Hyperbolic orbit ($e>1,\epsilon >0$)

An unbound Kepler orbit under attractive inverse-square law gravity is a hyperbola with the attracting center at a focus of a conic. Writing $\mu =GM$ and $h$ for angular momentum per unit mass, its eccentricity satisfies $e^2=1+2\epsilon h^2/{\mu }^2$, where $\epsilon >0$ is the specific orbital energy. A nonzero incoming speed $v$ at infinity gives $\epsilon =v^2/2$.