Trajectory Approximation for Low-Performance Electric Sail with Constant Thrust Angle

Analytic trajectories for a spacecraft subjected to a low, continuous, propulsive acceleration are available only for very special cases [1–3], even though these solutions find significant utility in preliminary mission design and optimization [4]. If a closed-form trajectory corresponding to a given thrust control law cannot be recovered, a possible option is to resort to a shape-based approach [5–7], or to suitably simplify the differential equations of motion [8–10]. Within the latter context, in this Note an analytical, albeit approximate, expression for the heliocentric trajectory of a spacecraft propelled by a low-performance electric sail [11, 12] is discussed. Using a two-dimensional model and under the assumptions of constant thrust angle and low propulsive acceleration modulus, the spacecraft heliocentric trajectory is obtained in a parametric way as a function of time. The effectiveness of the mathematical model is checked by comparing the analytic solution with a numeric integration of equations of motion.