 Impulse approximation

In a rapid encounter, the impulse approximation holds stellar positions fixed while integrating an external acceleration over time. A stellar velocity kick is $\Delta \mathbf{v}=\int {\mathbf{a}}_{\mathrm{tidal}}(t)dt$. If the encounter time $p/v$ is much shorter than the orbital time ${\Omega }^{-1}$, this gives reliable leading tidal heating for a weak, distant encounter. Slow perturbations require adiabatic shielding of tidal encounters instead.