Tidal impulse heating of a spherical galaxy
= Tidal impulse heating of a spherical galaxy
{title2=$\Delta U_g=\frac{4G^2m_p^2m_g}{3v^2p^4}\langle r^2\rangle$}
If the initial stellar velocities are uncorrelated with the <impulse approximation> kicks, mean specific heating is $|\Delta\mathbf v|^2/2$. Spherical position averaging gives total heating $4G^2m_p^2m_g\langle r^2\rangle/(3v^2p^4)$, where the mass-weighted mean square radius must be finite.