Initial Costate Approximation for Rapid Orbit Raising with Very Low Propulsive Acceleration

The transfer between two circular, coplanar Keplerian orbits of a spacecraft equipped with a continuous thrust propulsion system is usually studied in an optimal framework by maximizing a given performance index. Using an indirect approach, the optimal trajectory and the maximum value of the performance index are obtained by numerically solving a two-point boundary value problem (TPBVP). In this context, the computation time required by the numerical solution of the TPBVP depends on the guess of unknown initial costates. The aim of this paper is to describe an analytical procedure to accurately approximate the initial costate variables in a coplanar, circle-to-circle, minimum-time transfer. In particular, this method considers a freely steerable propulsive acceleration vector, whose magnitude varies over a finite range with a sufficiently low maximum value. The effectiveness of the analytical method is tested in a set of both geocentric and heliocentric (simplified) mission scenarios, which model the classical LEO-GEO or interplanetary transfers toward Venus, Mars, Jupiter, and comet 29P/Schwassmann-Wachmann 1.