Optimal strategy for geostationary orbit acquisition using ion propulsion

The geostationary satellite for telecommunication, Artemis, is equipped with a chemical propulsion system and an ion propulsion system. Because of the third-stage ignition failure of the Ariane V launcher, the low-thrust propulsion system is used to complete the transfer orbit to geostationary Earth orbit. The optimal trajectory is determined using Pontryagin's principle. All constraints for the thrust direction, due to the initial design and onboard breakdown, are considered in the optimization process, and the minimum-time problem is solved. The effect of perturbations, namely, the gravitational force of the sun and the moon, the oblateness and triaxiality of the Earth, and the solar radiation pressure, are considered. The performances of the transfer orbit and the optimal thrust strategy are presented for every case. The transfer time, considering the perturbations, increases by 20 days with respect to the Keplerian case, but this does not imply an increase in propellant mass consumption. Finally a comparison with a solution obtained using a parametric optimization process is given. The parametric optimization results are close to those of the Pontryagin solution, but do not allow the satellite to obtain the best transfer time. In fact, the control strategy efficiency depends on the number of variables used in the process, and a time-variable strategy is possible only with an enormous increase of the computational effort, although it is natural when the Pontryagin principle is applied.