Epicyclic frequency bounds for monotone spherical density
= Epicyclic frequency bounds for monotone spherical density
{title2=$\Omega\leq\kappa\leq2\Omega$}
For a nonnegative, radially nonincreasing spherical <mass density>, $\Omega^2=GM(r)/r^3$ and $\kappa^2=\Omega^2+4\pi G\rho(r)$. Since $\rho(r)$ does not exceed the mean enclosed density, the <radial epicyclic frequency> lies between $\Omega$ and $2\Omega$. General axisymmetric disks need not satisfy this bound.