Relative equilibria of point vortices that lie on a great circle of a sphere

Relative equilibrium configurations of n point vortices lying on a great circle of the unit sphere are shown to satisfy a system of n polynomial equations. An upper bound for the number of relative equilibria is thereby obtained. The system can be reduced if some of the vortices have the same circulation. For identical vortices, computation of the relative equilibria reduces to finding the roots of a single polynomial in one complex variable. Several numerical examples are presented.