QUOTE(ScrewBallX @ Sep 16 2010, 11:39 PM)
Adding ...
Gravitation Inside A Uniform Hollow Sphere
The gravitational force inside a hollow sphere shell of uniform areal mass density is everywhere equal to zero, and may be proved by the following argument:
Let the sphere have a radius a. Place a point P inside the sphere at a distance r from the center where r < a; i.e., r is strictly less than a. Draw a line through P to intersect the sphere at two opposite points. Call these points and. Let the distance from P to be r1, and the distance from P to be r2.
Now place a differential area dA at , and project straight lines through P to acquire its image dA at . These two areas subtend a solid angle d at P. Let the sphere have areal mass density (kg/m2). Then the net differential attraction dF of dA and dA at P directed toward is just
dF = ( dA /r12 - dA/r22).
But dA = r12 d, and dA = r22 d by definition of the solid angle. Thus,
dF = ((r12 d)/r12 - (r22 d)/r22) = 0.
This result is true for all choices of dA and dA. The gravitational force within the sphere is everywhere equal to zero.
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holy crow.
first, newton's universal law of gravitation:
F=GMm/rr
let me state the flaw in your maths above.
first you messed up everything.
label and statement are all messed up, and could not be understand.
I tried to do your math above but I just could extract the information.
2. how do you know the mass of the inner sun and the outer right of sphere/crust?
how do you know the density of them ==
3. the gravitational force exerted on between 2 mass still obey the inverse square law.
there is only one locus neutral point (zero gravity), not everywhere.
when getting close to one side of mass, the resultant gravity will be dominant on that side.
4. to do the calculation you need the correct dimension and the mass of the whole structure,
which you don't have here, and definitely would not be able to find out.
5. such a complicated system (the hollow sphere with a core suspending at its centre),
the math would have been far more complicated.
last of all,
I might not be the champion of national math olympiad,
yet I did win some title in some national and overseas math competitions.
=)
whose word is more convincing now?
and don't tell me the next reply you are going to type is,
'I can claim that I'm Math olympiad too! no one can disprove it!'
okay okay enough =)
This post has been edited by KeNGZ: Sep 16 2010, 11:09 PM