Solar sail orbital motion at the non-autonomous oblate earth-moon system: family of periodic orbits

Abstract

The primary objective of this paper is to identify periodic orbits for solar sails within the oblate Earth-Moon Circular Restricted Three-Body Problem (CR3BP). Incorporating solar acceleration into the Earth-Moon system modifies the governing orbital equations, transforming the traditional CR3BP from an autonomous to a non-autonomous system. As a result, the procedure for identifying periodic orbits diverges from the conventional autonomous CR3BP method. Thus, this paper introduces a novel methodology to identify new periodic Halo and Lyapunov orbits within the non-autonomous CR3BP. Our proposed approach comprises four hierarchical steps: first, a surface of section simulation (Poincaré map) is conducted to obtain an initial approximation of the orbital state vector within the autonomous CR3BP. Second, a periodic orbit correction algorithm is developed using the autonomous CR3BP equations to acquire precise initial conditions. In the third step, initial conditions for solar sail periodic orbits are derived by applying the initial conditions of autonomous CR3BP periodic orbits as inputs to the periodic orbit correction algorithm, which is now executed using non-autonomous CR3BP equations. In the final step, a family of orbits is generated by gradually increasing the sail's characteristic acceleration. Our work addresses limitations in previous studies that relied on initial guesses derived solely from the unperturbed autonomous CR3BP reported in earlier research, which often resulted in the missing of numerous solar sail periodic orbits in the non-autonomous system. This approach enables the discovery of new periodic orbits within the Earth-Moon system, accounting for perturbations from the oblate primaries, including zonal harmonic terms from \({j}_{2}\) to \({j}_{6}\). The methodology is validated through simulations of solar sail Lyapunov and Halo orbits, offering a comprehensive understanding of the Earth-Moon CR3BP under non-autonomous conditions.