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.

Adiabatic shielding suppresses the heating of an orbit when an external tidal tensor varies slowly compared with its orbital frequency. In a nonresonant slow encounter, adiabatic invariance of an orbital action lets the orbit adjust approximately reversibly, so a frozen-position impulse approximation overestimates the energy transfer. An orbital resonance can invalidate the simple slow-variation argument.