  The aim of this note is to compare the averaged optimal coplanar transfer
towards circular orbits when the costs are the transfer time transfer and the
energy consumption. While the energy case leads to analyze a 2D Riemannian
metric using the standard tools of Riemannian geometry (curvature computations,
geodesic convexity), the time minimal case is associated to a Finsler metric
which is not smooth. Nevertheless a qualitative analysis of the geodesic flow
is given in this article to describe the optimal transfers. In particular we
prove geodesic convexity of the elliptic domain.
