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A broadband satellite network uses a constellation of a number of similar satellites to provide wireless networking services to the Earth. A number of these constellation networks are under development. This article introduces the types of satellite constellation networks, and examines how overall performance of TCP communications carried across such a network can be affected by the choice of routing strategies used within the network. Constellations utilizing direct intersatellite links are capable of using multiple paths between satellites simultaneously as a strategy to spread network load. This allows more general routing strategies than shortest-path routing, but we show these strategies to be detrimental to the performance of individual TCP connections