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