# How to calculate the corotation radius?

I am studying this paper:

P.Ghosh & F.K.Lamb, APJ, 232, pag.259 (1979)

I do not understand how the authors calculate the corotation radius, $$r_{co}$$, where the matter of the disk has the same angular velocity of the neutron star.

• It turns out that the corotation radius is the light cilynder radius. See Shapiro & Teukolsky "The physics of Compact Objects" pag. 284. Commented Jan 22, 2019 at 15:07
• If you know the rotation rate of the center of mass body, then you can calculate the Keplerian orbital velocity required to match that rate, which will also give you the orbital altitude/radius. This is for non-relativistic orbits. Things change slightly if relativistic speeds are necessary. Commented Jan 22, 2019 at 15:08

If we assume a test mass orbiting a body of mass $$M$$, with spin rate $$\omega$$ and assume Kepler's third law holds, then the co-rotation radius $$r_{\rm co}$$ is given by $$r_{\rm co} = \left( \frac{GM}{\omega^2} \right)^{1/3}\ .$$