Optimization of roundtrip, time-constrained, finite burn trajectories via an indirect method

An indirect trajectory optimization method is used to compute optimal, time-constrained, roundtrip, finite burn trajectories between any two orbits around a common central body. This method involves solving the optimal control problem as a multipoint boundary value problem with two discontinuities in the controls corresponding to the arrival at and the departure from the target. Solutions are provided that minimize the propellant, given either an initial or final mass, while constraining the stay time at the target to be greater than or equal to a specified minimum value and while constraining the total roundtrip time to be less than or equal to a specified maximum value. The results are applied to human-crewed, one-year Earth-Mars roundtrip missions with a minimum two-month stay at Mars and four year Earth-Jupiter missions with a minimum one-year Jovian stay. These missions utilize high-power, nuclear electric propulsion with either a constant or variable specific impulse engine. This theoretical formulation was used to find quick, efficient, converged solutions that are shown to be at least as optimal or slightly more so compared to another optimization method that is hybrid in nature but still uses continuous control where the thrust is along the primer vector.