Quantitative and Qualitative Results from Orbital Plane Precession of Medium-high Near-circular Orbits

Abstract The theoretical analysis of Allan & Cook on the mechanisms of orbital plane precession for medium-high circular orbits is briefly reviewed, and the fact that there are two types of possible precession mechanisms (not only the classical Laplace precession) for the long-term evolution of the orbital plane of medium-high near-circular orbits is especially emphasized. Based on two types of possible precession mechanisms, the analytical formulae of the quantitative variation ranges of orbital inclination derived by Zhao et al. are revised, and the complete analytical formulae for medium-high near-circular orbits are obtained. The qualitative characteristic formula for the variation of orbital inclination-longitude of the ascending node of geostationary orbits in Zhao et al. is generalized to medium-high near-circular orbits, and the more general analytical formulae are obtained. Taking the near-circular orbits with the altitudes as the geosynchronous and medium orbits of the BeiDou navigation satellites as examples, the theoretically quantitative and qualitative results from orbital plane precession are verified by the first-order semianalytical calculations with simplified models and numerical calculations with precise models to a certain extent. Moreover, the specific quantitative and qualitative results for medium-high near-circular orbits with the given initial inclinations and different initial longitudes of the ascending node are particularly presented, from which some conclusions are summarized. Due to the high similarity of orbital plane precession for natural satellites to that of artificial satellites, the results and methodology in this paper can be directly extended to the long-term evolution of the orbital plane for natural satellites and help to understand and explain some orbit dynamic phenomena of natural satellites.