential velocity in the inertial frame. That radial expansion is a reality that is independent of any frame of reference.

If the physics establishment are confused about this, then I don't know what the solution should be for your Wikipedia article. The current article as it stands, and was made prior to any edits by myself, does at least acknowledge that centrifugal force has got a real dimension. It is however very confused, and it muddles up real scenarios with fictitious scenarios, as well as limiting the discussion to circular motion. There is no mention of hyperbolic orbital paths.

I'm certainly not going to continue a petty edit war. That was never my original intention. But I think that somebody should re-write the main page at some stage. This cannot happen until the main guardians of the page have accepted the reality of 'Real Centrifugal Force'.

When you have accepted that centrifugal force is a reality, you will be surprised what doors are opened up for you. You will be able to appreciate better the writings of the great masters such as Bernoulli and Maxwell. You might even be willing to open up your minds to the role of both real centrifugal force and real Coriolis force in magnetism.

Anyhow, as a bear minimum, I think that the page should be re-written in such a way as to acknowledge the fact that a dispute exists. Fictitious centrifugal force should be discussed, and so should real centrifugal force. At the moment, you have real centrifugal force catered for under the title of 'Reactive Centrifugal Force'. That is not too bad a way of describing it. It emphasizes the fact that it is felt when we restrain it. But it leaves people wondering how a fictitious artifact can actually be physically restrained in the first place. David Tombe 11th February 2007 ( 13:23, 11 February 2007 (UTC))

David - The only person around who disputes the accuracy of this page is you. Under the NPOV policy, a viewpoint that is help by an extremely small monority (and one person is almost as small as it gets) is not appropriate for inclusion in Wikipedia. Also note that such a view is not appropriate "regardless of whether it is true or not; and regardless of whether you can prove it or not". In simple truth, you are totally confused about the difference between a coordinate acceleration and a physical acceleration. In a Cartesian coordinate system (under which Newton's laws hold as stated), the two are the same. However, you have chosen to use a polar coordinate system, and the equations for inertial motion in that case are as stated above, and include your so-called centrifugal term. If you wish to persist in assigning that term a physical meaning that no other physicist cares to give it, then be my guest. However, you have no business trying to impose that which is only your personal viewpoint on Wikipedia. --EMS | Talk 16:13, 11 February 2007 (UTC)
P.S. I have yet to see anyone accuse the physics community of being mistaken without being mistaken themselves. People have been studying this kind of thing of centuries now, and you need to have some respect to for that. --EMS | Talk 16:25, 11 February 2007 (UTC)

EMS, you are ducking the issue and trying to confuse it with coordinate frame transformations. Two objects with mutual tangential velocity will be accelerating apart. That is a real effect whether the acceleration vector is rotating or not.

There is no need to play the numbers game here and act like as if I am the only person who can see this simple fact. I am outnumbered at the moment by the guardians of the article. That proves nothing.

You are in total denial of a very simple fact. Show me two objects with mutual tangential velocity that are not accelerating apart from each other. David Tombe 11th february 2007 ( 17:02, 11 February 2007 (UTC))

We're trying to tell you that a coordinate acceleration is not a real acceleration, because it is not. Coordinate frame issues seem to be the root of why you're mistaken. Let me suggest a simple experiment you can try to do. (1) Take a slide rule and place it face up on a horizontal tabletop. (2) Remove the sliding part in the middle, and let a small ball roll along the notch where the slider used to go. (3) Observe the progress of the ball as measured by the logarithmic scale. Perhaps it takes one second to progress from 1 to 10, then one second to progress from 10 to 100 and yet a second to progress from 100 to 1000. By golly! it's accelerating! No it's not - its moving with constant velocity but measured in a nonuniform coordinate system. In this case, like in your polar coordinates, the coordinate system is not accelerating, but it is non-uniform, which is enough to cause spurious coordinate accelerations. To be concrete, a 1° difference in correspond to different euclidean distances at different points in the plane, which means that the metric is not spatially constant; thus the Christoffel symbols will be nonzero; thus spurious coordinate accelerations like the one you're fixated on will turn up. Henning Makholm 17:28, 11 February 2007 (UTC)

Hi Henning, coordinate frames don't need to come into it at all, never mind coordinate frame transformations. All we need to look at is two objects that possess a mutual tangential speed. They will be accelerating away from each other. It is as simple as that. That is the basis of centrifugal repulsion. v^2/r is as fundamental as Newton's inverse square law of gravity. The two of them operate in tandem with each other along the line of connection between any two particles, and it leads to elliptic, parabolic, or hyperbolic orbits. It is of no concern that the radial vector joining the two particles happens to be rotating, yet you seem to think that this is indeed a matter of concern, but only for the centrifugal component.

Anyway, if we are going to use a coordinate frame, the polar coordinate frame is the most simple one to use. You said that I have a fixation about it? I have never seen orbital theory analyzed in anything other than polar coordinates. I'm sure it can be done in cartesian coordinates too. But why would you bother?

I can't believe that you think that a cartesian coordinate frame would cancel the outward centrifugal radial acceleration between the two objects. David Tombe 11th february 2007 ( 17:46, 11 February 2007 (UTC))

It's fairly easy to measure. Your car turns a corner and you're accelerated into the car door, right? But watch how you move with respect to the ground, it's obvious you're not accelerating at all. WilyD 18:01, 11 February 2007 (UTC)

No WilyD, if you get thrown against the inside of the door of a swerving car, that is not a fictitious effect. That is a real effect. The car door was reacting against a radial acceleration in the inertial frame. Look at it from the perspective of the inertial frame of reference and there will be a real radial acceleration between the person and the centre of the circle of which the car's path forms part of. There will most certainly be objects inside that circle with which the passenger shares a mutual radial repulsion. You are totally mistaken when you say that there is absolutely no acceleration in the inertial frame.

The fundamental theory goes down to the tangential motion between any two particles, leading to a radial repulsion. If you walk past a lamp post in a straight line, there will be an outward radial acceleration between you and the lamp post. If we combine this outward radial centrifugal acceleration with the inward radial acceleration due to gravity, we will get a conic section solution. If gravity is very small compared to centrifugal force, the solution will be a hyperbola. In the case of a walker passing a lamp post, gravity will be negligible and the hyperbola will effectively become a straight line.

Even when the car is not swerving around a corner, the passenger will have radial acceleration relative to many objects but it will not be felt because the car is following the same straight line trajectory that the passenger would be following and hence it does not restrain the centrifugal force on the passenger. It's when the car swerves that it brings the door against the passenger and forces the passenger to swerve out of their natural straight line motion. The straight line motion, as I said earlier is the natural solution to centrifugal force and gravity when gravity is negligible.

The truth of the matter is that polar coordinates are actually the system of coordinates that best correspond to reality. It doesn't mean that they are the only correct kind of coordinates, but they are clearly the best system for transparency of the nature of space.

I think the problem that you guys are having is accepting the idea that radial acceleration is an ongoing reality between most particles even if there is no acceleration in the cartesian frame. It is the reality of this radial acceleration which you are failing to notice. In everyday life it doesn't seem relevant. But when we expand it into the large scale, it leads to a picture of ellipses, parabolae and hyperbolae. David Tombe 11th February 2007

David - Wikipedia is not USENET. Wikipedia is not a debating society. Wikipedia is not for original research, and it is not that place to challenge long-accepted scientific fact (although we can and are expected to report on notable challenges which are taking place in the field). You wrote above that
[t]wo objects with mutual tangential velocity will be accelerating apart
as if that is the issue. It is not. Instead the issue is the cause that you ascribe to that phenomenon. As for "ducking the issue": I have learned that people like yourself are not worth arguing with here. Most of your ilk do not care to learn what they do not know, and even when your ilk is willing it takes longer than one would like to educate someone like you. We are not here to be your teachers, but instead are here to help build an encyclopedia. So kindly take your disagreements elsewhere. I will agree that "radial acceleration is [a] ... reality", but I will not agree that it is due to a force. More importantly, I will not agree without appropriate supporting references ...
I gave you supporting references but you blatantly ignored them. I gave you links that showed that Newton's gravity radially inwards and centrifugal force radially outwards combine together in the planetary orbital equation. It is established fact but you are sweeping it under the carpet. David Tombe 12th February 2007
... that your viewpoint is notable and therefore worthy on inclusion in Wikipedia. --EMS | Talk 04:43, 12 February 2007 (UTC)
ema57fcva, This is not original research. This is about basic realization. I'm glad that you have finally acknowledged that two objects with mutual tangential velocity will be accelerating apart. That is centrifugal force. It doesn't matter what system of coordinates we use. If two objects are accelerating apart radially, then that is not a fictitious effect. A centrifuge invokes Archimedes' Principle because the particles possess tangential velocity in the inertial frame of reference. The radial acceleration is real.
Radially outward centrifugal force in conjunction with radially inward gravity leads to hyperbolae, parabolae and ellipses. How can the gravity be real but the centrifugal force only be fictitious? David Tombe 12th February 2007 ( 09:24, 12 February 2007 (UTC))
It has already been explained to you that all orbits can be derived by assuming inertia and the inverse square law for gravity in Newtonian physics. In addition, the references you cite do not make any claim that the radial acceleration is due to a force. That assertion is your novel synthesis of the available data, and so is original research. I have nothing more to say on this issue. --EMS | Talk 14:09, 12 February 2007 (UTC)

ems57fcva, orbital dynamics can be done purely kinematically. There is absolutely no reason to have to involve force at all. However if you so wish, you can convert a centrifugal acceleration into a centrifugal force simply by multiplying it by inertial mass. Let me quote you here,

"In addition, the references you cite do not make any claim that the radial acceleration is due to a force."

No claim is necessary. Multiply any acceleration by inertial mass and you have got a force. That is Newton's second law of motion.

Now let's look at another of your quotes,

"It has already been explained to you that all orbits can be derived by assuming inertia and the inverse square law for gravity in Newtonian physics."

This is arrant nonsense. If there is no centrifugal force in the orbital equation, you will not get elliptical, parabolic, or hyperbolic solutions. It is ludicrous to suggest that inertia can substitute for the vital v^2/r expression in the differential equation. It is also untrue to say that this has already been explained to me. It was never explained to me and I doubt if it could possibly be explained to anybody. I'd be more than happy if you could show me the derivation of conic orbits using inertia but no centrifugal force. David Tombe 12th February 2007

David I have looked at both references you point out. In both cases the equation in question does not say anything about forces. In fact, that equation simply has two terms that compose a radial acceleration. Do we at least agree that F=ma? If so, you've told me what the mathematical expression of "a" is, but you have not related it to F. Are you saying that Newton's law of gravity only results in the first term of the equation? If so, could you point that out to me in your first reference? As far as I can tell, the one and only force that comes into the derivation is Newton's law. I will not deny the fact that there is a centrifugal component to the acceleration. However, as the subsequent equations in reference 1 (that you brought up) show, the centrifugal acceleration term is also a result of the Newtonian gravity force. I would be interested in seeing how the centrifugal Force, shows up, as right now I don't see any term that captures it.
You also mentioned, that "orbital dynamics can be done purely kinematically". I would propose you modify your statement to read "orbital dynamics can be analyzed using pure kinematic techniques". You cannot "do" orbital dynamics without bringing in forces and masses since it is the forces that drive the motion! Please don't confuse mathematical analysis (which is perfectly valid) with the actual physical phenomena it is representing. --Spaceman13 23:20, 5 April 2007 (UTC)

If an object has a centrifugal acceleration, multiply it by its mass and you will obtain the centrifugal force. David Tombe 14th April 2007 ( 16:14, 14 April 2007 (UTC))

One more point. A simple numerical integration of F = ma in 3-dimensional Catesian space will yield all sorts of beautiful conical sections without any additional centrifugal forces. I would be interested in seeing where the centrifugal forces comes into play in my numerical integration, and how I can be getting valid results without it. Polar coordinates are great for analytically representing the physical phenomena, but the beauty of numerical methods is that they hold true in frames where the phenomena cannot be represented analytically. Sadly, the equations you put down won't even represent the real world. By the time you get through adding 3rd body perturbations, gravity harmonics such as J2, and other influences, it becomes impossible to represent orbital motion in polar (or Cartesian) coordinates in any sort of analytical method - Orbital dynamics cannot be done purely kinematically. At this point, only numerical methods will work, and F = ma will still hold true! --Spaceman13 23:27, 5 April 2007 (UTC)

The basic equation F = ma tells us absolutely nothing. We need to know the expressions for a before we can even begin to solve the trajectory. David Tombe 14th April 2007 ( 16:14, 14 April 2007 (UTC))

  1. ^ 'On Faraday's Lines of Force', reprinted: The Scientific Papers of James Clerk Maxwell, Editor - W.D. Niven, Cambridge University Press 1890 Vol. I, p160