On one approach to the optimization of low-thrust station keeping manoeuvres

A simple and effective mathematical method to calculate optimal station-keeping manoeuvres by means of electric propulsion is suggested. The method is based on a linearization of the satellite motion near a reference orbit. Two versions of the method allow station keeping both in an assigned position and in any position of the orbit. The method is fully analytical for the two-body problem and takes a simpler form for the circular assigned orbit. The suggested method may also be used in the case when constraints are imposed on the thrust direction due to specific features of the satellite stabilization mode. An application of the method to any force field is shown. Illustrative examples of satellite station keeping in a circular orbit are given. Both cases of the station keeping, i.e., in an assigned position and in an assigned orbit, are considered without and with a constraint on the thrust direction.