Re: Saturday Morning Puzzle, Part 2

["John S. Denker" <jsd@MONMOUTH.COM>]

At 09:01 AM 10/6/01 -0700, John Mallinckrodt wrote:

> Hmm.  I'd be interested in knowing how a distribution that places
> most of the mass in one object at arbitrarily large distances (not
> to mention in directions that cover a solid angle of nearly 2*pi)
> from any given portion of the other object could end up giving a
> larger net force than a distribution that keeps all of the mass
> within a small distance *and* a smaller range of solid angles.

Hint:  Olber's paradox.

If that's not enough of a hint, read on.

================================================================

Consider a small patch of mass ("Moe") on one disk looking across the gap
at a similar small patch of mass ("Joe") on the other disk.  Assume the gap
is tiny compared to the diameter of the disks, and assume Moe and Joe are
not too near the edge.

Now move the disks apart, doubling the size of the gap.  The effect of Moe
on Joe goes down by a factor of 2 squared.  But when Moe looks out at the
other disk, he sees not just Joe but Joe and three of Joe's friends in his
field of view (the field that used to be occupied by Joe alone).  So there
are four times as many effective sources.  Result:  the force on the two
disks is constant, independent of gap-size (except in the fringing field
near the edge).