Abstract
The costate along a coast arc on an optimal space trajectory contains critically important information about the trajectory. For free-time fuel-optimal flight, the costate at the start of the coast determines completely the optimal length of the coast. Yet most closed-form solutions for costate under various coordinate systems available in the literature are only for two-dimensional flight. In this paper complete three-dimensional closed-form costate solutions in flight-path coordinate system are derived for all conic orbits. These results, as an example of their practical usefulness, enable the optimal duration of any non-circular Keplerian coast arc to be accurately determined from the appropriate root of a polynomial of 5th degree in true anomaly, and a 4th degree polynomial for circular orbits. The value of the development in the paper is demonstrated by solving two relatively difficult multi-finite-burn orbital transfer problems.
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