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This work presents an analytical perturbation method to define and study thedynamics of frozen orbits under the perturbation effects produced by theoblatness of the main celestial body. This is done using a perturbation methodpurely based on osculating elements. This allows to characterize, define, andstudy the three existing families of frozen orbits in closed-form: the twofamilies of frozen orbits close to the critical inclination, and the family offrozen orbits that appears at low values of eccentricity. To that end, thiswork includes the first and second order approximate solutions of the proposedperturbation method, including their applications to define frozen orbits,repeating ground-track orbits, and sun-synchronous orbits. Examples ofapplication are also presented to show the expected error performance of theproposed approach.

Analytic frozen and other low eccentric orbits under J2 perturbation