Analytical propagation for third-body perturbed orbits

With the increasing complexity of space missions, traditional Keplerian models no longer satisfy the precision requirements for spacecraft orbital calculations in modern deep space exploration and lunar transfer missions. Unlike J₂ perturbations, third-body perturbations induce long-period oscillations in orbital eccentricity and inclination, resulting in significant nonlinear changes in long-term orbital evolution that present challenges for deriving analytical solutions. This paper proposes an analytical method for spacecraft orbit propagation under third-body perturbations, which divides the calculation into long-term and periodic components. The long-period terms are determined by solving the mean orbital dynamics using elliptical integrals, while the periodic terms are computed using von Zeipel theory. The proposed method enables the analytical computation of satellite orbital states at arbitrary epochs. This method accounts for the perturbing body's orbital eccentricity and inclination, making it applicable to all scenarios, including both circulating and librating orbit types. The effectiveness of the proposed method is verified through numerical simulations. This analytical propagation method provides robust support for orbital optimization and autonomous control in deep space exploration missions.