An investigation is made of several manifestations of the orbiting of two scattering partners. One focus is the effect on the l-average coupled states approximation and its first-order perturbational improvement, the l-average recoupled states approximation. Both methods are shown to fail completely when applied to m-dependent and degeneracy averaged differential and integral cross sections for inelastic collisions of an atom and a rigid rotor when there is significant orbiting behavior. A series of calculations is made for the He-SiO system scattering at 2.25, 9.01, 18.0, and 27.0 meV. The gradual improvement of both approximations with energy is clearly demonstrated. Additionally, close coupling differential and integral cross sections are shown to be extremely sensitive to slight energy changes in the orbiting regime. Moreover, single energy results in this regime are shown to differ significantly from results averaged over a molecular beam's energy distribution.