Analysis on the long term orbital evolution of Molniya satellites

Long term evolution of the Molniya satellites are investigated by means of historical data analysis, theoretical analysis and numerical integration. Both the mean motion resonance problem and the critical inclination problem are studied. The period and the amplitude of the semi-major axis for each satellite are obtained analytically and compared with the observational data. In addition, the reason of the observed sudden changes in the center and the amplitude of the oscillating semi-major axes is determined as the effect of the atmosphere drag. For the long period perigee motion, the dominant perturbations come from the luni-solar gravity. A two-degree-of freedom system is established by adding the two periodic terms of the neighbor resonances to the Hamiltonian of the classical single resonance model. In theory, the resulting resonance overlap model is responsible for the chaotic layer between the libration region and the circulation region. In practice, it is applied to explain the quick decay of the earliest Molniya satellites and to study the satellites that still orbiting the Earth at present.