= Solution
The <corotation radius> is where the stellar spin matches <Keplerian rotation>:
$$
r_{\rm co}=\left(\frac{GM}{\Omega_m^2}\right)^{1/3}.
$$
A parcel forced into corotation at $r_m$ has outward <centrifugal acceleration> $\Omega_m^2r_m$. This exceeds the inward <gravitational acceleration> when
$$
\boxed{r_m>r_{\rm co}\quad\Longleftrightarrow\quad\Omega_m>\Omega_K(r_m).}
$$
This is the onset condition for a centrifugal <propeller effect>. It does not by itself guarantee escape to infinity. For example, a parcel released with only azimuthal speed $\Omega_m r_m$ has nonnegative <specific orbital energy> only if
$$
\frac12\Omega_m^2r_m^2-\frac{GM}{r_m}\geq0
\quad\Longleftrightarrow\quad r_m\geq2^{1/3}r_{\rm co}.
$$
Additional magnetic work, radial motion or <pressure> can alter that escape condition.
Back to article page
