Two-dimensional Heliocentric Dynamics Approximation of an Electric Sail with Fixed Attitude

This work analyzes an approximate solution of the equations of motion for a spacecraft propelled by an Electric Solar Wind Sail with a fixed attitude. The peculiarity of such a propulsion system is that its thrust scales as the inverse heliocentric distance. This represents a substantial difference from a classical solar sail, whose propelling force is known to be proportional to inverse square distance from the Sun. Assuming a heliocentric, two-dimensional mission scenario, the polar form of the spacecraft trajectory equation is obtained for a closed parking orbit of given characteristics by means of an asymptotic expansion procedure. The proposed approach significantly improves the existing results as presented in the literature. A suitable choice of propulsion system parameters and parking orbit characteristics provides interesting similarities with recent solutions obtained for a solar sail-based spacecraft in a heliocentric, two-dimensional, mission scenario.