= Velocity kick on a circular Kepler orbit
{title2=$a'/a=(1-2\gamma\cos\theta-\gamma^2)^{-1}$}
For an instantaneous in-plane change of <velocity> of magnitude $\gamma v_K$ on a <circular orbit>, with angle $\theta$ measured from the forward tangential direction, the new <specific orbital energy> gives $a'/a=(1-2\gamma\cos\theta-\gamma^2)^{-1}$. The <specific angular momentum> gives $e'^2=1-(1-2\gamma\cos\theta-\gamma^2)(1+\gamma\cos\theta)^2$. The signed <semi-major axis> becomes negative for an unbound <hyperbolic Kepler orbit>.
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