In reply to my derivation of the ratio of the value of ‘g’ (gravity) of Pangea vs. today’s ‘g’ which I calculated to be r^2/d^2, where r is the radius of the Earth and d is the distance between the center of mass of Pangea and the center of mass of the Earth after the core(s) shifting, you wrote:
“As I stated previously, your formula assumes the entirety of the earth's mass is moving; that is the only condition under which this ratio will produce an accurate result.”
To be precise, reread my statement before your quote above, it is pretty clear.
And it is still wrong. Being clear about a wrong concept doesn't make you right - it makes you clearly wrong.
I did the math, using the universal law of gravitation, that the only way your formula provides the shifts you claim it does is if you shift the entire mass of the earth.
You were unable to refute that - in fact, you cut that direct disproof of your formula from your reply. And you've steadfastly ignore the two scientific papers I provided that directly disproved your hypothesis.
So, in summary, you're argument in favour of your hypothesis is to ignore data.
[sarcasm] very sciency of you[/sarcasm]
Your example of splitting the Earth into two hemisphere’s is irrelevant; it has nothing to do with what we are discussing and therefore, those calculations are meaningless.
100% wrong. we are talking about the effects of shifting a
portion of the earths mass on the gravity felt at a specific point. Moving half the earths mass is
exactly the same - only simplified as we do not have to worry about movement of other portions of the earth.
And the results of those calcs are clear - your math is wrong.
BTW, your calculations in that example are totally wrong. You would have to find the COM of each hemisphere and use the distances from those points to the fixed reference point to get a meaningful number.
I was keeping things simple, since you seem to have difficulty following the math we've used already - i.e. not understanding how a ratio is not a delta. But, for the sake of accuracy, lets re-do it, using the proper COM for a hemisphere; which, BTW, is 3/8ths the radius of the sphere for a uniform object. In the case of a split earth it'll be larger (back-of-the-napkin approximation gives me ~2/3rds), due to the denser core, but for simplicity we'll use 3/8ths:
Fg = 1/(3/8)^2 + 1/4^2
Fg = 0.141 + 0.0625
Fg = 0.2035
Your calc:
1^2/4^2 = 1/16 = 0.0625
You're math is still wrong. The only way your math provides the correct shift is to move the entirety of the earth.
You are confusing what I wrote. The unbalanced centripetal (or centrifugal) forces that I specified applies to the core(s) that have shifted from the central position, I was not referring to the entire Earth.
You cannot do that - the cores are not closed systems, and therefore you cannot ignore the outside environment. The very force applied to the cores comes from the remainder of the earth; no "rest of earth" = no forces = no movements of the core. This is basic mechanics - you cannot treat an open system as a closed one.
My wording is very clear but you are distorting what I wrote.
In addition, your comment that the movement of the core would reestablish the Earth’s COM on the axis of rotation is the biggest error you have made. I must emphasize this point:
THE CONSOLIDATED CRUSTAL MASS OF PANGEA IS MUCH, MUCH SMALLER THAN THE CORE(S), THEREFORE THE SHIFT OF THE CORES RESULTS IN THE EARTH’S COM MOVING AWAY FROM THE AXIS OF ROTATION.
That is no different that what I was saying previously. But what you consistently get wrong is where the force that moves the cores comes from, its magnitude, and what happens to it as the core moves. I assume you're errors come from a lack of understanding of newtons 3rd law and the conservation of momentum - that is all you need to see you are wrong.
Lets make it simple, lets first define terms:
COM = center of the
earths mass
COR = center of the earths rotation
1) The force on the core is solely a product of the uneven distribution of mass due to pangea. Pangea's additional mass moves the COM towards pangea, and away from the COR. This now creates a force, as the COM is no longer at the same position as the COR.
I.E. COM != COR.
2) This precessionary force is outwards - i.e. as viewed from the COR, the moment of this force will be towards pangea..
3) The
magnitude of the presessionary force (specifically, its moment) is proportional to the separation COR is separated from COM. The larger the separation, the larger the force (moment).
I.E. F is proportional to COR-COM
4) Since the mantle is an incompressible fluid, this force will be passed onto the solid core (ignoring viscosity). This force will push the core away from pangea, as dictated by by newtons 3rd law (equal and opposite reaction).
I.E. F(pangea) = -F(core)
5) As the core moves away from the pangea, the earths COM also moves away from pangea. Therefore the separation of COM and COR decreases
I.E. [COM-COR]
t=0 > [COM-COR]
t>06) At some point the core will move sufficiently such that COM = COR. At this point COM-COR is zero. Since F is proportional to COM-COR, F is now zero.
At this point the core no longer moves; equilibrium has been re-established.
You cannot have a larger shift than that - it defies both newtons 3rd law, and the law of conservation of momentum.
Anyways, I've clipped much of the rest you wrote, as you're simply repeating the same mistake again and again. You've invented some magical force that simply does not exist.
Wrong again! As the core(s) move away from Pangea, the Earth’s COM also moves in the same direction. The densest part of the mantle will move directly toward that new COM, hence away from Pangea and lowering ‘g’ on Pangea further.
You love shooting yourself in the foot - don't you. You're treating the core as if it were in a vacuum and gravity was the only force present. Problem is, the core is suspended in a fluid, so we're talking about fluid dynamics - AKA a major part of my ol' PhD thesis. What we have here is the movement of an incompressible fluid around a solid object; gravity is not a factor here as the particles making up an incompressible fluid don't experience a net gravitational force - the force of gravity is exactly equaled in a fluid by the buoyancy of the fluid itself (otherwise, fluids would compress).
So you're assumption #1 is fatally flawed - the mantle will flow as a fluid would; not as a particulate solids in a vacuum.
Secondly, when a solid object moves through a fluid, the fluid around it stays stationary (ignoring the effects of viscosity), and thus it is
only the displaced fluid that flows. So what you will end up with, when the core moves, is a movement of the mantle in front of the core to behind the core. If the core remains in the lower mantle, then that is the mantle that will flow. If it goes above that depth, then lower-density upper mantle will be what flows.
Because the mantle is viscous (i.e. not a perfect fluid) there will be some flow of the surrounding material - generally speaking this will result in draw-down of the upper mantle on the pangea side, and upwelling of denser mantle on the antipodal side. Since the mantle is constrained, this will have the effect of pushing additional upper mantle from the antipodal side to the pangea side.
In response to Laze’s Assumption #5, you wrote:
“Once again, total nonsence. The material being pushed upon has two options - flow up, or flow around the core to fill the void. Unless you're proposing crust-rupturing flows, the later will predominate.”
Wrong again! It can’t flow around, read my response to Laze’s Assumption#4. The resultant densest part of the mantle will still be a concentric (or as close to concentric as possible) ring layer around the shifted core(s) resulting in the COM moving further away from Pangea. Therefore, your “flow around” is wrong.
Only in a world free of fluid dynamics would this be the case. But hey, 100 pages of my PhD thesis were only on particles movements in fluids - so what would I know?
BTW, a primer for you:
http://books.google.com/books?id=KbzBnE6...ved=0CDUQ6AEwAQ==================================================
So long story short:
1) You are still completely unable to refute my math, other than by your same old trick of sticking your fingers in your ears and repetitively screaming "you're wrong, you're wrong, you're wrong" whilst rocking back and forth.
You remind me of these guys:
Anyways:
1) If you had legitimate, mathematic/scientific proof that I was wrong, you'd have shown it to us by this point. Ergo, the only logical conclusion for us at this junction is you cannot disprove the math.
2) Your "hypothesis" requires that we ignore newtons 3rd law, ignore the law of conservation of momentum, and ignore fluid dynamics in general. I.E. it requires that we ignore science. That makes you "hypothesis" a clear-cut case of pseudoscience.
If it were legit, you'd be able to show us
mathematically how you are not defying ma = -ma and F = d/dt(mv).
Show us the math - show us how your little forumla is something more than the ratio of force when a single object is moved relative to the observer. Show us how you can move the core past the equilibrium point without violating the law of conservation of momentum. Show us where the force to move the core comes from without violating newtons 3rd law.
Don't worry, my expectations for you are low. I'm ready for another round of "you're wrongs" combined with more scientifically illiterate ramblings.
Bryan
