I'm sad to say, this is exactly the reply I was expecting. As I expected, you
completely failed to show my math was wrong. You
completely failed to show my math was inconsistent with the Newtons Universal Laws of Gravitation. You
completely failed to support your position, other than to repeat the exact same things you said before.
To keep this short, in order to disprove my math in a scientific manner you simply cannot say "it is wrong". What you need to to discredit my math in anything vaugly resembling a scientific argument is:
- Show where the math is inconsistent with physical laws. You did not.
- Show where an error in the derivation was made. You did not.
- Show that the calculation does not produce the expected result given a known configuration. You did not.
Simply saying "your math is inconsistent with my assumptions" doesn't cut it - as we'll see below, your assumptions do not pass scientific muster - or high school physics for that matter. You can either disprove my math using the laws of physics - not personal assumption - or you have
no scientific argument against it.
ImagingGeek,
The letter ‘r’ is used, I assume, because Newton was dealing with the Earth (and maybe the Moon) when he developed this law. Therefore, ‘r’ was used in writing this law because the radius of the Earth was the specific value of the variable distance that he was concerned with.
No, the letter 'r' is used because radius is the correct measure to use. The universal law of gravitation assumes point masses; in the case of non-point masses you must use the radius (i.e. distance from the
center of mass) for the math to work.
Now, lets look at your "derivation":
g =Gmm’/d^2 =Gmm’/r^2 Where the value of r is the radius of the Earth.
If the center of mass of the Earth shifts away from the object on the surface so that the distance between the object and the new center of mass of the Earth is ‘x’ then the new weight of the object is:
g’=Gmm’/d^2 = Gmm’/x^2
The ratio of the new weight to the old weight of the object is:
g’/g =(Gmm’/x^2) / (Gmm’/r^2) =r^2/x^2
You've not added anything here you didn't have before, and the math is still wrong (or at least isn't saying what you want it to).
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.
Keep in mind that a core shift would only move a
portion of the earths mass - your formula does not take that into account. Nor does it take into account the gravity of the material which fills in the space. All it does is measure the relative change in gravity when the distance between two masses (the earth and the observer - AKA m and m') is increased.
And its easy to prove this is the case. Take an example where we rip the earth into two equal hemispheres, and move the second hemoisphere 4 radi away:
Before the rip:
Fg = Gmm'/1^2 = 1
After the rip:
Fg = 0.5(Gmm')/1^2 + 0.5(Gmm')/4^2 = 0.5 + 0.03125 = 0.53125
Your calculation:
1^2/4^2 = 1/16 = 0.0625
Obviously the wrong answer. But we can get that answer if we move the whole planet to 4 earth radi:
Fg = Gmm'/4^2 = Gmm'/16 = 1/16 = 0.0625
That there is proof-positive you math is wrong - the only way we can get your result is to move the
entire earth, rather than just the piece.
1. LAZE’S ASSUMPTION #1:
The process of consolidation of the masses forming Pangea caused a wobble in the Earth’s rotation. This wobble was countered by a force (Newton’s Third Law) whose action was to move the core(s) away from Pangea. For simplicity, I’ll say that this net force could be described as a single vector force between Pangea’s center of mass and the center of mass of the core(s) (at least initially).
This is correct. Keep in mind that under this condition the earths center of mass is to one side of the earths center of rotation, due to the unbalanced mass of the crust.
2. LAZE’S ASSUMPTION #2:
When the core(s) moved from the Earth’s center (also the axis of rotation), the inner core no longer remained at the center of the outer core; it could move independently within the molten core under the force of the previously mentioned vector force and also subject to the, now unbalanced, centripetal forces.
This is incorrect - the centripetal force was unbalanced
before the core shift; that is why there would be a precession (wobble) of the earth. Movement of the core would correct this precession, not make it worse, by re-establishing the earths center of mass on the axis of rotation. This is a simple concept you consistently get wrong.
Its so easy:
1) With an unshifted core, the earths center of mass (COM) lies between the axis of rotation and pangea, due to the extra thickness of the crust at pangea.
2) This imbalance will create a precession (wobble) of the axis of rotation, as the axis of rotation will, itself, rotate around the center of mass (tracing out a circle, if observed from a pole).
3) That wobble produces a force opposite to the direction of pangea, this will "push" the cores away from pangea.
4) As the core moves away from pangea, the wobble will decrease because COM will move back towards the axis of rotation. Once the COM is recenetered at the axis of rotation, this force will be zero and no further movement will occur.
5) In this now balanced state, there will be an equal distribution of
mass between pangea and its antipod, resulting in equal gravity at both sites.
That is what physics states will happen.
3. LAZE’S ASSUMPTION #3:
When the core(s) moved from the Earth’s center, the outer core, like the inner core, was subject to the vector force previously mentioned as well as the centripetal forces. These two forces would have distorted the shape of the outer core, the effect of which would be to shift the center of mass of the Earth further than if the outer core were able to remain spherical. An analogy would be a balloon that is depressed at its center (by the vector force) and the opposing surface spreading out due to the centripetal forces.
You're missing an important point here - that "compressive" force existed before any core shits, as it is due to the rotation of the earth and not the uneven mass distribution. The compression you speak of occurs along the rotational axis. That is why the earth has a smaller polar circumference than it's equatorial circumference. It will not be changed by anything other than changes is the rotational velocity of the earth - the law of conservation of momentum dictates that.
Nor does this provide you with a larger gravitational shift. The distortion will be centered on the cores center of mass, and extend evenly in all directions. Ergo, an equal amount of the "squished" core will be displaced towards pangea, and an equal amount "squished" away from pangea. The law of conservation of momentum dictates this. The end effect is the center of mass remains the same - you do end up with more mass along the plane of rotation, but the center of mass (from where we calculate gravity) remains the same.
4. LAZE’S ASSUMPTION #4:
As in any planetary body, density increases with depth. The densest part of the mantle surrounds the outer core. When the outer core shifts antipodally from Pangea, the spherical volume that is left vacant by the shift is filled with the densest material from the mantle. Hence, an additional movement of the center of mass (COM) of the Earth away from Pangea. This is a nonlinear movement of the COM; the rate of increase increases with shifting of the outer core.
This is simply nonsense. The denser mantle material will be filling in the space between the core and pangea,
adding not subtracting gravity. Gravity is purely attractional; adding mass can only increase it.
5. LAZE’S ASSUMPTION #5
When the outer core shifts antipodally from Pangea, the densest part of the mantle at the leading edge of the outer core (i.e., furthest away from Pangea) is shifted away from Pangea, again moving the COM of the Earth further away from Pangea. This is a nonlinear movement of the COM; the rate of increase increases with shifting of the outer core.
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.
I believe all of the above assumptions are reasonable and are based on “basic physics.”
The first is reasonable, the rest are totally wrong and could only have been derived in the complete absence of Newtons 3 laws and the conservation of momentum.
ImagingGeek, Your calcs are based on assumptions that are in conflict with those that I have listed above and are not “real world” assumptions.
And once again, you miss the point. This isn't about how you
assume the world works, but rather it is about what physics
dictate must happen.
Your assumptions fall afoul of the newtons lows of motion, and the law of conversation of momentum. That means they are wrong - start with a wrong assumption, come to a false conclusion.
The very fact you are unable to directly disprove my math, using the laws of physics is proof-positive you cannot do so. So instead you give us some laughably false "assumption" which you use in place of actual physical laws.
Now, take my calcs; premised on the following
facts:
1) The total mass of the earth, and thus its total gravitational field,remain constant. All that changes is the
distribution of that mass.
2) The changes in
local gravity will be determined by
- the "extra" gravity due to pangeas additional crustal thickness
- the "lost" gravity, due to movement of the core away from pangea
- the "added" pangea gravity due to the backflow of mantle into the space taken up by the core
- the "lost" gravity from the mantle that was displaced by the core
I know I’m starting to sound like a broken record, but your calcs must be discarded. I have shown that a shift in the COM of the Earth not only involves the cores but also the densest part of the mantle and the outer core does not maintain its spherical shape which is part of the basis for your facile analysis.
You've shown no such thing. Instead, you've made a series of unfounded and scientifically illiterate assumptions, and used them to replace the laws of physics which so readily demonstrate you are wrong.
So I reiterate my challenge - show how my calculation is wrong. Show it - using math - to be inconsistent with any law of physics. Show the math itself to be erroneous - errors in derivation, formulation or solving. Or provide an example of known grivtational shifts in which my math does not work.
After all, I was able to disprove your math using all three methods. Certantly you can disprove mine with one.
But, as I said at the beginning, this was exactly the pseudoscientific BS answer I was expecting - repetition of things you said before, a complete failure to address the math and laws of physics which show you to be wrong, and "disproofs" based on personal beliefs (assumptions in your words) rather than hard-and-fast scientific principals.
Bryan
