= Natal kick binding criterion
{title2=$|1\pm q|<\sqrt{2f}$}
For an initially circular binary losing mass instantaneously, let $f$ be the retained total mass fraction and $q$ the kick speed in units of the initial relative orbital speed. A kick exactly parallel or opposite to the exploding star's <velocity> leaves negative relative <orbital energy> precisely for the title inequality. Equality is marginal escape. For an opposite kick $q=1$, the relative <velocity> and <angular momentum> vanish: negative <energy> then produces a radial collision, rather than a persistent finite-pericentre binary.
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