Radial-impulse circularization of a harmonic central orbit
= Radial-impulse circularization of a harmonic central orbit
For $\mathbf F=-A\mathbf r$, the turning radii obey $L^2=mAr_{\min}^2r_{\max}^2$. A radial impulse preserves <angular momentum>. Its circular orbit therefore has $r_c^4=L^2/(mA)$, or $r_c=\sqrt{r_{\min}r_{\max}}$. Cancel the radial velocity where the original orbit crosses $r_c$.