Artificial halo orbits for low-thrust propulsion spacecraft

We consider periodic halo orbits about artificial equilibrium points near to the Lagrange points L1 and L2 in the circular restricted three-body problem, where the third body is a low-thrust propulsion spacecraft in the Sun-Earth system. Although such halo orbits about artificial equilibrium points can be generated using a solar sail, there are points inside L1 and beyond L2 where a solar sail cannot be placed, so low-thrust, such as solar electric propulsion, is the only option to generate artificial halo orbits around points inaccessible to a solar sail. Analytical and numerical halo orbits for such low-thrust propulsion systems are obtained by using the Lindstedt Poincaré and differential corrector method respectively. Both the period and minimum amplitude of halo orbits about artificial equilibrium points inside L1 decreases with an increase in low-thrust acceleration. The halo orbits about artificial equilibrium points beyond L2 in contrast show an increase in period with an increase in low-thrust acceleration. However, the minimum amplitude first incresaes and then decreases after the thrust acceleration exceeds 0.415 mm/s². Using a continuation method, we also find stable artificial halo orbits which can be sustained for long integration times and require a reasonably small low-thrust acceleration 0.0593 mm/s²