Invariant manifolds of a periodic orbit are very important dynamical aspects to understand the quantitative as well as qualitative behaviour of non-linear phenomenon in a dynamical system. This paper presents the computation of invariant manifolds of Lyapunov periodic orbits near artificial equilibrium points (AEPs) \(\bar{L}_1\) and \(\bar{L}_2\) for a solar sail equipped with reflectivity control device (RCD) under the frame of circular restricted three body problem with dipole secondary. The families of Lyapunov periodic orbits near \(\bar{L}_1\) and \(\bar{L}_2\) points are obtained by continuation technique and then impacts of sail lightness number \(\beta \) and dipole distance d of the dipole secondary are observed in the context of initial conditions and time period. It is noticed that in the presence of dipole secondary, the family of Lyapunov periodic orbits are unstable. Next, the stable and unstable branches of invariant manifolds of Lyapunov periodic orbits are computed under the influence of sail lightness number and dipole secondary and it is found that effect of \(\beta \) and dipole distance d are negligible. These results will to the study about the construction of transfer trajectories and to execute the low-energy transfer.
