Angular acceleration of the earth

tvanflandern
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21 years 4 months ago #6230 by tvanflandern

Reply from Tom Van Flandern was created by tvanflandern

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=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.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

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.)

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Question 1: Do you believe the orbit of the earth is elliptical?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

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

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=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?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

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.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Q3: If your answer to Q2 is positive, don't you agree that changes in angular velocity result in an angular acceleration?<hr height=1 noshade id=quote></BLOCKQUOTE id=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.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Q4: If an angular acceleration is present in the orbit of the earth, is it of a constant magitude or not?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

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
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21 years 4 months ago #5975 by makis

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<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>

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

<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

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?

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=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.

<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

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

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=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.

<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

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

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=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.

<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

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
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21 years 4 months ago #6042 by Jim

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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.

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tvanflandern
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21 years 4 months ago #6112 by tvanflandern

Replied by tvanflandern on topic Reply from Tom Van Flandern

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>[makis]: I gather you do not agree then with my definition of angular acceleration being the time rate of change of angular velocity.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

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.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>But this is a definition in every physics books.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

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.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Do you imply than in the context of orbital mechanics, as you have learned it, this definition is not used?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

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

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Your statement above does not provide a reason or indication of why my queries are wrong<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

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.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>What is a "normal meaning" of angular acceleration? Is there a "normal" and "some not normal" meaning?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

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.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Transverse acceleration is the product of the orbital radius and the angular acceleration.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

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.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>If the angular acceleration of the earth is zero everywhere then its radial velocity is also zero and therefore its orbit is circular.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

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

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=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?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

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

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
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21 years 4 months ago #5977 by Jim

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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
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21 years 4 months ago #6113 by makis

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<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=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.

<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

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.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=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.

<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

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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