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

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