Integrated tidal tensor of a straight-line flyby
= Integrated tidal tensor of a straight-line flyby
{title2=$\int T\,dt=\frac{2Gm_p}{vp^2}\operatorname{diag}(1,-1,0)$}
For a perturber following $(p,0,vt)$, the <impulse approximation> integrates its <tidal tensor> to $2Gm_p\operatorname{diag}(1,-1,0)/(vp^2)$. A fixed target position therefore receives $\Delta\mathbf v=2Gm_p(x,-y,0)/(vp^2)$. The longitudinal kick vanishes after integrating the symmetric trajectory.