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Topological dynamics and periodicity are two of the major differences between LEO satellite networks and terrestrial networks. In this work, we first propose MAPSS (Method to Analyze Periodicity of Satellite System) to obtain the system period of satellite networks based on spectral analysis. Then the topological dynamics of satellite networks, including the number of snapshots in one system period, is characterized by using this new method. Our method could be used in the development of routing algorithms as well as the design of satellite constellation.