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The problem of handoffs in cellular networks is compounded in a low earth orbit (LEO) satellite-based cellular network due to the relative motion of the satellites with respect to a stationary observer on earth. Typically, the velocity of motion of mobiles can be ignored when compared to the very high velocity of the footprints of satellites. We exploit this property of LEO satellite systems and propose a handoff scheme based on a channel sharing approach that results in a substantial decrease in handoff dropping. For the same handoff dropping performance, our scheme has significantly lower new call blocking probability than the conventional reservation scheme. We also present an analytical approximation that is in very good accord with simulation results.