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Interplanetary transfers represent one of the most interesting themes of astrodynamics, because of its complexity and outcomes for human exploration of the Solar System. A wide number of works concerning different aspects of the interplanetary mission have been developed. The examination of these works leads to the conclusion that, by far, there is not a preferential propulsion system or an optimal trajectory to perform an interplanetary mission, but a precise kind of transfer according to a given mission profile. Here, minimum time trajectories to Mars for small payload transportation with different electric propulsion systems have been analyzed; results have been obtained considering the initial impulse given by the Ariane 5 upper stage. Additionally, an adaptative, multiple shooting optimization algorithm is proposed to solve the problem of optimality in interplanetary transfers with a low continuous thrust. The algorithm searches for the optimal set of initial Lagrange multipliers solving the two point problem by adapting the search intervals according to the unsmooth shape of the augmented cost function.

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