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The main purpose of this work is to perform an analysis of realistic new trajectories for a robotic mission to Saturn's largest moon, Titan, in order to demonstrate the great advantages related to the Direct Fusion Drive (DFD). The DFD is a D -$^3$He fuelled, aneutronic, thermonuclear fusion propulsion system. This fusion propulsion concept is based on a magnetically confined field reversed configuration plasma, where the deuterium propellant is heated by fusion products, and then expanded into a magnetic nozzle, providing both thrust and electrical energy to the spacecraft [1]. The trajectories calculations and analysis for the Titan mission are obtained based on the characteristics provided by the PPPL [1]. Two different profile missions are considered: the first one is a thrust-coast-thrust profile with constant thrust and specific impulse; the second scenario is a continuous and constant thrust profile mission. Each mission study is divided into four different phases, starting from the initial low Earth orbit departure, the interplanetary trajectory, Saturn orbit insertion and the Titan orbit insertion. For all mission phases, maneuver time and propellant consumption are calculated. The results of calculations and mission analysis offer a complete overview of the advantages in term of payload mass and travel time. It is important to emphasize that the deceleration capability is one of the DFD game changer: in fact, the DFD performance allows to rapidly reach high velocities and decelerate in even shorter time period. This capability results in a total trip duration of 2.6 years for the thrust-coast-thrust profile and less than 2 years considering the continuous thrust profile. The high payload enabling capability, combined with the huge electrical power available from the fusion reactor, leads to a tremendous advantage compared to present technology.