Minimum-time Earth–Moon and Moon–Earth orbital maneuvers using time-domain finite element method

In this paper, the minimum-time orbital trajectories for Earth–Moon and Moon–Earth flights of a continuous-thrust spacecraft are obtained by the time-domain finite element method. The problem is formulated using a simplified version of the restricted three-body model at the Cartesian coordinate system. Moreover, the performance index is considered as the minimum-time problem with free final time. Through the calculus of variation, the problem is discretized in the time-domain and the resulting equations are constructed in finite element form. Finally, by setting out the discrete equations, a set of nonlinear algebraic equations is generated. The optimum answer is then attained using the Newton–Raphson method. The capability of the time-domain finite element method is examined to verify its accuracy. The trajectory results are also compared with the published results and good agreement is observed. Numerical simulations highlighting the effects of the effective exhaust velocity parameter on the shape of flight trajectory and time-of-flight are presented.