Circular-orbit migration rate from disk torque
= Circular-orbit migration rate from disk torque
{title2=$\dot r_0=-2\Gamma/(M_sr_0\Omega)$}
For a fixed mass on a Keplerian <circular orbit>, $L_s=M_s\sqrt{GM_*r_0}$ has derivative $M_sr_0\Omega/2$. The <torque> on the satellite is minus the <torque> $\Gamma$ on the disk. This gives the displayed drift law. In the <density-slope satellite torque> model, $\dot r_0=-(8\chi/9)\beta q(\Sigma_0r_0^2/M_*)r_0\Omega(H/r_0)^{-2}$.