This paper presents explicit open and closed-loop guidance solutions for power-limited transfers of a spacecraft between two coplanar circular orbits, performed under the Keplerian class of continuous thrust programs, Introduced in an earlier paper, the Keplerian class is parametrized by an arbitrary, differentiable. explicit function of time, given the name the throttling function, and gives rise to a special type of analytically soluble two-dimensional orbital motion. The resulting qualitative and computational simplicity, exact guidance, probable power-limited near optimality, and unlimited two-dimensional maneuverability are the primary characteristics of such motion. The Quadratic subclass of the Keplerian class for which the the throttling function is a quadratic polynomial is used to obtain open and closed-loop solutions that satisfy the boundary conditions exactly, but at the expense of sacrificing part of optimality. By relaxing however the requirement that the initial and final orbits be precisely circular and by replacing it with the practiclly much more meaningful requirement that they be only very nearly circular, with very small (but unimportant) eccentricities, it is shown that the Tangential subclass, corresponding to a constant throttling function and tangential thrust, can be used to obtain open and closed-loop guidance solutions that are identical, trivially, simple to compute in real time, and for sufficiently high transfer duration as good as the corresponding optimal power-limited solutions for all practical purposes.
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