Vertical correction of an approximate planar periodic orbit about the larger primary

An approximate solution to the circular restricted three body problem, for small mass parameter and motion near the first primary, is subject to an analytic iterative correction. The iterative scheme is based on adding small terms with order of magnitudes less than the base solution. These terms are entirely obtained through solving differential equations with periodic coefficients using a perturbation method. As a by product a qualitative stability analysis is introduced using Floquet theory. The out of plane motion is found to be decoupled from the in plane motion and only exist under out of plane initial conditions excitation.