Research on the long-term eccentricity drift of critical inclination orbits

Abstract

For about 3 years observation on satellites operating in the frozen orbit round the earth, we found the eccentricity has a nearly constant dri fting rate. The frozen orbits at critical inclination were part of periodic orbits, and once supposed to be stable in eccentricity and perigee argument on average. Focusing on the 0.00033-per-year-growth eccentricity of some long-term observed critical inclination orbit, a numerical method was proposed to analyze the effects of perturbative force on the eccentricity, such as solar radiation pressure, third-body perturbation and nons pherical earth gravity. Ignoring the high-order Earth gravity and other perturbative force, it was illustrated that the eccentricity drift is mainly caused by the J5 term with 40% and J7 term with 55% in the earth gravitation field model. Moreover, for the satellites operating on the al titude of 1100km with the perigee argument 4 o, which were affected by the high-order perturbative factors, the frozen eccentricity orbit inclination needed to exceed 64o and the frozen perigee-argument orbit inclination should be less than 63.4 o . The dri ft was yielded in both the eccentricity and perigee-argument when the orbit inclination angle was between 63.4 o and 64o. We found it’s di fficult to obtain a critical orbit inclination that freezing both the eccentricity and perigee argument for specified semi-major axis and perigee argument. However, the problem could be solved in hamiltonian dynamics. A hamiltonian function analysis method was proposed to search “stable equilibrium” that corresponding to periodic orbits. The research results demonstrated that stable equilibrium drifted with high order gravity perturbation terms taken into account. If perigee argument was treated as a free parameter, we could find continuous periodic orbits with varying orbit inclination at specified semi-major axis.