Indirect Optimization of Three-Dimensional Finite-Burning Interplanetary Transfers Including Spiral Dynamics

摘要

The indirect optimization problem for a three-dimensional transfer from low Earth orbit to low Mars orbit isrnsolved. A step-by-step process developed for a two-dimensional model and techniques for accurately estimating thernunknown costates for three-dimensional escape and capture spirals are used. Minimum-propellant trajectories forrnfinite-burning engines are calculated. Solutions are considered with and without control limits on specific impulsernand compared with previous research. Unlike other research, the entire trajectory, including the Martian capturernsequence, is integrated in an Earth-referenced frame. Additionally, the capture sequence is not found by iterativelyrnlowering the final targeted lowMars orbit, but the desired final orbit is directly targeted with no successive iterationsrnof increasingly smaller lowMars orbits. As in the two-dimensional case,more fuel-efficient trajectories are found forrnthe same mission objectives and constraints published in other research, emphasizing the importance of thisrntechnique.Whereas previous research only achieved finalMartian orbits of 6Mars radii DUM (20,382 km), the newrnapproach finds solutions for final Martian circular orbits of 1.47–2.00 DUM (5000–6794 km).