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erratum Re: Newtonian gravitational field energy (long)



I just noticed a couple of mismatched parentheses in my last post in
a couple of equations in which I manipulated the expression for u_g.
If the equations were written with normal math symbols and not in an
ascii format they would be much easier to read, and I wouldn't have made
the typo. Since the equations *need* parentheses in my ascii
representation I thought I better correct them, because even the correct
forms are somewhat difficult to read--let alone the errant ones, and I
do not want to be more obscure than necessary.

I wrote:
"
u_g=(|g|^2)/(8*[pi]*G) = (|grad([phi]|^2)/(8*[pi]*G)
=div([phi]*grad([phi])/(8*[pi]*G)) - [phi]*div(grad([phi])))/(8*[pi]*G)
=div(-[phi]*g/(8*[pi]*G)) - [phi]*[rho])/2
"
What I *meant* to write was:
"
u_g=(|g|^2)/(8*[pi]*G) = (|grad([phi])|^2)/(8*[pi]*G)
=div([phi]*grad([phi])/(8*[pi]*G)) - [phi]*div(grad([phi]))/(8*[pi]*G)
=div(-[phi]*g/(8*[pi]*G)) - [phi]*[rho]/2
"
Also, about 8 lines further down I wrote:

"Here the -[phi]*[rho])/2 term in u_g cancels against 1/2 of the
interaction energy term."

What I *meant* to write was:

"Here the -[phi]*[rho]/2 term in u_g cancels against 1/2 of the
interaction energy term."

I hope these corrections will make my obscure notation a little less
difficult to read.

David Bowman
dbowman@georgetowncollege.edu