Optimization of a Molniya-Type Orbit Transfer Using a Combination of High- and Low-Thrust Propulsion

Optimization of a spacecraft transfer from a low Earth orbit to a Molniya-type orbit using a combination of high-thrust and an electric propulsion systems is considered. Mathematical models of motion and trajectory optimization methods are presented, taking into account the constraint on the minimum perigee altitude during the low-thrust transfer phase. For optimizing the multirevolution low-thrust transfer trajectory, an approach based on the maximum principle, Newton homotopy, thrust function smoothing, and averaging is employed. To solve the problem, asymptotic properties of multirevolution optimal trajectories are used. Averaged optimal multirevolution trajectories with minimal propellant consumption are computed on a two-dimensional parameter grid (the initial orbit apogee altitude and the ratio of the considered transfer duration to the minimum transfer duration). The resulting dependences of the required characteristic velocity and minimum perigee altitude are approximated using 2D B-splines or 2D linear interpolation. These dependences are used in formulating and solving a constrained optimization problem, which aims to maximize the spacecraft’s final mass while satisfying inequality constraints on transfer duration and minimum perigee altitude. Numerical examples of optimization for the considered combined transfer scheme are provided.