Under the steady condition, the spherical geostrophic wind relationship in spherical coordinates (λ,φ,r) is applied to illustrate that when isobars take the simplest zonal distribution, the Antarctic is at a low ambient pressure, while the Arctic is at high. However, when friction is incorporated into the geostrophic wind relationship, the closed vortex over Antarctic and Arctic will turn to a spiral vortex, and there will exist a three-dimensional heteroclinic orbit between Antarctic and Arctic on the spherical surface.