A set of orbital elements to fully represent the zonal harmonics around an oblate celestial body

This work introduces a new set of orbital elements to fully represent the zonal harmonics problem around an oblate celestial body. allows obtain complete linear system for unperturbed and, in addition, polynomial when considering perturbation produced by from gravitational force These present no singularities and are able any kind orbit, including elliptic, parabolic hyperbolic orbits. In application this formulation Poincar\'e-Lindstedt method is included approximate first order solution case J2 perturbation.