Active legs of extremal trajectories in linear central field

Consideration was given to the Mayer variational problem of determining the optimal spacecraft trajectories. The spacecraft center of mass was assumed to move in a thin spherical layer in the neighborhood of a certain reference orbit with a limited mass flow rate and constant jet-pipe gas velocity. The main assumption states that the motion occurs in a linear central field. For the canonical equations of the variational problem for the extremal legs of the intermediate and maximum thrusts, three new classes of analytical solutions were obtained. Transfer between the given circular orbits in the Newtonian field that has two maximum-thrust legs was considered as an example. For the relations between the radii of the boundary orbits and the parameters of the transfer orbit, the transfer conditions were obtained. A numerical example was presented.