Deflection angle ($\delta$)

For a trajectory with incoming and outgoing straight asymptotes, the deflection angle is the angle between its limiting incoming and outgoing velocity directions. For an attractive hyperbolic orbit of eccentricity $e$ and impact parameter $d$, $\sin (\delta /2)=1/e$ and $\tan (\delta /2)=GM/(d{v}^2)$, where $v$ is the incoming speed at infinity. The incoming velocity points opposite to the incoming radial direction; ignoring that reversal gives the wrong angle.