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In the current study, a double-averaged analytical model including the actionof the perturbing body's inclination is developed to study third-bodyperturbations. The disturbing function is expanded in the form of Legendrepolynomials truncated up to the second-order term, and then is averaged overthe periods of the spacecraft and the perturbing body. The efficiency of thedouble-averaged algorithm is verified with the full elliptic restrictedthree-body model. Comparisons with the previous study for a lunar satelliteperturbed by Earth are presented to measure the effect of the perturbing body'sinclination, and illustrate that the lunar obliquity with the value 6.68\degreeis important for the mean motion of a lunar satellite. The application to theMars-Sun system is shown to prove the validity of the double-averaged model. Itcan be seen that the algorithm is effective to predict the long-term behaviorof a high-altitude Martian spacecraft perturbed by Sun. The double-averagedmodel presented in this paper is also applicable to other celestial systems.

Long-term perturbations due to a disturbing body in elliptic inclined orbit