Centrifugal barrier ($V_{\mathrm{eff}}(r)=\Phi (r)+L^2/(2r^2)$)

For a central gravitational potential and nonzero specific angular momentum $L$, the positive $L^2/(2r^2)$ contribution to the radial effective potential can prevent the orbit reaching the centre at finite energy. It dominates the attractive $-\mu /r$ term at small $r$ in a Kepler orbit. A more singular attractive term may overcome it: for $\Phi =-\mu /r-\mu a/r^2$, the net inverse-square coefficient is $(L^2-2\mu a)/2$, so a central barrier exists only when that coefficient is positive.