The main goal of this thesis is to prove the validity of an optimizer based on the MATLAB program GPOPS, for solving complex problems on orbital transfer dynamics. Nowadays, optimization is one of the most important fields in space exploration. The high cost of space missions makes that every project developed must be perfectly studied, calculated, optimized and well executed. Hence, optimization programs appear as a very suitable solution for trying not only to prove the validity of a solution already designed, but also to provide a more optimal solution for any problem proposed . In this study, a program has been developed based on an open source program called GPOPS, a MATLAB software for solving optimal control problems. This tool is able to return an optimal solution for problems approached as a dynamical system whenever it has a consistent initial guess. This initial guess generally is the mission wanted to be analysed and optimized. It is very important for the optimizer, since it will have a strong dependence on the performance of the tool, for example, computation time and accuracy. The problem studied has been a Jovian transfer previously proposed in a di erent study. This journey implies moving from the Jovian moon Callisto, to an other Jovian moon, Ganymede, using an interesting element from Space mechanics, invariant manifolds, a really useful element for Low Thrust manoeuvres. This mission in particular, has as main objective the exploration of these celestial bodies, being the transfer time not a key factor. This fact ends with a multi-revolution Low Thrust manoeuvre. During this thesis, di erent solutions were analysed such as: three and two body problem for the dynamics point of view, inertial and non-inertial reference systems and di erent mathematical methods. After the results obtained, it can be concluded that the tool was able to prove the validity of the solutions or initial guesses given. However, after all the time spent working on the program, it has been demonstrated that this tool has a considerable room of improvement and a considerable number of upgrades have been proposed.