The family of Quasi-satellite periodic orbits in the circular co-planar RTBP

In the circular case of the coplanar Restricted Three-body Problem, we studied how the family of quasi-satellite (QS) periodic orbits allows to define an associated libration center. Using the averaged problem, we highlighted a validity limit of this one: for QS orbits with low eccentricities, the averaged problem does not correspond to the real problem. We do the same procedure to L 3 , L 4 and L 5 emerging periodic orbits families and remarked that for very high eccentricities F L4 and F L5 merge with F L3 which bifurcates to a stable family.