This thesis research has focused on developing an analytical solution for low-thrust transfer orbits. Low-thrust propulsion is an attractive option for space manoeuvres and transfers, since it provides a large specific impulse and hence efficient use of propellant. Thus, the propellant mass can be decreased, which brings advantages such as higher payload mass and extended mission life.
Two constraints have been posed on the thrust acceleration, which often appear as a result of optimal solutions. Firstly, only bang-bang control is allowed, thus the rocket engine can only be turned on or off. Secondly, no radial thrust is allowed, such that no gravity losses occur. The modified equinoctial elements have been chosen to describe the trajectory. If it is assumed that the eccentricity is equal to zero, analytical solutions have been derived. While this seems as a substantial restriction on the developed method, it is shown that the analytical solution provides very reasonable results for eccentricities smaller than 0.2. Furthermore, separate analytical expressions have been developed when no in-plane thrust acts on the spacecraft. For the implementation of the bang-bang control, each individual revolution around the central body is allowed to have two thrust arcs and two coasts arcs, where the analytical solutions have been used to describe the motion of the spacecraft during the thrust arcs. By cleverly choosing the switching points where the rocket engine is turned on and off, the transfer orbit is achieved in an efficient way. The performance of the developed algorithm has been assessed for different input parameters. More specifically, different magnitudes of thrust accelerations have been analyzed. Furthermore, the lengths of the thrust and coast arcs, together with the direction of the thrust force, have been varied to evaluate the applicability of the algorithm. Lastly, the algorithm has been tested with the introduction of a stop criterion, which determines the required propellant and time of flight to arrive at a set target element. The algorithm has proved to give results with relatively good accuracy for orbits with an eccentricity smaller than 0.2. However, if the time of flight or the thrust acceleration become too high, less feasible solutions are perceived.