Minimum-separation binding-energy bounds
= Minimum-separation binding-energy bounds
{title2=$B_0\leq rU\leq A_0$}
For positive <masses>, let $r$ be the actual minimum pairwise separation and use positive binding <energy> $U=\sum_{j<k}Gm_jm_k/r_{jk}$. If $m_{(1)},m_{(2)}$ are the smallest <masses>, then $Gm_{(1)}m_{(2)}\leq rU\leq G\sum_{j<k}m_jm_k$. Thus $U^{-1}$ is comparable to $r$ with constants depending only on the masses.