= Single-encounter escape velocity bound
{title2=$u>(\sqrt2-1)/2$}
For a particle initially having <semimajor axis> one and encountering a circular <planet> at radius one, the incoming stellar-frame speed is one. A conservative encounter at <planet>-relative speed $u$ changes the stellar-frame velocity by at most $2u$. Since stellar escape requires speed $\sqrt2$, a necessary bound is $u>(\sqrt2-1)/2$. Retaining the outgoing relative-velocity geometry sharpens the necessary bound to $u>\sqrt2-1$. Neither inequality by itself guarantees a realizable deflection at a specified <impact parameter>.
Back to article page
