M = ρ V = ρ(\frac{4}{3})πR^{3}

L ∝ M ∝ R^{3}

L^{1/3} ∝ R

\frac{v^{2}}{R} = \frac{GM}{R^{2}} = \frac{G (\frac{4}{3})πρR^{3}}{R^{2}}

v ∝ R

v ∝ L^{1/3}

Δ(log v) = \frac{1}{3} Δ(log L)