Re: [Vo]:Black Holes from Newtonian Gravity? - discs.gif - segements.gif

[Robin van Spaandonk]

In reply to  Horace Heffner's message of Mon, 13 Oct 2008 02:08:35 -0800:
Hi,
[snip]
>I disagree.  You are ignoring the 1/r^2 nature of gravity or  
>electrostatic charge.
>
>The field near a line charge is 1/r normal to the line.  The field  
>near a plane charge is uniform and normal to the plane. The closer  
>you get to a finite line or plane segment the closer it approximates  
>an infinite line or plane.
>
[snip]
Consider the attached diagram.

With the exception of "C" (for Center), all letters label intersections. The
line segment "DF" is perpendicular to the radial line segment "BC".

Let there be a test mass at "A". We examine the component of the gravitational
forces within the plane for the moment. The arc segment "DEF" is a mirror image
of "DBF" about the line segment "DF". The forces acting on A within the plane
due to the two segments "DEFAD" and "DBFAD" exactly cancel, because these two
regions have the same area (uniform thickness of the disc is assumed). The rest
of the mass of the disc, excluding these two segments, is all to the left of A.
Hence there is a net force acting on A, pulling it to the left. This remains
valid if A is outside the plane of the disk. It only ceases to be true when A is
exactly on the axis of the disc, at which point the two segments each comprise
half the area of the disc.
Of course, the attractive force exerted by the mass of the disc also has a
component normal to the plane, and the combination of the two vectors (in the
plane and normal to the plane), produces the total force acting on the test
mass.

Regards,

Robin van Spaandonk <[EMAIL PROTECTED]>

<<attachment: segements.gif>>