Periodic orbits for space-based reflectors in the circular restricted three-body problem

The use of space-based orbital reflectors to increase the total insolation of the Earth has been considered with potential applications in night-side illumination, electric power generation and climate engineering. Previous studies have demonstrated that families of displaced Earth-centered and artificial halo orbits may be generated using continuous propulsion, e.g. solar sails. In this work, a three-body analysis is performed by using the circular restricted three body problem, such that, the space mirror attitude reflects sunlight in the direction of Earth’s center, increasing the total insolation. Using the Lindstedt–Poincare and differential corrector methods, a family of halo orbits at artificial Sun–Earth $$\hbox {L}_2$$ points are found. It is shown that the third order approximation does not yield real solutions after the reflector acceleration exceeds 0.245 mm $$\hbox {s}^{-2}$$ , i.e. the analytical expressions for the in- and out-of-plane amplitudes yield imaginary values. Thus, a larger solar reflector acceleration is required to obtain periodic orbits closer to the Earth. Derived using a two-body approach and applying the differential corrector method, a family of displaced periodic orbits close to the Earth are therefore found, with a solar reflector acceleration of 2.686 mm $$\hbox {s}^{-2}$$ .