This is very strange. I noticed that if I use a density that falls with 1/r, 1/r^2, 1/r^3, even 1/r^1.1 or 1/r^1.01, the force and energy at the edge of the disk are still the same as that of a sphere with the same total mass at the same distance. The only way it doesn't appear to work this way is with 1/r^0, for uniform density. Apparently, as long as the density climbs toward infinity at the center, we will get the same force and energy as that of a sphere. I'll play around with it some more to be sure.

__________________
Let's put together the pieces of The Grand Puzzle . (website)

"Let's define another operator, Sz, which we won't pay any attention to."
"This transformation will automatically make zero equal zero."
"It may be true that zero equals zero -- and that is certainly an equality -- but I don't want to go into the details at this time."