Circular-orbit stability for a power-law central force
= Circular-orbit stability for a power-law central force
{title2=$\Omega_r^2=(n+3)ka^{n-1}$}
For the radial <acceleration> $-kr^n$ with $k>0$, a <circular orbit> of radius $a$ has squared <specific angular momentum> $h^2=ka^{n+3}$. At fixed $h$, its radial <small oscillations> have squared frequency $(n+3)ka^{n-1}$, so the orbit is stable for $n>-3$. This is a special case of the <effective potential stability criterion>.