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Some Numerical Integrations of Cavendish's Bobs



Well, I fixed a couple of little problems in my 18 line 3d numerical
integration code: used double precision to handle the infinitesimals;
then eliminated the radial component of self force which cancels,
leaving the axial components to be summed.

How thick does a disk - or cylinder, if you will, need to be
to compete with the spherical configuration?

Well, according to this little model (which would look much the
same in basic, pascal, fortran, who knows, maybe even VBasic),
a disk of equal volume and in contact with a sphere of radius r,
would need to be about 1/3 r thick to equal a sphere's attractive
quality, at which point the disk's radius is about 2r
If it gets any thicker it starts to make a second sphere look
*mildly* less attractive.
If in contact with a sphere, the disk's gravitational force of attraction
appears to be maximized for a cylindrical thickness of 1 r and a radius
around 1.16 r.

The disk seems to maintain its modest superiority for any separation
from a sphere.

How very intuitive! :-)



brian whatcott <inet@intellisys.net> Altus OK
Eureka!