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Friday, November 21, 2014

Flux It,

The derivation for force in this post is wrong, although the conclusion that the force is zero at infinity is true.  Please refer to posts "Opps! Lucky Me" and "Flux It Too" dated 25 May 2015.

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

F0, as x

It is not absurd after all.  And the universe is safe from ever expanding.

F=i2mc212πxG.tanh(G2mc2(xxz))

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(x1)  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.