 Minimum-separation binding-energy bounds

For positive masses, let $r$ be the actual minimum pairwise separation and use positive binding energy $U={\sum }_{j<k}G{m}_j{m}_k/r_{jk}$. If $m_{(1)},m_{(2)}$ are the smallest masses, then $G{m}_{(1)}{m}_{(2)}\le rU\le G{\sum }_{j<k}{m}_j{m}_k$. Thus $U^{-1}$ is comparable to $r$ with constants depending only on the masses.