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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).