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Low Earth Orbit (LEO) satellite constellations combine great flexibility and global coverage with short propagation delays when compared to satellites deployed in higher orbits. However, the fast movement of the individual satellites makes inter-satellite routing a complex and dynamic problem. In this paper, we investigate the limits of unipath routing in a scenario where ground stations (GSs) communicate with each other through a LEO constellation. For this, we present a lightweight and topology-aware routing metric that favors the selection of paths with high data rate inter-satellite links (ISLs). Furthermore, we analyze the overall routing latency in terms of propagation, transmission, and queueing times and calculate the maximum traffic load that can be supported by the constellation. In our setup, the traffic is injected by a network of GSs with real locations and is routed through adaptive multi-rate inter-satellite links (ISLs). Our results illustrate the benefits of exploiting the network topology, as the proposed metric can support up to 53% more traffic when compared to the selected benchmarks, and consistently achieves the shortest queueing times at the satellites and, ultimately, the shortest end-to-end latency.