Let's deal with some of Mr. Stojanowski's comments made on Getting Crankier.
Only the latitudinal movement is relevant to angular momentum.But again, the latitudinal movement of Pangea, and its remnants, during the past 350 myrs is what is important, not just the dispersal movement after its breakup.
No. Any change in I, a body's moment of inertia (the distribution of its mass about a rotation axis), is relevant to angular momentum.
…it was the displacement of the core elements, an action which would increase the Earth’s AM to balance the reduction of AM from Pangea’s center of mass moving closer to the spin axis as it moved to a higher latitude.… an action which would increase the Earth’s AM to balance the reduction of AM from Pangea’s center of mass moving closer to the spin axis as it moved to a higher latitude.
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| CREDIT: J. Stojanowski |
Let's apply Mr. Stojanowski's hypothesis to the problem. In his work, he claims that the Earth's core was displaced by 1000 km in the equatorial plane. (see his Fig. 3 to the left). He also references a paper in Geophysical Research Letters* in which he claims they show movement of Pangaea's center of mass. More on the center of mass later. Figure 3(a) in this article (shown below) does show variation in a parameter the authors label D. The authors are attempting to quantitatively estimate the "asymmetry of continental surface." To calculate D, the authors use the first moment of the distance to the equator with respect to the surface area. This is not the center of mass.
.png) |
| CREDIT: Petrelis et al. |
However, let's use Mr. Stojanowski's assumption that the two are the same and apply the conservation of angular momentum to his model. See the previous article for a brief introduction to this principle.
Plug away. In the meantime, let's recap. I've used the conservation of angular momentum and Stojanowski's model and numbers. We find that the consequence of his model is that the Earth rotates once every 16.6 hours. This contradicts what we know the length of the day; then it was about 23 hours long.
Yes, I did assume in Getting Crankier that the center of mass stays on the equatorial plane. However, as I clearly showed in my first attempt, the moment of inertia is not the same over 250 million years. There I modeled Earth 250 mya as a sphere and a object (Pangaea) located 6371 km from the axis. And my calculation clearly demonstrates that the angular velocity must change as a result of conserving momentum.His assumptions in his calculation are:1. Pangea’s center of mass was located on the equator 250 myr.2. Today, the continental crust is distributed uniformly across the globe.Based on the above assumptions, in both cases, the center of mass of continental crust is on the equator. Therefore, the moment of inertia in both cases must be the same, meaning the angular velocity must also be the same to conserve AM.
I mentioned above that I would say something about the Earth's center of mass, but I ran across another blog that has dealt with this issue quite well. Ed Brayton** blogged at Dispatches from the Creation Wars, and on Dec. 27, 2010, guest blogger W. Kevin Vicklund wrote New Explanation for Dinosaur Extinction? Revisited. He shows how bad Mr Stojanowski's figure of 1000 km is for the core offset. The short version is that if the Earth is to rotate about its axis then the Earth's center of mass must remain at the Earth's geometric center. Mr. Stojanowski's model doesn't do that. If the core moved as he claims, the Earth would have precessed like crazy.
Yes, surface gravity at the poles is less than at the equator based on difference in distance to the Earth’s center of mass. This is evident from the inverse square law (relative to distance) postulated by Newton. It’s exactly why surface gravity on Pangea changed when the Earth’s core elements moved off-center and away from Pangea, moving the Earth’s center of mass further away from Pangea.No. The effect is due to the centrifugal term in Newton's 2nd law as I explained in the previous post. If you want to use Newton's law of universal gravitation to find the magnitude of the gravitational field near the Earth's surface, here's what you do.
The polar radius is 6357 km, and the equatorial one is 6378 km, only 0.3% larger. Use these to calculate the gravitational field, and you will quickly see that the equatorial field is only 0.6% smaller. Mr. Stojanowski may counter that his model yields a value 8% smaller for Pangaea, but as I and Mr Vicklund have shown, that core motion he postulates violates what we know about the Earth's rotation.
Mr Stojanowski. Should you reply once again, I ask that you back up any claims with physics, mathematics, and numbers.
*Plate tectonics may control geomagnetic reversal frequency, F. Pétrélis, J. Besse, J.-P.Valet, Geophysical Research Letters, vol. 38, issue 19, October 2011.
**I highly recommend Ed Brayton's Dispatches from the Culture Wars.
Getting Crankier - Part 2
ReplyDeleteIn response to my statement that only latitudinal movement is relevant to angular momentum, Mr. Priest wrote:
“No. Any change in I, a body’s moment of inertia (the distribution of its mass about a rotation axis), is relevant to angular momentum.”
If, for example, the supercontinent of Pangea had moved longitudinally without a latitudinal change, there would be no change in the magnitude of Earth’s angular momentum. Similarly, if Pangea broke apart and all continental plates could have dispersed without any change in their latitude, there would not be a change in the Earth’s angular momentum. Do you agree?
To clarify, I use the terminology “core elements”, not core, in order to make it clear that there are three elements (inner core, outer core and densest part of the lower mantle) that can take part in the displacement. All three of the core elements comprise a total of 80-85% of the Earth’s mass.
While Mr. Priest is correct in stating that the CNRS study is based on asymmetry of continental surface area relative to the equator, I don’t think it is unreasonable to suggest that continental mass followed a similar pattern.
Mr. Priest’ s calculation is not valid for several reasons:
1. He uses a core element mass of 1/3 that of the Earth, rather than the 80-85% number.
2. He uses the 2/5 MR2 equation for the I of the (Earth - core elements - Pangea). This equation is for the I (moment of inertia) of a solid, homogeneous sphere or at least spherically symmetrical to the center of the Earth in terms of mass distribution. The Earth is not a perfect sphere and when the core elements are displaced, the resulting Earth is not spherically symmetrical about the center (i.e., less dense mantle material fills the void where the core elements originally were and the large space occupied by the displaced core elements would be a vacuum since it is excluded in the second term).
3. He states D is about 100 km south of the equator. I’m not sure what period of time he is considering and, if he is using 100 km as the distance from the center of mass of Pangea to the equator, he is using an invalid number. I don’t know if is possible from the CNRS study to obtain an accurate number because the study is using an approximate, large envelope of continental mass. In other words, the value of the D parameter is not the distance from the Pangea’s COM to the equator.
4. He states that he is using 1000 km as the core element displacement because it was used in the theory. Not sure where that reference came from.
5. He omits, in his equation, the loss of Earth’s AM due to the Moon’s gravitational drag. It has been posited elsewhere that the Earth’s day gains about 14 second every hundred years due to the loss of AM to the Moon.
He then calculates what the Earth’s current angular velocity should be and finds a discrepancy between what we know it is and what he calculated. The calculation is not valid based on all of the above.
Note that if Mr. Priest believes that the latitudinal movement of Pangea was compensated for by a change in the Earth’s angular velocity, which he states, then based on the chart he posted (Petrelis et al.), scientists should have discovered changes in the Earth’s angular velocity which correspond to this chart. As far as I know, they haven’t
The same assumptions that Mr. Priest made in the prior post’s calculation were used here. They will not produce an accurate result. As stated earlier, the theory posits that the displacement of the core elements compensated, or offset, the latitudinal movement of Pangea in order to conserve the Earth’s angular momentum. Any AM difference between 300 mya and today in the length of day is due to the moon’s gravitational drag on the Earth.
Getting Cranky Part 2 continued......
ReplyDeleteMr. Priest suggests that if the core elements moved off-center the “Earth would have precessed like crazy.”
Yes, and it did when Pangea broke up. This was reported in an article that attempted to attribute the demise of the dinosaurs to this wobble:
http://archives.cnn.com/2001/TECH/space/07/05/dinosaur.wobble/
I believe the wobble was caused by the rapid longitudinal movement of the core elements as they moved back toward Earth-centricity at the end of the Cretaceous and not by the cause attributed in this article. A major wobble can dampen itself out because the Earth’s interior is deformable. The same process is designed into Earth satellites to dampen out wobbling.
I notice you criticize my calculations, but do not provide your own. I await your calculations.
DeleteGetting Crankier - Part 2
ReplyDeleteMr. Priest,
Would you agree that if the Angular Momentum effects of latitudinal movement of Pangea were compensated for by changes in the Earth’s angular velocity then scientists would find that those changes would parallel the Petrelis, et al. chart?
If you agree that it would but no matching changes in angular velocity have been found, that would imply something else compensated for the latitudinal movement of Pangea. Do you agree?
Despite your lack of calculations, I will respond.
DeleteYou write "I use the terminology 'core elements', not core." From your own work THE RISE AND FALL OF THE DINOSAURS-PART III [http://www.dinoextinct.com/page11.htm], "The shift of the Earth’s solid inner core or both the solid inner core and the liquid outer core must be considered." No mention of the mantle. Later in the same document you wrote "A shift of the inner core (and possibly outer core) would reduce the net surface gravity of Pangea."
You claim "it is [not] unreasonable to suggest that continental mass followed a similar pattern." Please back this claim up with a calculation or a reference.
I will follow your numbering to address your concerns about my calculation.
1. I use the mass of the the core, because your own work uses the core, not the mantle. See http://www.dinoextinct.com/page11.htm.
2. Fine. So instead of of (2/5)MR^2, use the more accurate [(2/5)(M-mc-mu)R^2 - (2/5)mcRc^2 - mcrc^2]. Plus where I oversimplified the core I, so use (2/5)mcrc^2, too. Plug in the numbers and you'll see that my conclusion holds. Here Rc is the radius of the core and rc is the distance from the axis to the core.
3. I got the value of D by reading the graph. Look at 250 mya, and you can see that D = -100 km. You then criticize my use of the Geophys. Res. Lett. article. I find this curious, because you are the one who introduced this article, and you intended its use as a approximation for Pangaea's center of mass. You then comment "the value of the D parameter is not the distance from the Pangea’s COM to the equator." I never wrote that it was. What I wrote is "We use a bit of elementary geometry and trigonometry to find the distance from the axis to Pangaea; rp = 6370 km."
4. You're not sure where I got the 1000 km figure from. Your own work! Let me quote THE RISE AND FALL OF THE DINOSAURS-PART III [http://www.dinoextinct.com/page11.htm: "Using a core-shift of 1000km would result…"
Delete5. I ignored many effects. See for example "Variations in the duration of the day" [http://www.iers.org/nn_10398/IERS/EN/Science/EarthRotation/LODplot.html?__nnn=true] and Lunar Laser Ranging: A Continuing Legacy of the Apollo Program. [http://www.physics.ucsd.edu/~tmurphy/apollo/doc/Dickey.pdf]. You however seem to be ignoring that I am not trying to explain the Earth's changing rotational velocity. I am only showing the deficiencies in your model, and your model fails based on elementary physics. Physics you have yet to challenge.
You then comment "if Mr. Priest believes that the latitudinal movement of Pangea was compensated for by a change in the Earth’s angular velocity, which he states." Excuse me, but where did I state that. Once again, I am only challenging your model and finding the consequences of your model based on solid physics. So your claim "any AM [sic] difference between 300 mya and today in the length of day is due to the moon’s gravitational drag on the Earth" boldly disregards the implications of your model.
With regard to the wobble, I must conclude you did not read the CNN post. The wobble in that article is in the Earth's orbit. The wobble I mention is with the Earth's rotation. The CNN article also mentions that this wobble may have occurred 65 mya. You claim that the Earth did wobble, but this article is quite clear that this result of a computer model, and this model has its skeptics. Mark Bailey, director of the Armagh Observatory, said "I'm skeptical. It seems to me that this is a very long chain of assumptions. There is no independent evidence of the wobble in the Earth's orbit, much less of the precession you claim "was caused by the rapid longitudinal movement of the core elements."
Finally, when you ask "Would [I] agree that if the Angular Momentum effects of latitudinal movement of Pangea were compensated for by changes in the Earth’s angular velocity," I must say I do not know, because there are many sources that can and will effect the Earth's angular momentum. I do know however that your model is widely in disagreement with what we know.
This will be my final comment on the matter unless you can provide calculations based on your model.
Mr. Priest,
ReplyDeleteThank you for responding, I will read your 2 posts. I would like to point out that the dinoextinct references you cite are from about 2004, when the theory was first written. Maybe they should be removed but they show the evolution of the theory.
That is why I always cite the pdf www.dinoextinct.com/page13.pdf which is the latest description of the theory (i.e, particularly with reference to core elements).
I'm not sure what calculations you want to see. There is a two-phase scenario that we can view:
1. Current continental configuration reconfigures to the Pangea supercontinent where the supercontinent's center of mass is on the equator. Since this requires continental mass to move to higher latitude, both north and south, surface gravity would be lowered due to the effect of core(s) displacement. But by how much? I can only guess (10%, 15%, 20% ?) because there is no research, that I know of, that quantifies this latitudinal mass movement.
2. Beyond (1.) above, we know that the supercontinent's center of mass did move significantly above and below the equator. These movement would have altered the Earth's angular momentum if nothing else compensated for it, the same is true of (1.) above. These movements (core and supercontinent) can be estimated and I will try to do that.
I'm not sure I know what you mean by "there are many sources that can and will effect the Earth's angular momentum" aside from extra-terrestrial impacts and the Moon's influence.
Mr. Priest,
ReplyDeleteWasn't able to post equations, etc. on this blog so I have to refer you to mine:
http://gravitytheoryofmassextinction.blogspot.com/
Please comment in (this) Oenobareus blog.