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With the advent of large LEO satellite communication networks to provide global broadband Internet access, interest in providing edge computing resources within LEO networks has emerged. The LEO Edge promises low-latency, high-bandwidth access to compute and storage resources for a global base of clients and IoT devices regardless of their geographical location. Current proposals assume compute resources or service replicas at every LEO satellite, which requires high upfront investments and can lead to over-provisioning. To implement and use the LEO Edge efficiently, methods for server and service placement are required that help select an optimal subset of satellites as server or service replica locations. In this paper, we show how the existing research on resource placement on a 2D torus can be applied to this problem by leveraging the unique topology of LEO satellite networks. Further, we extend the existing discrete resource placement methods to allow placement with QoS constraints. In simulation of proposed LEO satellite communication networks, we show how QoS depends on orbital parameters and that our proposed method can take these effects into account where the existing approach cannot.