Exponential-disk Keplerian asymptotic
= Exponential-disk Keplerian asymptotic
{title2=$v_c^2=GM/R\,[1+9R_d^2/(2R^2)+O(R^{-4})]$}
For an <exponential galactic disk>, the first nonspherical term in the <Legendre expansion of thin-disk gravity> is positive and proportional to $R^{-3}$ in $v_c^2$. The missing enclosed mass and exterior-ring terms are exponentially small at large radius. Hence the <galaxy rotation curve> approaches the point-mass Keplerian curve from above.