Trajectory Approximation of a Passively Actuated Solar Balloon in Near-Earth Mission Scenarios

The aim of this paper is to investigate the heliocentric motion of a passively actuated solar balloon placed at a distance of about one astronomical unit from the Sun. The analysis exploits a recent thrust model, according to which a solar balloon undergoes a passive control of its lightness number (that is, the ratio of the generated thrust to the local weight of the entire spacecraft) in the form a proportional feedback controller of constant gain. The spacecraft trajectory is obtained with a regularization of the equations of motion, in such a way that the heliocentric dynamics of the passively actuated solar balloon becomes equivalent to that of a nonlinear oscillator with a single degree of freedom. The approximate solution available for this type of nonlinear oscillator is then used to accurately describe the heliocentric motion of the passively actuated solar balloon and to analyze a couple of mission scenarios, that is, the execution of a phasing maneuver on an elliptical working orbit and the rotation of the apse line of the osculating orbit.