Artificial Periodic Orbits Around L1-Type Equilibrium Points for a Generalized Sail

The available results for artificial periodic orbits (APOs) maintained by a propellantless propulsion system to the case of purely radial (continuous) propulsive acceleration, whose modulus depends on a given power of the Sun?spacecraft distance are reported. Lyapunov planar orbits may be generated as a function of the spacecraft performance, except for some isolated points when a resonance occurs between the imaginary eigenvalues of the linearized motion around the equilibrium point. As for the halo families, the numerical simulations show that, for each thruster type, a critical value of the propulsive acceleration exists beyond which such orbits disappear. The critical value is associated to the existence of a 1:1 resonance between the imaginary eigenvalues. As far as halo orbits are concerned, two other critical values can be detected for each propulsion system type. These values correspond to a change in the way the families of artificial periodic orbits evolve. Simulations show that, for the same value of lightness number, the size and shape of Lyapunov planar orbits are similar. On the contrary, halo orbits are characterized by different sizes and shapes.