The efforts to replace the successful, albeit aging, TCP/IP Internet architecture with a better suited one have driving research interest to information-centric alternatives. The Named Data Networking (NDN) architecture is probably one of the main contenders to become the network layer of the future Internet thanks to its inbuilt support for mobility, in-network caching, security and, in general, for being better adapted to the needs of current network applications. At the same time, massive satellite constellations are currently being deployed in low Earth orbits (LEO) to provide a backend for network connectivity. It is expected that, very soon, these constellations will function as proper networks thanks to inter-satellite communication links. These new satellite networks will be able to benefit from their greenfield status and the new network architectures. In this paper we analyze how to deploy the network caches of an NDN-based LEO satellite network. In particular, we show how we can jointly select the most appropriate caching nodes for each piece of content and how to forward data across the constellation in two simple alternative ways. Performance results show that the caching and forwarding strategies proposed reduce path lengths up to a third with just a few caching nodes while, simultaneously, helping to spread the load along the network.