= Gravitational binding-energy lower bound for a spherical star
{title2=$|\Omega|\ge GM^2/(2R)$}
If all mass of a spherical body lies within radius $R$, then $r(m)\le R$ in the shell-assembly <integral> for its <gravitational binding energy>. Therefore $|\Omega|=\int_0^M Gm/r(m)dm\ge(G/R)\int_0^M m\,dm=GM^2/(2R)$. The inequality is strict for an extended interior mass distribution; a thin shell gives equality. Dividing by a stipulated <luminosity> gives a lower bound on that reservoir-to-luminosity ratio. A <Kelvin-Helmholtz cooling time> also needs a structure model and the accessible fraction of gravitational release.
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