Paradoxes Resolved, Origins Illuminated - Angular acceleration of the earth

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makis

Greece
259 Posts

Posted - 08 Jul 2003 : 04:59:53

Dr Van Flandern,

In the past our exchanges about the subject of the angular acceleration of the earth created a bit of controversy and as a result some posters here, for reasons not clear to me, became very hostile against me and I left the board. I would like to take one more shot at this issue and I believe this time it will be cleared up. Last time I tried to resolve this by referring to some equations and that seemed not to work. So this time let's have a short dialectic discussion about this and I hope you will be willing to participate.

Question 1: Do you believe the orbit of the earth is elliptical?

Q2: If your answer is No, let's stop here. If your answer to Q1 is Yes, do you agree that the angular velocity of the earth changes as it moves in an elliptical orbit around the sun with its radious changing?

Q3: If your answer is No, please explain. If your answer to Q2 is positive, don't you agree that changes in angular velocity result in an angular acceleration?

Q4: If an angular acceleration is present in the orbit of the earth, is it of a constant magitude or not?

I think this is enough for a first round.

tvanflandern

USA
2793 Posts

Posted - 08 Jul 2003 : 10:34:36

quote:
[makis]: In the past our exchanges about the subject of the angular acceleration of the earth created a bit of controversy and as a result some posters here, for reasons not clear to me, became very hostile against me and I left the board.

I won't speak for others here. However, we would like to keep this Board directed toward interesting astronomy-related questions. Here, a subtle distinction comes into play. We encourage thoughtful challenges to basic assumptions and the fundamentals upon which all else is based. However, these should be challenges based on full familiarity with those basic assumptions and fundamentals, and the reasons they were adopted in the first place. This is not a place to obtain that familiarity because that requires teaching of elementary concepts, which wastes the time and taxes the patience of the regular participants. Books, classrooms, and the internet are examples of places where one can learn the existing fundamentals of any field.

Your queries below seem to betray unfamiliarity with the adopted meanings of angular velocity and/or angular acceleration. This is not a place to obtain that familiarity. But once you have it, this might be a place to challenge it for cause. ("Cause" does not include not liking the existing definition because it is inappropriate or confusing. The field is filled with such strained definitions. "Electromagnetic" in reference to light is a leading example of an inappropriate, confusing definition. But it is here to stay, and we must work with it as is.) What is lacking below (and in certain of your previous comments) is any indication of the familiarity with existing definitions that is a prerequisite to an interesting challenge.

One must understand the existing paradigm the way others understand it before one cab mount a reasonable challenge to it. (Understanding it as others do does not imply agreeing with it.)

quote:
Question 1: Do you believe the orbit of the earth is elliptical?

I agree with others who have deduced from observations that Earth's orbit is a very good approximation of an ellipse.

quote:
Q2: do you agree that the angular velocity of the earth changes as it moves in an elliptical orbit around the sun with its radius changing?

The Sun's motion relative to the star background is a mirror of Earth's motion around the Sun, and there is no doubt that the angular velocity of the Sun is observed to vary.

quote:
Q3: If your answer to Q2 is positive, don't you agree that changes in angular velocity result in an angular acceleration?

Look up the definitions of these terms. The term "angular acceleration" is not normally used with this implied meaning. With the normal meaning of that term, Earth has no angular acceleration. If it did, its period would change.

quote:
Q4: If an angular acceleration is present in the orbit of the earth, is it of a constant magitude or not?

See previous answer. Please make yourself familiar with the ordinary meaning of "angular acceleration", and also with "angular velocity" if need be. Regarding its elliptical motion, all of Earth's acceleration is radial, not transverse or normal. "Angular" acceleration is something different, and does not normally enter the subject of orbital motion. If Earth had thrusters to change its angular velocity directly, that would be called a "transverse" acceleration. -|Tom|-

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makis

Greece
259 Posts

Posted - 08 Jul 2003 : 11:13:46

quote:

Please make yourself familiar with the ordinary meaning of "angular acceleration", and also with "angular velocity" if need be.

Suprised. I gather you do not agree then with my definition of angular acceleration being the time rate of change of angular velocity. But this is a definition in every physics books. Do you imply than in the context of orbital mechanics, as you have learn it, this definition is not used?

quote:

Your queries below seem to betray unfamiliarity with the adopted meanings of angular velocity and/or angular acceleration. This is not a place to obtain that familiarity.

Your statement above does not provide a reason or indication of why my queries are wrong and show unfamiliarity with the subject.

quote:

Look up the definitions of these terms. The term "angular acceleration" is not normally used with this implied meaning. With the normal meaning of that term, Earth has no angular acceleration. If it did, its period would change.

What is a "normal meaning" of angular acceleration? Is there a "normal" and "some not normal" meaning?

quote:

"Angular" acceleration is something different, and does not normally enter the subject of orbital motion. If Earth had thrusters to change its angular velocity directly, that would be called a "transverse" acceleration.

Transverse acceleration is the product of the orbital radious and the angular acceleration.

Obviously, you model is also subject to the same fundamental problems of Newtonian gravitation and in this way your reaction to this very basic question can be justified.

I challenge you about the following:

If the angular acceleration of the earth is zero everywhere then its radial velocity is also zero and therefore its orbit is circular.

If I can prove this to an independent review committee would you be willing to publicly admit it and concede via a press release?

You are free to assign the members of the review committee.

P.S. It is a short proof, by the way.

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Jim

1607 Posts

Posted - 08 Jul 2003 : 11:38:46

This topic was aired before and it seems to be headed in the same direction. That is a sad thing to see. The idea is a good detail to kick around.

tvanflandern

USA
2793 Posts

Posted - 08 Jul 2003 : 15:05:19

quote:
[makis]: I gather you do not agree then with my definition of angular acceleration being the time rate of change of angular velocity.

Almost certainly not, in the context of orbital mechanics. However, you have not defined "angular velocity", so it is difficult to be sure of the meaning of your words. You seem to use the words "angular velocity" in the sense that it is used in rigid-body rotational mechanics. With that caveat, your definition would be true and convey meaning.

quote:
But this is a definition in every physics books.

It might be possible that, in a search of many books, one might be found by a confused author who misunderstands the basics. While it is common to use terms such as "angular velocity" and "angular acceleration" in connection with rigid-body rotation, I challenge you to find any physics book that defines "angular acceleration" as "the time rate of change of angular velocity" in connection with orbital motion. That just is not done because it would create a horribly wrong impression in the mind of any student about how Newtonian mechanics works.

I have the increasing concern that you are a former student who was victimized by exactly the cited erroneous impression.

quote:
Do you imply than in the context of orbital mechanics, as you have learned it, this definition is not used?

Correct. I can't speak for everyone everywhere. But no one familiar with Newtonain mechanics would make such a basic blunder.

quote:
Your statement above does not provide a reason or indication of why my queries are wrong

True. As I explained, I have no enthusiasm for teaching the basics at that level in this forum. I had hoped this might be a place to discuss interesting problems, not to study orbital mechanics 101. I fear it would tax the patience of readers, and I've chosen to spend the bulk of my personal time in research rather than teaching (although nearly everyone does some of both).

But the place for you to start is with the difference between "speed" and "velocity", which is the difference between a scalar and a vector. Once you understand vectors, orbital mechanics will become much easier to master.

quote:
What is a "normal meaning" of angular acceleration? Is there a "normal" and "some not normal" meaning?

The term can be used for the spin of a rigid body because the angular speed of rotation is approximately uniform, and any slowing or speeding of rotation can be represented by a simple scalar "angular acceleration" that is direction-independent. For example, the books I consulted define angular acceleration as "the rate of rotation change" or "the rate at which the rotation of a rotating body changes".

But if you tried to use that term in orbital mechanics, no one could tell if you meant a scalar or a vector acceleration. So the term is not used because it would be hopelessly confusing and lead students into wrong, even impossible, dilemmas.

Consider, for example, the second time derivative of the radius vector along a circular orbit. If we consider the radius vector a scalar, then this "radial acceleration" is everywhere zero. But if we consider it a vector, then the radial acceleration is -GM/r^2 in the same direction as the radius vector. So it contains the whole Newtonian universal law of gravitation.

quote:
Transverse acceleration is the product of the orbital radius and the angular acceleration.

Only for rigid rotations. Angular acceleration is not used in orbital motions because its meaning would be ambiguous, especially with regard to its directional component, as you see from my example above.

quote:
If the angular acceleration of the earth is zero everywhere then its radial velocity is also zero and therefore its orbit is circular.

I am now guessing that you are unfamiliar with vectors, or you would not make such a statement.

quote:
If I can prove this to an independent review committee would you be willing to publicly admit it and concede via a press release?

Meta Research offers both free advice and fee-based advice for those who need it: http://metaresearch.org/publications/PMRS/PMRS.asp.

At the moment, I can't see that this thread offers anything of further interest to me. But I'll keep monitoring, in case something of wider interest does turn up. -|Tom|-

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Jim

1607 Posts

Posted - 08 Jul 2003 : 19:19:33

This topic is of interest to me because there is no data that has been posted on the web to prove any of the points being made. The use of models is fine but data should be available somewhere. It seems to me the point about angular acceleration being zero is clear since there is no force to cause this to happen. But, still there seems to be no data indicating if or how much radial acceleration the orbit of Earth is subjected to by the gravity field of the sun. Models are not data as has been established in prior forums.

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makis

Greece
259 Posts

Posted - 08 Jul 2003 : 21:37:49

quote:

But the place for you to start is with the difference between "speed" and "velocity", which is the difference between a scalar and a vector. Once you understand vectors, orbital mechanics will become much easier to master.

In no place in my postings I referred to speed. I used the term velocity all along, which implies a vector. I studied Dynamics in graduate school from the book by Leonard Meirovitch, amongst others, which is heavy on vectors.

quote:

While it is common to use terms such as "angular velocity" and "angular acceleration" in connection with rigid-body rotation, I challenge you to find any physics book that defines "angular acceleration" as "the time rate of change of angular velocity" in connection with orbital motion.

True, I agree, but that's why we are here to discuss the issue. If we were to believe books on face value, Metaresearch and the Meta Model would sound absurd and there would be no point for you to even have this message board.

The term angular acceleration is avoided in orbital mechanics books but it is hidden in the integral term resulting in the angular momentum conservation. By integrating out angular acceleration variations, the prob;em is eliminated and it is carefully and cleverly omitted from orbital mechanics books. This is because no one wants such a perfect foundation to collapse on the face of very simple observations, as Jim points out in regard to astronomical data, so a lot of hand waving and cursing, just like you did, is brought against those raising the issue.

I expected better from you. I know you understand the problem but you will just go ahead and defend what you have learned and went through qualifying exams. It is a natural reaction. You have convinced yourself and everyone your taught that this is the way it should be and whoever questions it is crazy, idiot, or in the best case uneducated. I know you can do better than that.

Needless to say you never answered the question but only said that the term "angular acceleration" is not used in orbital mechanics. But if the term is a valid kinematic variable, forget about mechanics, is it zero or no in the case of the earth orbit as predicted by kinematics alone? Just forget about rigid body mechanics and consider the earth and the sun as particles, just like Newton did. You will find out that Newtonian mechanics are in conflict with observations because it is true that the earth has no angular acceleration in reality but Newtonian mechanics falsely predicts it has.

Mixing dogmatism, physics, cursing and hand waving is beyond my interests. I am interested in deciphering the Newtonian tautology and variable manipulations that assigned a physical cause to a pure geometric effect known since 550 BC and explicitely defined and computed in the Antikythera machine built in the first century BC.

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Larry Burford

USA
1355 Posts

Posted - 09 Jul 2003 : 08:23:14

Hello Makis,

I'm not sure why Dr Van Flandern is being so picky on this issue (since I'm not an orbital mechanics expert, it might be that I'm just not aware of a VERY GOOD reason for taking this stand), but it seems to be getting in the way of finding out what your complaint is. And it seems possible to work around it.

For the purposes of this discussion, I define a flexible body as "similar to a rigid body, but able to stretch and compress to a certain extent".

quote:
[makis]
Just forget about rigid body mechanics and consider the earth and the sun as particles ...

Perhaps you should move the other way - treat the Earth and Sol as a single rotating flexible body. Ignore the fact that one or more parts of this body are themselves rotating-in-place at independent rates.

Now it makes sense to speak of the ANGULAR velocity and the ANGULAR acceleration of this rotating body. And we can imagine a one to one correspondence between the various parts of this flexible body and the real Earth/Sol system.

We can define a reference angle by imagining a line between Sol and one of the "fixed" background stars.

Observations indicate that as this flexible body rotates:
1) its instantaneous angular velocity varies between a minimum and a maximum value
2) its instantaneous angular acceleration varies between a small negative and a small positive value.
3) its instantaneous "length" (the distance between the part of the flexible body that is analogous to Sol and the part that is analogous to Earth) varies between a minimum and a maximum value.

Over an integer number of rotations of this flexible body both the angular velocity and the angular acceleration are constant (at 1 rev/yr and zero rev/yr^2, respectively).

=======

Jim, Makis, Dr Van Flandern -

Can this setup be used to explore Makis' issue?

Regards,
LB

makis

Greece
259 Posts

Posted - 09 Jul 2003 : 09:38:17

[quote]

from Larry:

Perhaps you should move the other way - treat the Earth and Sol as a single rotating flexible body. Ignore the fact that one or more parts of this body are themselves rotating-in-place at independent rates.

[quote]

Larry, I am not talking about the angular acceleration of a rigid body as a result of its rotation about an axis through it, such as for instance a car wheel where the angular acceleration vector is perpendicular to the wheel plane. I am talking about the angular acceleration of a particle rotating around another particle. In the case of circular uniform motion, the angular acceleration is zero. My question was dealing the the concept of elliptical orbits. I claim that if the orbit of the earth is trully elliptical then Kinematics predicts an angular acceleration. This is avoided in orbital mechanics books because according to Newton's second law it would imply a torque application on the particle and therefore some type of aether to transmit that torque. This does not preclude conservation of angular momentum and energy. However, astronomical observations do not show a angular acceleration and this is in contradiction with Kinematics. In Mechanics, this was cleverly hidden out by the use of symbols and by hidding the resulting angular acceleration in the integration resulting in constant angular momentum.

There is more meat into this than TVF wants to admit there is. TFV claims adherence to existing doctrines and declares me ignorant.

But I will ask you a simple question: if you are rotating a bucket of water attached to a string and you release a small lenght of the string, won't the angular velocity of th bucket change? If not, something holds it constant and just increases the linear speed. If there is a radial velocity in the orbit of the earth, angular velocity must either change and so angular acceleration or a process that keeps it constant must be defined. Something is then transmititng a torque, some place, and either Newtonian mechanics is absurd or there is something out there doing that.

My solution to this is that the orbit of the earth is circular and the stories about elliptical orbits are to be investigated. In my view, the orbits are "apparently" elliptical to a Euclidean geometry based observer frame but circular in "reality" when other parameters are added.

TVF thinks this is not an interesting subject. It's his prerocative of course. He seems not interested in challenging 400 year old ideas developed when there was not even an accurate clock to measure time and distance. Like Galileo's false observations about free fall, etc.

I understand you have to reinforce certainty at schools otherwiese the educational foundation will collapse. Doing that "dirty" job requires teaching people a lot of "crap", often indistinguishable from religious doctrines. But here is Metaresearch board, our last hope...

tvanflandern

USA
2793 Posts

Posted - 09 Jul 2003 : 11:12:34

quote:
[makis]: I'm not sure why Dr Van Flandern is being so picky on this issue

Meta Research encourages challenges to mainstream science based on reasoning, observations, or experiment. At the same time, we try to provide guidance to the far-more-numerous faulty challengers out there to show them where they have gone wrong.

As a result, we hear continually from people all over the world. Experience with trying to help these people has quickly led to a few generalizations about who can be helped and who is not really seeking help at all. Especially, the former are appreciative and the latter are resentful when help is offerred.

Makis has created a situation. Instead of simply asking why mechanics is this way or how changes in angular velocity are explained, he has declared that the world is full of idiots who don't understand what they are doing and are rationalizing to maintain their picture of reality; whereas his personal genius has at last discovered the one true picture of reality regarding orbital mechanics. Meta Research does not encourage challenges based on a failure to understand the mainstream position on any issue.

In order to maintain this self-centered opinion, he has to maintain ignorance of vector mechanics, treat things called "vectors" as if they were scalars, deny the role of radial accelerations in changing angular velocity, and remain ignorant of basic astronomical observations. In this last camp, he denies simple observations showing the angular velocity of the Sun relative to the background stars increasing to a maximum in January and decreasing to a minimum in July. He ignores simple measurements of the Sun's angular diameter showing it is larger in January and smaller in July, making accurate solar eclipse predictions possible. He hasn't a clue that we can now use radar ranging to measure directly the distance from Earth to other solar system bodies, and plainly see that we are closer to the Sun in January than in July.

All these distorted world views are correctable, but only with the cooperation of the party to be educated. If his responses are always of the form that you are a genius too when you agree with him, but part of the world's mass self-delusion when you disagree with him, where is there room for change or evolution? If the mere effort to help is resented and attacked, how is one supposed to help?

quote:
Can this setup be used to explore Makis' issue?

You already have your answer from Makis. I encourage you to continue to try to find a way to get through to our friend. I would love to be shown a way. But I haven't discovered an effective approach yet. In earlier discussions, when helpful people here explained simple basics that were in conflict with the world views of various posters, those psoters became increasingly defensive and hostile, and finally left the Message Board with a few uncharitable salvos.

If you can get this individual to listen thoughtfully to a possible explanation and respond in a positive way, I will be mightily impressed with your diplomatic skills, and am prepared to apologize to Makis for treating him as learning invincible if you can discover a way to get through to him. But I don't know what else to try after reason, observations, and experiments have failed. Any delusion can be maintained if one is willing to believe that the rest of the world is part of a conspiracy of malefactors and sheep.

We all have strengths and weaknesses. One of the possible weaknesses that some people suffer from is the inability to unlearn something once learned incorrectly. As things stand, I don't see a way to deal with people who at least superficially appear to have this disability. For example, teaching Makis orbital mechanics on this MB would surely lead to another argument, probably over the definitions of terms, but not a resolution. -|Tom|-

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Jim

1607 Posts

Posted - 09 Jul 2003 : 11:44:16

All this emotiom has nothing to do with science. The simple fact is there is no force to cause angular acceleration of any orbit and I don't think this is open to any debate. What Makis is saying and me too is that data is not avalible to confirm the statements being made by TVF about the truth of Earth's orbit. There are lots of models to show that TVF is correct-where is the data?

makis

Greece
259 Posts

Posted - 09 Jul 2003 : 11:47:50

quote:

In this last camp, he denies simple observations showing the angular velocity of the Sun relative to the background stars increasing to a maximum in January and decreasing to a minimum in July. He ignores simple measurements of the Sun's angular diameter showing it is larger in January and smaller in July, making accurate solar eclipse predictions possible. He hasn't a clue that we can now use radar ranging to measure directly the distance from Earth to other solar system bodies, and plainly see that we are closer to the Sun in January than in July.

All thsee should ring a bell to you. Because you seem to lack basic understanding of what a contradiction between theory and observation means. This is due to a lack of rigor and philosophical insight. Your example of how Zeno's paradox is resolved illustrates your superficial and mandane undrertanding of science and its problems. Your so called latest "resolution" to the twin's paradox clearly illustrates you do not understand what the paradox means.

quote:

Makis has created a situation. Instead of simply asking why mechanics is this way or how changes in angular velocity are explained, he has declared that the world is full of idiots who don't understand what they are doing and are rationalizing to maintain their picture of reality; whereas his personal genius has at last discovered the one true picture of reality regarding orbital mechanics.

Uncalled for. Find a statement of mine declaring the world full of idiots or calling myself a genious. You perceive it that way because you are full of racial, scientific and other kind of biases.

There are others reading these threads and if they are unbiased will judge your statements accordingly. You are spending a lot of time attacking me instead of focussing at the issue at hand. I just asked a question based on my own interpretation of Kinematics and their relation to Newtonian Mechanics. I cannot see how a reasonable man with an acceptable sanity level will make all these statements and personal attacks.

I feel sorry once more for coming back to these threads. I let you continue your sales job of FTL gravitons to the uninformed public TVF.

Larry thanks, I won't be coming back. Metareasch is being deleted from my favorites list. It was a grand mistake coming back here.

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tvanflandern

USA
2793 Posts

Posted - 09 Jul 2003 : 12:43:14

quote:
[makis]: I just asked a question based on my own interpretation of Kinematics and their relation to Newtonian Mechanics.

And what question would that be? The only unanswered question that I saw was about whether I would hold a press conference extolling your praises if you could convince an independent review committee of your genius. I ignored the disingenuous "question" and implied insult.

Anyone who wants to understand Newtonian orbital mechanics mathematically just needs to understand one equation, which contains Newton's universal law:
d^2(r-vector)/dt^2 = (GM/r^3) r-vector
Merely knowing what the symbols mean would allow anyone to program a computer and see what trajectories result from this single equation. It is obvious to others, though apparently not to you, that any body moving at an angle relative to a circular orbit must be increasing or decreasing its speed because of changes in the radial acceleration. Those changes are sufficient to explain all "angular acceleration", whatever you chose that ambiguous expression to mean.

Anyone who wants to understand Newtonian orbital mechanics physically would be well-served by reading chapter six of Dark Matter, Missing Planets and New Comets.

quote:
I won't be coming back. Metareasch is being deleted from my favorites list. It was a grand mistake coming back here.

You have had your say through several incarnations now, and are clearly not interested in learning answers, but only in promoting your own estranged viewpoints. So let's avoid doing this repeatedly.

If you stay, let's agree that you will confine your remarks in this thread to questions about how standard Newtonian mechanics works, and forget about promoting your own agenda in this forum. You can go elsewhere on the internet for that (e.g., USENET), or set up your own Message Board.

If you leave, please take all your alter egos with you. One thing that has aggravated us from the start was when you would sign up as several personalities and post messages under another name praising your own posts. It is easy for our webmaster to trace these aliases these days. -|Tom|-

Jeremy

USA
284 Posts

Posted - 09 Jul 2003 : 22:05:35

In hopes of redirecting this thread to something less hostile I would like to ask a question about this issue. In order for perihelic shift of an orbit to occur doesn't a slight increase of the angular velocity have to happen in order for the orbit to overshoot where it "should" have been, and isn't this an angular acceleration? It seems a "torque" has to be applied and mechanical work performed to get this to happen. I know Tom that you have ascribed this effect to the Earth's interaction with the elysium. Is work being performed by the elysium to create this acceleration?

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tvanflandern

USA
2793 Posts

Posted - 09 Jul 2003 : 22:30:25

quote:
[Jeremy]: Is work being performed by the elysium to create this acceleration?

Good question. It is really the same phenomenon as trying to accelerate a body near the speed of light. It takes disproportionately more work to get a given speed increment for a body traveling near c than for a body near rest. (This is for the same reason that it takes more time and work to paddle a canoe round trip downstream and upstream when there is a current than when the water is still. So it takes more time and work for electrons to orbit atoms when the atoms are moving through the elysium than when they are at rest.)

As this applies to perihelion advance, it takes more work by the Sun's gravity to accelerate Mercury through the elysium when Mercury is traveling faster than when it is traveling slower. And that differential is what produces the torque.

The expression "angular acceleration" is not used because it is ambiguous. We have two different words to distinguish scalar motion ("speed") from vector motion ("velocity"); but we have only one word for both types of acceleration. Is "angular acceleration" a scalar or a vector? It is undefined. -|Tom|-

kingdavid

United Kingdom
61 Posts

Posted - 10 Jul 2003 : 08:59:35

quote:

quote:

(makis)
Q3: If your answer to Q2 is positive, don't you agree that changes in angular velocity result in an angular acceleration?

(Flandern)
Look up the definitions of these terms. The term "angular acceleration" is not normally used with this implied meaning. With the normal meaning of that term, Earth has no angular acceleration. If it did, its period would change.
[quote]

Hi makis, i myself thought of a similar concept of earths orbit. Hi Flandern, the above says the period would change, but what if the earth had both angular/orbital acceleration and decceleration which keeps it in a constant steady orbital period? Could this not then appear as though earth orbits in a constant motion?

Cheers
Self-teaching
dave