Sticky Particles...

From the previous post "New Discrepancies And Hollow Earth" dated 23 Jun 2016, where we now denote,

$ln(cosh(\cfrac { G }{ \sqrt { 2{ mc^{ 2 } } }  }a_{\psi\,c}))=\cfrac{1}{4}$

$ln(cosh(0.7369))=\cfrac{1}{4}$

and

$ln(cosh(\cfrac { G }{ \sqrt { 2{ mc^{ 2 } } }  }a_{\psi\,\pi}))=ln(cosh(\pi))=2.450311$

what is between $a_{\psi\,c}$ and $a_{\psi\,\pi}$, where the force increases with distance away from the center?

An accumulation of other like particles.  At distances greater than $a_{\psi\,c}$, up to $a_{\psi\,\pi}$, the attached particle experiences a greater attractive force due to the increasing value of $F_{\rho}$.

$a_{\psi\,c}$ is then interpreted as the minimum value for $a_{\psi}$ that holds up a particle.  Values of $a_{\psi}$ less than $a_{\psi\,c}$ collapses the particle.

And we have a lumpy issue...Particles of various sizes that stick together.  Interestingly,

$F=\int{F_{\rho}}dx$

at $x=a_{\psi\,c}$,

$F=m\cfrac{c^2}{2}$

This is the attractive force that holds the particles in the lump together.