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In this paper, a location-assisted on-demand routing (LAOR) protocol for low earth orbit (LEO) satellite systems is proposed and evaluated. This protocol can be viewed as a variant of the well-known ad-hoc on-demand distance vector (AODV) routing protocol, tailored to the requirements imposed by the characteristics of LEO satellite systems' topology. The LAOR protocol is assessed for different link-cost metrics and compared to centralized routing protocols proposed in the literature thus far. Simulation studies further document and confirm the positive characteristics of the proposed protocol.