Analytical Solution of Martian Frozen Orbits Up to J4 and Applications

Mars has long been regarded as the primary target for deep space exploration due to its similar planetary physical parameters and evolutionary history to Earth. This paper, set against the backdrop of Mars system exploration missions, focuses on the analysis and design of Martian frozen orbits under nonspherical perturbation up to J₄. First, for Mars-orbiting trajectories, through magnitude comparison of non-spherical gravitational perturbations, the J₂, J₃ terms are selected for analysis, and the orbital dynamics equations under these perturbations are derived. Second, two categories of Marian frozen orbits are obtained. The characteristics of frozen orbits are analyzed and compared with the Earth's. Then, the variations of critical inclination on Mars are analyzed and a correction method considering J₂, J₃, and J₄ perturbations is proposed, which reduces the cumulative drift of the argument of perigee from 8° to 3°. Finally, the proposed method is applied to design a large elliptical frozen orbit to achieve the relay communication for Mars landing exploration, which could provide reference for future Mars sample return missions.