Analytical low-thrust transfer design based on velocity hodograph

Shape-based models can be used to approximate low-thrust transfer orbits between celestial bodies. Here, a new model is proposed, which is based on simple analytical base functions that together represent the velocity of the spacecraft. After integration, these base functions also yield analytical expressions for distances traveled. As a result, both the velocity and the trajectory of a transfer can be modeled analytically with a series of such base functions, which can be chosen and scaled at will. Constraints (i.e. conditions on initial and final position and velocity) can be satisfied directly, and a constraint on the final polar angle can be met with a straightforward, fast numerical integration. The technique allows for direct solutions with no degrees of freedom, but also facilitates a more extensive analytical modeling where certain aspects of the resulting transfer trajectory (e.g. required ΔV, maximum acceleration) can be optimized. The main characteristics of the technique are illustrated in a number of cases: transfers to Mars and Mercury.