BOUND ORBITS WITH POSITIVE ENERGY

A study of the gravitational interaction of a unit point mass moving e xternal to (r>R) but under the influence of a fixed very thin ring of radius R and mass of M (M much greater than m) is presented. We consid er the case when the motion of the point mass is restricted to the pla ne of the ring. With this restriction, it is possible to find trajecto ries for which the system has a positive total energy, and yet the poi nt mass is bound to, and doomed to collide with, the ring. An example of a numerically iterated trajectory is included to support and illust rate this conclusion. (C) 1998 American Association of Physics Teacher s.