Most research in satellite power management has focused on the component and/or link level, treating satellites as isolated entities. However, as satellite constellations are typically over-provisioned, selectively shutting down entire sections during periods of low demand has the potential to significantly reduce energy consumption -- thus, extending constellation lifetime -- without causing major disruptions to network activities. In this work, we address the problem of identifying the optimal set of links that can be shut down in a satellite constellation subject to maintaining full connectivity and bounding the maximum link utilization. With the problem being NP-hard, we introduce two heuristics, BASIC and SNAP, which represent different tradeoffs in terms of performance and simplicity. We evaluate BASIC and SNAP using realistic LEO topologies and traffic matrices. The results show that BASIC and SNAP can increase the satellite service life by as much as 40% and 80%, respectively. This is accomplished by trading off very little in terms of average path length and congestion.
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