Trajectory Approximation of a Low-Performance E-Sail with Fixed Orientation

The Electric Solar Wind Sail (E-sail) is a propellantless propulsion system that converts solar wind dynamic pressure into a deep-space thrust through a grid of long conducting tethers. The first flight test, needed to experience the true potential of the E-sail concept, is likely to be carried out using a single spinning cable deployed from a small satellite, such as a CubeSat. This specific configuration poses severe limitations to both the performance and the maneuverability of the spacecraft used to analyze the actual in situ thruster capabilities. In fact, the direction of the spin axis in a single-tether configuration can be considered fixed in an inertial reference frame, so that the classic sail pitch angle is no longer a control variable during the interplanetary flight. This paper aims to determine the polar form of the propelled trajectory and the characteristics of the osculating orbit of a spacecraft propelled by a low-performance spinning E-sail with an inertially fixed axis of rotation. Assuming that the spacecraft starts the trajectory from a parking orbit that coincides with the Earth's heliocentric orbit and that its spin axis belongs to the plane of the ecliptic, a procedure is illustrated to solve the problem accurately with a set of simple analytical relations.