Heliocentric Phasing Performance of Electric Sail Spacecraft

We investigate the heliocentric in-orbit repositioning problem of a spacecraft propelled by an Electric Solar Wind Sail. Given an initial circular parking orbit, we look for the heliocentric trajectory that minimizes the time required for the spacecraft to change its azimuthal position, along the initial orbit, of a (prescribed) phasing angle. The in-orbit repositioning problem can be solved using either a drift ahead or a drift behind maneuver and, in general, the flight times for the two cases are different for a given value of the phasing angle. However, there exists a critical azimuthal position, whose value is numerically found, which univocally establishes whether a drift ahead or behind trajectory is superior in terms of flight time it requires for the maneuver to be completed. We solve the optimization problem using an indirect approach for different values of both the spacecraft maximum propulsive acceleration and the phasing angle, and the solution is then specialized to a repositioning problem along the Earth's heliocentric orbit. Finally, we use the simulation results to obtain a first order estimate of the minimum flight times for a scientific mission towards triangular Lagrangian points of the Sun-[Earth+Moon] system