In plane correction of an approximate planar periodic orbit about the larger primary

An approximate planar solution to the circular restricted three body problem is analytically corrected for the in plane motion, the special case of small mass parameter and motion of the third body near the first primary is considered. The correction process is done iteratively through adding small correction terms of order of magnitudes less than the base solution. Variational equations of the corrections are found to be linear differential equations with periodic coefficients. Stability of the motion of the third body in the vicinity of the approximate solution is investigated using Floquet theory.