T = (\frac{L_{∗}}{16πa^{2}σ} )^{1/4}

t_{ff} = (\frac{3π}{32} \frac{1}{Gρ_{0}} )^{1/2}

L_{ff} ∼ \frac{ΔGP E}{t_{ff}} = \frac{\frac{3}{5} \frac{GM^{2}}{R}}{t_{ff}}