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Modern revisionism in centrifugal force

There has been considerable revisionism in attitudes towards centrifugal force in recent years. Advanced Level Physics by Nelkon & Parker 1961, page 34, openly talks about centrifugal force as being a real effect. A quote from this page reads,

If some water is placed in a vessel attached to the end of a string, the vessel can be whirled in a vertical plane without any water falling out. This is because the centrifugal force on the water (mv^2/r) is greater than its weight.

This section then went on to explain the operation of the centrifuge device in terms of centrifugal force.

By the year 1970, this entire section had been removed from Nelkon & Parker, and the centrifuge has since been explained in terms of an inward centripetal effect. A quote from the 1979 Nelkon & Parker in the equivalent section reads,

The net force urges the particles towards the centre in spiral paths and here they collect.

Similar revisions have occured in Herbert Goldstein's 'Classical mechanics' in which sections that once openly attributed the cause of certain effects to centrifugal force, have now been substantially modified so as avoid mentioning the word 'centrifugal force'.

I therefore suggest that this fact should be openly mentioned in the main article in a special section entitled 'Modern revisionism of attitudes towards the concept of centrifugal force'. David Tombe (talk) 14:47, 9 April 2009 (UTC)

I whole-heartedly agree. -AndrewDressel (talk) 16:27, 9 April 2009 (UTC)

Here are the relevant quotes from Goldstein,

First edition, 1950. Goldstein's original statement read,

Incidentally, the centrifugal force on a particle arising from the earth's revolution around the sun is appreciable compared to gravity, but it is almost exactly balanced by the gravitational attraction to the sun. It is, of course, just this balance between centrifugal force and gravitational attraction that keeps the earth (and all that are on it) in orbit around the sun.

But in 2002, this was altered to read,

If we analyze the motion of the Sun-Earth system from a frame rotating with Earth, it is of course just the balance between the centrifugal effect and the gravitational attraction that keeps the Earth (and all that are on it) and Sun separated. An analysis in a Newtonian inertial frame gives a different picture. As was described in Section 3.3, the angular momentum contributes to the effective potential energy to keep the Earth in orbit.

You can see that they have introduced the hall of mirrors in the 2002 edition. The hall of mirrors is of course the rotating frame of reference. He doesn't explain why the angular momentum contributes to the effective potential energy to keep the Earth up. But if we go to where he referred (he, not being the original author), you will see that the cause is still the centrifugal force. David Tombe (talk) 00:30, 10 April 2009 (UTC)

There is no "hall of mirrors". The later version in Goldstein simply introduces two frames of reference: the stationary inertial frame and the co-rotating frame, while the older version simply discusses the matter from the co-rotating frame without actually saying explicitly that this frame is being used. Thus, the new version is both compatible with the old, more general than the old, and clearer than the old version.

The word "cause" introduced here is treacherous, unless tied to a mathematical explanation. For example, in a co-rotating frame, the centrifugal force is present explicitly as a "force" in Newton's law. In that sense, in that frame, centrifugal force is a "cause". However, in an inertial frame there is no centrifugal force. The only force present is gravity. It is a one force picture. The satellite does not fall to Earth in this frame because it moves in an orbit, and this orbit is possible only if an attractive force is present (gravity). Else, the body flies off in a straight line, and does not orbit. Brews ohare (talk) 19:17, 10 April 2009 (UTC)

Brews, That's all fine until you place two planetary orbital systems side by side. Are you saying that where gravity will act mutually between any permutation of the four planets, that centrifugal force will only act between planet 1 and planet 2, and between planet 3 and planet 4? And that no centrifugal force will act between planet 1 and planet 3, planet 1 and planet 4, planet 2 and planet 3, and planet 2 and planet 4? If we consider all the permutations, two adjacent planetary orbital systems would repel each other, and it would not be so easy then to write centrifugal force off by disguising it in another language.

We have got absolutely no evidence whatsoever that either Goldstein in 1950 or Nelkon & Parker in 1961 held the viewpoint which you have suggested. You have merely taken hold of the revised viewpoints and stated your own opinion that this is what Goldstein and Nelkon & Parker really meant. If the unrevised versions meant exactly the same as the revised versions, as you are saying, then why did the revisions take place at all? Somebody somewhere was very keen to alter the way in which Goldstein and Nelkon & Parker presented this subject. David Tombe (talk) 19:51, 10 April 2009 (UTC)

Well, one approach to a discussion of two bodies is to say it is too simple and N-bodies are necessary to get the real idea. However, against that approach, if the two-body problem is beyond us, how are we to settle the N-body problem? To invoke William Shockley, one should solve the simplest case first. Is there any basis for thinking N-bodies is a simpler case than two bodies? Brews ohare (talk) 23:00, 10 April 2009 (UTC)

Brews, the points which I was making regarding revisionism have got nothing to do with the one body equivalent problem. I have no problem whatsoever with why we do the one body equivalent reduction. Nobody is arguing about the reasons for the one body problem. The only important thing is that there is a centrifugal force term present in the equation. And the attempts to deny the presence of the centrifugal force in the radial planetary orbital equation, by persons who had no knowledge of the topic, was the casue of a prolonged edit war. David Tombe (talk) 12:13, 11 April 2009 (UTC)

The one body equivalent planetary orbital problem

The one body equivalent planetary orbital problem requires the use of G(M + m) in the numerator of the gravitational term in order to yield the correct orbital period as per Kepler's 3rd law. GM alone cannot be used in this context as it will yield the wrong orbital period. I intend to re-revert Wolfkeeper's reversion unless anybody can give a satisfactory reason for leaving it as it is. David Tombe (talk) 14:13, 10 April 2009 (UTC)

No, don't revert. It looks right. Did you notice that M is defined as m1 + m2? Rracecarr (talk) 14:30, 10 April 2009 (UTC)

Rracecarr, Yes, you are correct. I hadn't noticed that. But the symbolism here badly needs to be cleaned up. It is normal to use M for the greater mass, and m for the smaller mass. The reduced mass often uses the Greek symbol (mu). It was very misleading to present the product of reduced mass and the sum of the masses ([m1m2/(m1 + m2)] X (m1 + m2)) using symbols that made it look like Mm. It certainly does multiply out to be Mm in the normal sense of M and m, but that wasn't the sense that M and m were being used here.

I don't think we even need to involve 'reduced mass' in this article. We only need to look at it kinematically. Normally when studying this problem kinematically we just use k for the numerator in the gravity term and l^2 for the numerator in the centrifugal term, where l is the Keplerian areal constant ωr^2.

I just tried to tidy it up myself, but I can't seem to get the Greek symbol μ to fit in. I suggest that somebody cleans this up so as to use μ for reduced mass and to use k for G(m1 +m2).David Tombe (talk) 19:23, 10 April 2009 (UTC)

I've made a stab at introducing μ for reduced mass. I hope it has been done correctly. Brews ohare (talk) 00:09, 11 April 2009 (UTC)

Brews, I'm not even sure that we need all this stuff anyway. But if we do have it in, it is important to use familiar and unambiguous symbolism. It is not good to use the large M symbol for m1 + m2. The condensed numerator G(m1 +m2) is normally written with the symbol k. People will look at large M and think of the single mass of the larger body. David Tombe (talk) 12:17, 11 April 2009 (UTC)

Reducing the planetary orbital section

In fact, I would suggest reducing the entire planetary orbital section to a few lines surrounding the radial equation,

${\ddot {r}}=\left({\frac {v^{2}}{r}}\right)-G(m1+m2){\frac {1}{r^{2}}}\ .$

and drawing attention to the centrifugal force term. After all, that's what the article is all about. It's all about illustrating situations where the centrifugal force arises.

Doing so would get rid of alot of unnecessary material and leave the main point about centrifugal force more clearly exposed.

If nobody objects, I'll do that. David Tombe (talk) 20:06, 10 April 2009 (UTC)

I object. The point of this discussion is to show how centrifugal force shows up in various views of the same problem, and it does that. All this discussion arose in the first place because of confusion that occurs when the equivalent one-dimensional formulation and the terminology it invokes are used in the other formulations where it is out of context and misleading. Brews ohare (talk) 23:05, 10 April 2009 (UTC)

Brews, There seems to be some confusion here. I am the one that first introduced the planetary orbital topic, and I did so for the very purpose of highlighting the involvement of the centrifugal force, which is what this page is about. Initially my edits were reverted due to the misinformed belief that I was trying to introduce original research. When it was reluctantly agreed that what I was trying to introduce was not actually original research, we then ended up with a much extended article on planetary orbits, which actually had the effect of clouding out the key point.

My suggestion is that we merely draw attention to the radial planetary orbital equation and point out the presence of the centrifugal term. We can state that it is a differential equation which solves to a hyperbola, parabola, or an ellipse, and that the solution, which is very detailed, can be found at the Kepler Problem page.

As it stands now, the extended section on planetary orbits is somewhat confused in its point in relation to the main article. I'll explain its weaknesses,

(1) There is no need to discuss the topic of reduced mass in this article.

(2) There is no need to mention polar coordinates.

(3) Polar coordinates have been introduced in connection with solving the equation, but the analysis is not present. I don't even think that the analysis should be present, but the way that the section has been written up gets the entire concept of the analysis and the solution mixed up with polar coordinates.

The section is also interspersed with unnecessary and somewhat dubious opinions. This entire section could be greatly trimmed, just as I have suggested. You say that all this was originally written to help with confusion. There never was any confusion on my part. I learned this topic in detail in the past. The confusion was with those who were only learning about this topic while simultaneously trying to prevent me form inserting a summary of the topic. David Tombe (talk) 12:05, 11 April 2009 (UTC)

My recollection is of an extended argument over the interpretation of ${\ddot {r}}$ as "acceleration", an interpretation that cannot be taken over to the Newtonian formulation of the two-body problem in 3-space, but is restricted to either the fictitious 1-D formulation, else to a Lagrangian formulation in terms of "generalized coordinates" and "generalized acceleration". Hence the lengthy development, almost entirely a response to these confusions largely promulgated by yourself. Brews ohare (talk) 17:21, 11 April 2009 (UTC)

Brews, your prolonged debate on this subject was with editor Fugal. I agreed with Fugal on alot of points, but not everything that he said. Unfortunately I was unable to get into the debate at that particular time, and Fugal disappeared after I was re-installed. I had always been hoping that Fugal would return. But meanwhile, I have realized that alot of it was a red herring. The only single point of significance is that a centrifugal term appears in the radial planetary orbital equation, and that was all that I was trying to insert at the height of the edit war, along with a section on the centrifuge machine.David Tombe (talk) 18:54, 11 April 2009 (UTC)

I agree with David on this one; the "sketch of the analysis" is way too long, and it's not likely that a reader is going to follow it. Better to just link other articles and say that the problem can be formulated as the fictitious 1D system in which there is a fictitious centrifugal force and state the simple equation and a bit of (sourced) interpretation of it. Dicklyon (talk) 17:36, 11 April 2009 (UTC)

Dick, This business about the fictitious 1-D problem. Yes, Goldstein said that the radial equation is equivalent to the fictitious 1-D problem. But he never said anything about centrifugal force being fictitious. You are confusing two issues here. Goldstein was referring to the fact that the real radial planetary orbital equation is equivalent to a fictitious 1-D problem. How could you even have a centrifugal force in a one dimensional problem? The planetary orbital problem is a 2-D problem. The transverse equation leads to an areal constant which can be substituted into the radial equation making the radial equation equivalent to the fictitious 1-D problem. David Tombe (talk) 19:06, 11 April 2009 (UTC)

David, the formula with r has to be interpreted as a 1D system in order for r-double-dot to be interpreted as an acceleration. Since r is in reality just one coordinate in a 2D or 3D system the 1D system with only r is "fictitious" in the intended sense. In the real 2D or 3D system, the only force acting on the planet is the centripetal force due to graviation, which is why the path of the planet is curved. But you've been told that enough times that I know it's pointless of me to be saying it again. Dicklyon (talk) 06:43, 12 April 2009 (UTC)

Dick, I never objected to the 1-D formulation. I promoted it and explained it in terms of the Kepler areal constant. You are now misrepresenting my position. David Tombe (talk) 13:01, 12 April 2009 (UTC)

The sentence: "In this formulation, the second term on the left side is simply one of two terms in the acceleration in polar coordinates. It is not an impressed force; it is part of the mathematics of derivatives in polar coordinates." is an essential point, disputed by David, and should not be omitted from the discussion. This point requires the introduction of polar coordinates.

It is no matter whether every reader will pursue this discussion: it is intended for those with an interest. Brews ohare (talk) 17:43, 11 April 2009 (UTC)

Brews, polar coordinates do not need to be discussed in this article. The planetary orbital problem is already well established theory. Nobody here is disputing aspects to do with the Kepler problem other than terminologies. Polar coordinates are only a language that is used in expressing the two planetary orbital equations. The only relevance which the planetary orbital problem has in connection with the centrifugal force topic, is the fact that the radial equation includes a centrifugal force term.

So all we need to do is give it a brief mention in passing as an example of centrifugal force. But what you have done is clouded it all up with unnecessary extras about reduced mass and polar coordinates and added in your own opinion that the rω^2 term is not an impressed force. You have not even mentioned its name. You have completely played down the star piece in the section.

The correct procedure would be to state the name of the rω^2 term and say nothing more. Leave it for readers to decide the physical significance of that term. David Tombe (talk) 18:48, 11 April 2009 (UTC)

David, you can't have it both ways. Either you have a "fictitious force" due to the rotating coordinate system that makes the 1D problem, or you have to say how the coordinate transformation affects accelerations and forces, and how r-double-dot, which is clearly NOT an acceleration, relates to those. We've been over this too many times already, so I'll go away again and let you guys deal with it. Dicklyon (talk) 20:01, 11 April 2009 (UTC)

Dick, Fictitious forces don't enter into the planetary orbital equation. So I don't what what you mean when you say that I can't have it both ways. There is a centrifugal force term in the planetary orbital equation which has got nothing to do with rotating frames of reference. The entire edit war has been over the fact that this centrifugal term is an inconvenience for those who have only ever been taught about centrifugal force in connection with rotating frames of reference. The edit war exposed the fact that most of those involved hadn't got the first clue about planetary orbital theory. So at first they denied the radial equation altogether. Then they accepted it and tried to hide the centrifugal force from view in an 'all in' radial acceleration box. Finally Brews brought the centrifugal force out of the box, but hid it discretely in the middle of a long section of irrelevancies without using its name. And he wrote his opinions underneath it regarding that he believed that it isn't an impressed force. And now you have decided that it is a fictitious force. You are the first one to have made this claim.

Can you show me a source which says that the centrifugal force in the planetary orbital equation is a fictitious force? Goldstein doesn't mention fictitious forces in his entire book. But you have latched unto the word 'fictitious' in another context and then opportunistically applied it to the centrifugal force.

The summary is that this article will remain in a mess so long as the editors refuse to come to terms with the reality that centrifugal force is a real term in the planetary orbital equation. David Tombe (talk) 23:59, 11 April 2009 (UTC)

If memory serves, editions of Goldstein later than yours make it clear that this centrifugal force is a fictitious force in the fictition 1D system that in the real world is rotating. Can you provide any source other than your old edition of Goldstein that treats this equation and calls the centrifugal force an actual force? Even this old Goldstein edition talk about a fictitious potential energy in the fictitious 1D problem. Sources that refer to it as a fictitious force include many of these. Dicklyon (talk) 01:43, 12 April 2009 (UTC)

David: Words are leading you astray: what does "real" mean here? I think "real" can be interpreted as a synonym of "appears in Newton's laws". In that sense, "real" applies to centrifugal force in a rotating frame. However, it does not apply in an inertial frame. Brews ohare (talk) 02:33, 12 April 2009 (UTC)

Dick and Brews, the issue in question wasn't altered in the 2002 revision. You are deliberately misrepresenting the issue here. Goldstein never talks about fictitious forces. He merely says that the radial planetary orbital equation is equivalent to the fictitious 1-D problem. In other words, we can analyze it as a problem in one variable. You have opportunistically seen the word 'fictitious' and you are using it out of context to try and link it with the concept of fictitious force in rotating frames of reference.

Neither is there any need to explicitly state that the centrifugal force term in the planetary orbital equation is real. State the facts and leave it for others to decide on whether it is real or not. Simply state the equation and point out the centrifugal force term? Why should that be such a problem unless you have a vested interest in denying the reality of centrifugal force? It seems that far too many people have invested heavily in the idea that centrifugal force is not real, and any evidence to the contrary must therefore be concealed out of view. And that's what you are trying to do here. You have buried the centrifugal force in the middle of a large chunk of irrelevancies, and deliberately refrained from using its name. And Dick has gone ahead to the next stage when that section will inevitably be condensed, and prepared the way for Goldstein to be misrepresented so that he can refer to the centrifugal term as a fictitious force. David Tombe (talk) 12:57, 12 April 2009 (UTC)

I gather that Dick's references are all screwballs? As has been pointed out in the past and in the article, the term "fictitious force" is a technical term, used with a particular meaning to imply a force that is present (for example) in a rotating frame, but not in an inertial frame. To fail to point this out is remiss, rather than an act of "letting the reader decide for themselves". Brews ohare (talk) 14:38, 12 April 2009 (UTC)

Brews, Dick's references are good references out of Goldstein. They don't disprove anything that I have said. Let's concentrate on the main equation,

${\ddot {r}}=-G(M+m)/r^{2}+l^{2}/r^{3}$

We have at last reached the stage where we have got this equation on the table and formally recognized. It is not my original research as you all once suggested. We are all now satisfied that this is a fully sourced equation. It appears at 3-12 in Goldstein.

What name do you suggest that we give to the inverse cube law term? And if not 'centrifugal force', then why do we have the planetary orbital section at all in this article about centrifugal force? David Tombe (talk) 20:57, 12 April 2009 (UTC)

Maybe we should call the term centrifugal force, a force in a fictitious 1D system; but without misrepresenting Goldstein, we can also cite others who refer to this centrifugal force as a "fictitious force." I do agree that the current long section is a mess, and really quite pointless in this article, as it's hard to find centrifugal force in it. It reads like a long essay trying to work around a POV that the writer doesn't care for, or something like that, and it's hard to work on as it's mostly not based on sources. Something short would be better, as this is not an article on planetary orbits. Dicklyon (talk) 00:28, 13 April 2009 (UTC)

I support deleting the entire planetary motion section. It seems to obscure more than it clarifies, and if this wall of formulas really is necessary to handle general Keplerian orbits in an on-average corotating system, then I think I'd prefer the inertial frame. If we must have an example from celestial mechanics, I suggest we use a simpler one, such as a geostationary satellite. –Henning Makholm (talk) 21:54, 14 April 2009 (UTC)

I agree. I don't see any difficulty getting to a short section that includes the equation out of Goldstein with a centrifugal force term, and saying what it means (it's not an on-average corotating system, but a system aligned with the line between the bodies, I think); the equation for the dynamics of r is very simple in this system. Dicklyon (talk) 04:54, 15 April 2009 (UTC)

Hm, is that analysis appreciably different from using a stationary cylindrical coordinate system? In a frame whose rate of rotation changes with time, the centrifugal force becomes just one among several different corrections necessary. Once the full equations of motion in either model are derived, they should differ only in that one says ${\dot {\phi }}$ and ${\ddot {\phi }}$ (for the angular coordinate $\phi$) and the other says $\omega$ and ${\dot {\omega }}$ (for the frame's angular velocity $\omega$). That does not strike me as a useful demonstration of the centrifugal force specifically. –Henning Makholm (talk) 13:53, 15 April 2009 (UTC)

I'd recommend the article Motion in a central-force field, J.S.S. Whiting, Phys. Educ. 18 No 6 (November 1983) 256-257 (if you can get access to it) as a good reference for a quick description of how the various inertial/fictitious/pseudo- forces enter into orbital motion when done in rotating frames. It addresses the nuances of a corotating system for non-circular orbits - ie, where $\omega$ is not constant. It briefly touches on the appearance of the Coriolis and Euler pseudo-forces which cancel each other out. It also consistently uses the term "pseudo-forces" when referring to these and the centrifugal force. Chapter 9 in John Taylor's "Mechanics", specifically pg 357-359, might also be useful. --FyzixFighter (talk) 06:15, 15 April 2009 (UTC)

FyzixFighter, If you want to use the term fictitious or pseudo-forces to describe the centrifugal force, the Coriolis force, and the so-called Euler force in the planetary orbital equation, then so be it. I personally don't see anything fictitious about them. But if you can provide sources that call them fictitious, then so be it. But why do you want to use a source that uses rotating reference frames when we already have a source that doesn't use rotating reference frames?

Meanwhile there are other editors who are denying that centrifugal force is involved in the planetary orbital equation in any shape or form. Henning Makholm is quite wrong in this regard. Before we continue with the discussion on terminologies we must first at least reach a consensus that Henning Makholm was quite wrong to state that the equation in the section below is wrong. Until this matter is resolved, I can't see any hope of progress. David Tombe (talk) 16:16, 15 April 2009 (UTC)

Dick, I agree with most of what you say apart from the reference to the fictitious 1-D system which I think you have misunderstood. But I'll discuss that later. Meanwhile, I intend to reduce the planetary orbital section to a rump, giving the basic relevant facts. I will point out the centrifugal force term in the planetary orbital equation. I will make no pronouncements regarding whether it is real, reactive or fictitious. I will then await to see what additional points of view are added in by other editors. I agree with you that there are endless references stating that centrifugal force is fictitious. But these references are few and far between in relation to the planetary orbital problem. David Tombe (talk) 11:48, 13 April 2009 (UTC)

Centrifugal force in non-circular motion

Two bodies with similar mass orbiting around a common barycenter with elliptic orbits.

This topic actually is covered in general terms in the subsection Skywriter. IMO it is interesting to look at this topic again from the two-body viewpoint, but it is a digression. To cover this topic without producing more uncertainty in the reader, general motion of two orbiting bodies has to be introduced carefully. In particular, the example in the image does not come immediately to mind, and such examples would have to be drawn to the reader's attention. Then the rotating frame has to be introduced for such a case. I am unfamiliar with all the ramifications, but from the image it appears in this example that the rotating frame is actually only an instantaneous co-rotating frame that must be continuously adjusted from moment to moment, because the angular rate actually varies in time. In any event, this topic will become quite a lengthy discussion unless supporting articles or sub-articles are written under other articles that may be used here by reference. Brews ohare (talk) 12:38, 17 April 2009 (UTC)

Respectfully Brews, I disagree with you on some points. Yes the co-rotating frame that corresponds physically to the 1D equivalent problem is an "instanteous" co-rotating frame - Whiting says so explicitly. But I don't see it as adding too much additional complexity. Most of the complexity can be, is already, and should be handled by other articles that we can link to from here. This is encyclopedia and not a textbook. I am certain that we can explain the general central-force example with much less complexity that currently exists in the current planetary orbits section, and also reduce the complexity by using the pre-existing articles. I do not think that we need to create new articles or sub-articles, perhaps improve the articles that we will be linking to. The complexity that we should allow should be directly related to the topic at hand, such as is in the derivation section. I'm not saying that my shortened version is perfect - far from it, but it is about the right size and about the right level of depth in term of details about the scenario/example. I'll put up another revision of the shortened form taking into account some of your comments, and I would again like to discuss ways to improve it but not bloat it. --FyzixFighter (talk) 19:45, 17 April 2009 (UTC)