Re: shell theorem

On Nov 10, 4:04 pm, winston71 <donke...@xxxxxxxxxxxxx> wrote:
On Nov 11, 1:48 am, eric gisse <jowr.pi.nos...@xxxxxxxxx> wrote:



On Mon, 10 Nov 2008 15:30:03 -0800 (PST), winston71

<donke...@xxxxxxxxxxxxx> wrote:
Hello,
From wikipedia "1. A spherically symmetric body affects external
objects gravitationally as though all of its mass were concentrated at
a point at its center."

I don't understand the integration.

Does this mean that you do not understand integration in general
(i.e., you don't know Calculus), or just not in this specific case?
Have you had multi-variable calculus? Do you know know the
"divergence theorem"? If so, just apply it; if not, look it up. For
example, http://en.wikipedia.org/wiki/Divergence_theorem is a fairly
clear presentation.

I tried to make a computer
simulation (million random points represent a sphere, there is a test
point outside the sphere, calculate and add each gravity force
vector), but the results came out wrong; total force is minimum when
sphere radius touches test point, and gets stronger as sphere radius
gets smaller (number of sphere points is constant and test point
coordinates is constant). Did anyone try such a simulation and got
good results? Thanks.

Divergence theorem.

Look it up.

Sorry I don't understand that either. At least can you clarify for me
what "spherically symmetric" means? Would a mass system of 6 points
which are at the center of a cube's faces be spherically symmetric?

No. Spherically symmetric means that any rotation (about the center)
leaves the mass distribution exactly the same. In your case, a small
rotation moves the masses off-axis, so you do not have spherical
symmetry. I suspect your million random points are also not
spherically symmetric---not even close.

R.G. Vickson

I
could add just 6 vectors and see where my simulation went wrong..

.

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