= Free-fall time of a uniform sphere
{title2=$t_{\rm ff}=\sqrt{3\pi/(32G\rho)}$}
= Uniform-sphere free-fall time
{synonym}
A pressureless uniform sphere initially at rest collapses under Newtonian gravity in a time depending only on its initial mass density. Solving the radial shell equation gives $\sqrt{3\pi/(32G\rho)}$. It is commonly used as a dynamical-time benchmark for cooling and <star formation>, with the gravitating density rather than gas density alone when other matter supplies gravity.
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