Periodic orbits of circular restricted 3B problem

At collision, the circular restricted 3 body Equations of motion possess singularities which play a key role under computational, theoretical, and physical aspects. In this paper, an attempt is made for finding periodic orbit of regularized circular restricted three body system near the L-points L1 and L2 by applying Kustaanheimo-Stiefel transformation when the infinitesimal body moves closely to smaller primary. The fourth-order approximation is chosen as the starting initial guess for the Newton's method for the computation of halo orbits numerically. The linear stability of the halo orbits is discussed by finding the Eigen values of the monodromy matrix. Using the differential continuation method, it is found that there exists a stable range of periodic orbit near L-point L2 of Sun-Earth, Earth-Moon, and Sun-Mars systems. The invariant manifolds associated to the halo orbit are evaluated by exploiting the Eigen vectors of the monodromy matrix.