Artificial halo orbits for low-thrust propulsion spacecraft

We consider periodic halo orbits about artificial equilibrium points (AEP) near to the Lagrange points L ₁ and L ₂ 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 L ₁ and beyond L ₂ 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 L ₁ decreases with an increase in low-thrust acceleration. The halo orbits about artificial equilibrium points beyond L ₂ in contrast show an increase in period with an increase in low-thrust acceleration. However, the minimum amplitude first increases 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.