Simple Semi-Analytic Model for Optimized Interplanetary Low-Thrust Trajectories Using Solar Electric Propulsion

This paper describes a simple semi-analytic model for mass-optimized interplanetary solar electric low-thrust trajectories. A description is given of a model that accurately and quickly determines the performance of circular-coplanar low-thrust transfers with a series of simple empirical and physics-based relationships that can be implemented easily in a spreadsheet. The model takes flight time, departure and arrival velocity, initial power, initial mass, and propulsion-system efficiency as inputs and produces the optimum specific impulse, A v, final mass, and burn time that correspond to the mass-optimum trajectory as outputs. The development methodology is described, governing variables and fundamental relationships are identified, and a model is presented that efficiently calculates these parameters for a wide range of low-thrust trajectories. Models are presented for Earth-Jupiter/Trojan asteroid, Earth-Mars, Mars-Earth, Earth-Venus, and Earth-Main-Belt asteroid transfers using solar electric propulsion. The results show good agreement for estimates of both delivered mass (+8/-15%) and optimum specific impulse (+20/-20%). This model is well suited to classroom instruction, concurrent engineering, and the initial development of new mission concepts.