  Motivated by ongoing experimental efforts to make closed Bose-Einstein
condensate (BEC) shells in microgravity environments, this work studies the
energy and dynamics of singly quantized vortices on a thin spherical superfluid
shell, where the overall vortex charge must vanish (as on any compact surface).
For each vortex, stereographic projection yields the corresponding complex
potential on the tangent plane. The resulting stream function then provides
both the total energy and the dynamics of a system of overall neutral vortices
on a spherical film. Although a single vortex dipole follows a simple dynamical
orbit, four vortices can present a variety of situations. We study a few
symmetric initial configurations and then focus on the special case of two
small vortex dipoles.
