The increasing interest in solar electric propulsion techniques, that enable significant propellant mass savings for a wide class of transfers, has brought about a revolution in the approach to trajectory design and optimization, as a result of the complexity and diversity of the problem. To date, solutions of different nature exist, but numerical methods that require significant computational effort and user experience are typically used already in the early stages of mission design, due to the limited availability of reliable medium-to-low fidelity design tools for SEP transfers. This research project proposes a novel method that computes transfer performance parameters for Earth-Mars mass-optimal SEP transfers, by means of empirically derived analytic relations. The method is intended for applications such as concurrent engineering and early-phase concept development, which require the fast characterization of a broad design space. Besides accommodating a wide range of currently available systems, the method successfully deals with modelling the effect of non-zero infinity velocity at departure and/or arrival.

The methodology that has been applied consists of a first phase of generation and characterization of the transfers, and of the subsequent selection of the model variables, model functions and architecture. Regarding the generation of the transfers, it is assumed that the transfers are coplanar and that the initial and target orbits are circular. Hundreds of transfers are optimized in a semi-automatic way and characterized in terms of thrust profile and transfer performance parameters. In the investigated design space, different regimes are identified, but approximately 90% of the acceleration range of interest falls into the thrust-coast-thrust profile for any combination of departure and arrival infinity velocity. For a proper description of the underlying trends in the transfer parameters, three key variables have been identified, namely the average acceleration, the total infinity velocity and the infinity velocity at arrival (expressed as a function of the total infinity velocity). By means of curve-fitting, analytic relations are derived that successfully describe those trends, limited to the thrust-coast-thrust class of transfers.

The method that is presented computes near-optimal transfers in terms of ΔV cost, transfer time, transfer angle and departure date. While the first three parameters are the outputs of the mentioned curve-fit model above, the departure date is computed by solving analytically the problem of the phasing with Mars, in a subsequent step. The fit functions that are derived model circle-to-circle planar transfers with an accuracy in the order of 0.1% with respect to the ΔV , 1.5% to the transfer time and 1.2% to the transfer angle, successfully dealing with the dependence on the departure and arrival infinity velocities and generating instant estimates for all relevant transfer parameters. When the model performance is considered in relation to transfers derived in the full ephemeris model, the errors are within 1% for the ΔV , within 15% for the transfer time and within 12% for the transfer angle, which, together with the demonstrated efficiency and simplicity of implementation, make it suitable both for early-stage assessments and for generation of suitable first guesses.