On the existence of periodic orbits in the CR3BP

In the case of the circular restricted three-body problem (CR3BP), the existence of periodic orbits is strictly proved for the firstand third-order time dependent approximate system in the inertial frame. Moreover, the expression of periodic orbits for the first order nonautonomous system of CR3BP is presented analytically, which makes a difference for the known results obtained by semi-analytical and semi-numerical methods in the rotating frame.