Conclusion
Space Trajectories. Low Thrust Orbital Transfer

This article presents the two main problems involved in positioning an electrically propelled satellite, and the methods used to solve them.

For the positioning of satellites in high orbit, the objective is to ascend the perigee and apogee while minimizing the transfer time. The optimal control problem can be reduced to an unconstrained minimization with four angular variables taking values close to zero. The use of a gradient-free algorithm avoids the usual numerical difficulties (sensitivity to initial adjoint, integration accuracy). This method enables rapid resolution for all transfer configurations (initial orbit, illumination), taking eclipse transits into account.

When positioning satellites in low-Earth orbit, the aim is to change the orbital plane while minimizing power consumption. The optimum solution is to use a drift orbit to...