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In this paper, a geometrical analysis is proposed to analyse the performance of call blocking probability in low earth orbit (LEO) satellite networks. Call blocking probability is an important measure to analyse the performance of LEO satellite networks. Assuming shape of the corresponding cells in the footprint of a typical LEO satellite network is hexagonal, a theorem on calculating the maximum call blocking probability is proven. Furthermore, by applying the theorem, the impact of the peak traffic, half depression angle and the height of LEO satellite networks on call blocking probability is also analysed. The results we get can be used as a reference for the performance optimization of LEO satellite networks.