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

Abstract

The indirect optimization problem for a three-dimensional transfer from low Earth orbit to low Mars orbit is solved. A step-by-step process developed for a two-dimensional model and techniques for accurately estimating the unknown costates for three-dimensional escape and capture spirals are used. Minimum-propellant trajectories for finite-burning engines are calculated. Solutions are considered with and without control limits on specific impulse and compared with previous research. Unlike other research, the entire trajectory, including the Martian capture sequence, is integrated in an Earth-referenced frame. Additionally, the capture sequence is not found by iteratively lowering the final targeted low Mars orbit, but the desired final orbit is directly targeted with no successive iterations of increasingly smaller low Mars orbits. As in the two-dimensional case, more fuel-efficient trajectories are found for the same mission objectives and constraints published in other research, emphasizing the importance of this technique. Whereas previous research only achieved final Martian orbits of 6 Mars radii DU M (20,382 km), the new approach finds solutions for final Martian circular orbits of 1.47―2.00 DU M (5000―6794 km).