The motion of ions above the earth’s atmosphere is introduced by discussing the nonrelativistic motion of a charged particle in the field of a stationary magnetic dipole. Unlike the Kepler or Coulomb problem, no way is known to separate our problem into one‐dimensional problems andafortiorian exact analytic solution is not known. However, an effective potential can be identified whose study clarifies the qualitative and semiquantitative features of the bound states. We ask about the periodicity of bound states, taken for granted by one exposed only to the Kepler or Coulomb problem, and show how consideration of phase space can provide a partial answer, Poincaré recurrence. The treatment is accessible to students who have a first acquaintance with the canonical formalism and Liouville’s theorem, for example first‐year graduate students.