Optimal low-thrust trajectories using nonsingular equinoctial orbit elements

Low-thrust propulsion was proven to allow substantial propellant savings with respect to high-thrust systems, at the price of increasing the time of flight. This work addresses low-thrust orbit transfer optimization, which consists in finding the thrust direction time history that minimizes the time of flight. The indirect heuristic method is outlined and employed. It is based on the joint use of a heuristic technique and the necessary conditions associated with the optimization problem. If this is formulated using the polar coordinates for position and velocity, a major drawback resides in hypersensitivity on the initial values of the adjoint variables associated with the dynamics equations. This research proves that the use of nonsingular equinoctial elements allows overcoming this serious difficulty, by mitigating hypersensitivity. Two interesting low-thrust orbit transfer problems are considered, i.e. (a) from a circular, equatorial low Earth orbit to a geostationary orbit, and (b) between a circular, low Earth orbit and a hyperbolic trajectory. In both cases, the minimum-time transfer path is found with great accuracy.