Perturbation of the Sun on Frozen Orbits Around Mars

This work presents a study related to the perturbation of the Sun in the orbital evolution of artificial satellites on frozen orbits around Mars. The effect generated by the non-sphericity of Mars is considered. Frozen orbits are orbits that have the eccentricity and the argument of periapsis of the nominal orbit constant on average. Our goals are to verify how the gravity effect of the Sun affect such orbits and study their stability as a function of the parameters involved. We have performed numerical integrations considering different initial conditions for the frozen orbits. Using the method of the integral of the disturbing accelerations it is possible to calculate the magnitude of the total velocity variation due to each perturbation, as well as the degree and order of the most significant spherical harmonic over a long time. Our results showed that the effect of the perturbation of the Sun on the satellites depends on the initial values of eccentricity and semi-major axis of the orbit of the satellite.