Galactic dynamical time
= Galactic dynamical time
{title2=$t_{\rm dyn}\sim GM/\sigma^3$}
A <galaxy> of characteristic radius $R$ and <velocity dispersion> $\sigma$ has crossing time $R/\sigma$. Gravitational balance gives $GM/R\sim\sigma^2$, hence $t_{\rm dyn}\sim GM/\sigma^3$. A numerical coefficient depends on the radius definition, density profile, and whether one uses a crossing, orbital, or free-fall time; these are not identical clocks.