Many-revolution, low-thrust maneuvers in vicinity of geostationary orbit

Practical approaches to placing low-thrust spacecrafts at an operation poin t in geostationary orbit, transferring it between operation points, as well as de-orbiting the spacecraft (with a reactive acceleration of 10(-2)-10(- 5) m/s(2)) are considered. With the help of these approaches, the trajector ies of multi-revolution maneuvers for semicircular orbits with a duration u p to several months long (with the eccentricity up to 0.1) can be calculate d exactly. The presented methods use both continuous transversal multi-revo lution maneuvers and a series of finite-duration maneuvers. The proposed ma thematical model introduces pseudo-maneuvers with either positive or negati ve direction for every elementary interval, with the intervals being semi-r evolutions covering the whole possible duration of the maneuver. This makes it possible to state the problem in terms of classical linear programming with a dimension equal to four times the number of mission loops. The conti nuous transversal maneuvers are obtained by the conjugation of the adjacent transversal semi-revolution maneuvers with the same direction. For the inc lination correction, the maneuvers are placed on intervals that are free fr om transversal maneuvers-the thrust is low and is directed along the binorm al to the orbit. These approaches can easily take into account the operatio nal constraints on maneuvering. Illustrative examples for various types of flight trajectories of the YAMAL spacecraft family are presented. Software support programs, which may be used for the ballistic support of mission co ntrol of these spacecraft, are developed.