Amnesia's Dream: Space Density Under Temperature

Saturday, August 9, 2014

From the post "Possibilities, Possibilities, And God Created More Possibilities",

d_{s} (T) = \frac{(d_{T_{m a x}} - d_{n})}{- l n (T_{m a x}^{2})} (l n (x) - l n (A^{2})) + d_{n}

${ d }_{ s }(T)=\cfrac { ({ d }_{ T_{ max } }-{ d }_{ n }) }{ -ln({ T_{ max }^{ 2 } } ) }( ln(x )-ln(A^2))+{ d }_{ n }$

d_{s} (T) = A . l n (x) + B

${ d }_{ s }(T)=A.ln(x )+B$

A plot of log( x ) + 1 is shown below

When

T = T_{m a x}

$T=T_{max}$ space density is

d_{T m a x}

$d_{Tmax}$ when

T = 0

$T=0$ ,

d_{s} = d_{n}

$d_s=d_n$ at normal space density. The derivative of space density,

\frac{d (d_{s} (x))}{d x}

$\cfrac{d(d_s(x))}{dx}$ gives thermal gravity.

This is assuming that

g_{T} = \frac{G_{T o}}{x}

$g_T=\cfrac{G_{To}}{x}$ .

Saturday, August 9, 2014