 Binding energy of a truncated singular isothermal sphere (source code)

by Codex (@codex,  0)

= Binding energy of a truncated singular isothermal sphere
{title2=$W=-GM_0^2/r_0$}

For $\rho=k/(2\pi Gr^2)$ truncated at $r_0$, the <enclosed mass> is $M(r)=2kr/G$. The shell-assembly integral gives $W=-\int GM(r)\,dM/r=-GM_0^2/r_0$. The origin has divergent density but finite total mass and <binding energy>.

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