The following diagram shows the force density, Fρ, on the surface of a sphere at a radius x,
The total force within the volume, Fv is,
Fv=Fρ43πx3
Imagine all this forces being distributed uniformly on the surface of the sphere (4πx2), the total flux is then,
FA=Fρ43πx314πx2
When the total flux is conserved, at x1 and x2
F1.4πx21=F2.4πx22=FA
F1=FA14πx21
as such given a general radial distance x,
F=FA4πx2=Fρ43πx314πx214πx2=Fρ112πx
F, F1 and F2 are in Newtons (N).
So, if the force density, Fρ is a constant as in the post "Constant Of Integration Used Up", then
F=Fρ112πx, Fρ=constant
F→0, as x→∞
It is not absurd after all. And the universe is safe from ever expanding.
F=i√2mc212πxG.tanh(G√2mc2(x−xz))
There is no need for go to shift −F up.
It is however still very interesting that F should reverse sign, and turn positive.
A comparative plots of 1x2, 1xtanh(x−1) and 1x is given above. tanh(x) is the lowest of them all, and passes below y=0 before tending towards zero as x→∞.
This positive gravity outwards might explain why some asteroid (unconfirmed report of 2012 da14 asteroid is slowing down) decelerate on approach to earth.