  Low-thrust orbital transfers are difficult to optimize by indirect methods.
The main issues come from the costate guess and from the numerical propagation
accuracy required by the shooting method. In the case of a coplanar
minimum-time low-thrust transfer with eclipses, an analytical costate guess is
proposed. The optimal control problem reduces to an unconstrained minimization
problem with two unknowns. A derivative-free algorithm yields a quasi-optimal
solution from scratch in a few minutes. No specific guess is necessary and the
algorithm properties ensure finding the global minimum of the unconstrained
problem. The method is applicable to thrust levels from large to very low and
to any eclipse configuration, as exemplified on a transfer towards the
geostationary orbit.
