  We consider the Zermelo navigation problem on the ellipsoid of revolution
(spheroid) in the presence of a perturbation $W$ determined by a mild velocity
vector field, $|W|<1$, with application of Finsler metric of Randers type in
the context of the corresponding optimal control represented by a
time-efficient ship's heading $\varphi(t)$ (steering direction). As the example
we present the solutions to the problem on an oblate ellipsoid with acting
infinitesimal rotation.
