Two classes of extreme motion trajectories of a point with varying specific impulse

The variational problem to determine the optimal trajectories of the center of mass of a spacecraft moving in the central Newtonian field with limited power and specific momentum was considered. The extremal trajectory was shown to contain elements of zero, intermediate, and maximal power with a constant or variable specific momentum. For the circular and spiral trajectories, extremal analytical solutions were established. These elements can find use in the problems of departure and transfer to the parking orbit, as well as in the problems of orbital transfers. The problem of transfer to the given elliptical orbit was considered as an example.