Analysis of Electric Sail Heliocentric Motion under Radial Thrust

The contribution of this Note is to analyze the heliocentric trajectory of an E-sail with an outward radial thrust by reducing the problem, by means of a suitable change of variables, to the dynamics of a known equivalent nonlinear oscillator with a single degree of freedom. An analytical, albeit approximate, expression of the spacecraft heliocentric trajectory is also given in polar form when the motion is periodic. This result is shown to be sufficiently accurate for a preliminary mission analysis and is obtained with a reduced computational time, considerably smaller than what is necessary for a numerical integration of the spacecraft equations of motion.