Saturday, August 9, 2014

Thermal Mass

If we start from,

T(x)=AxT(x)=Ax

A body experiences gravitational effect wholly due the mass behind it,  the net effect of all mass above the sphere containing the hot mass is zero.

If we introduce the concept of thermal mass, where

Mthermal=T4(x)={Ax}4Mthermal=T4(x)={Ax}4,    numerically

We have the total  MthermalMthermal  behind the body at point  xx from the center of  TT.

MT=x04πx2T4(x)dx=Cx04πx21x2dx=C.4πxMT=x04πx2T4(x)dx=Cx04πx21x2dx=C.4πx

where  C=A4C=A4  is a constant.

Then we consider a hot body of total equivalent mass  C.4πxC.4πx,  what is its thermal gravity outwards?   If we consider spheres of area

4πx24πx2

and the total thermal gravitational flux through them from a unit mass of  TT,  assuming space is empty and nothing else affects the flux between  xoxo  and  xx,

gTo.4πx2o=gT.4πx2gTo.4πx2o=gT.4πx2

and that at  x=xox=xo,  GT=gTo.4πx2oGT=gTo.4πx2o

gT=GT4πx2gT=GT4πx2    per unit mass

GTGT  increases with equivalent mass by  C.4πx

gT=GT4πx2C.4πx

Let  GTo=GTC

gT=GTox

This gravity is in the direction of  x,  outwards.  This is the result from the post "Thermal Gravity And Lost Innocence" previously,  that is to say the equivalent Thermal Mass concept

Mthermal=T4(x)  

assumes that  gT=GTox.  This Thermal Mass generates a positive gravity outwards.