The potential, , for a Plummer sphere is shown. An orbit with particular angular momentum has an effective potential, _{eff}. The circular orbit, radius R_{g}, is the minimum energy orbit with this angular momentum. A radial impulse adds energy (but no AM) to yield an orbit that oscillates in radius.
In the limit of small amplitude oscillations, the form of the minimum in _{eff} is parabolic, giving SHM motion in radius.
