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For about 3 years observati on on satellites operating in the frozen orbit round the earth, we found the eccentricity has a nearl y constant dri fting rate. The frozen orbi ts at critical inclination were part of peri odic 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 perturbati ve force on the eccentricity, such as solar radiation pressure, third-body perturbati on and nons pherical earth gravity. Ignoring the high-order Earth gravi ty and other perturbati ve force, it was illustrated that the eccentricity drift is mai nly caused by the J5 term wi th 40% and J7 term wi th 55% in the earth gravitati on 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 perturbati ve factors, the frozen eccentricity orbi t inclinati on needed to exceed 64 o and the frozen perigee-argument orbit inclination shoul d be less than 63.4 o . The dri ft was yiel ded in both the eccentricity and perigee-argument when the orbit inclination angle was between 63.4 o and 64 o . We found it's di fficult to obtain a critical orbit i nclinati on that freezing both the eccentricity and perigee argument for specified semi-major axis and perigee argument. However, the problem coul d be sol ved in hamiltonian dynamics. A hamiltoni an functi on anal ysis method was proposed to search "stable equilibrium" that corresponding to periodic orbits. The research results demonstrated that stable equilibri um drifted with high order gravity perturbation terms taken into account. If perigee argument was treated as a free parameter, we coul d find continuous periodic orbits with varying orbit inclination at specified semi-major axis.

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