Large-scale low Earth orbit (LEO) remote satellite constellations have become a brand new, massive source of space data. Federated learning (FL) is considered a promising distributed machine learning technology that can communicate optimally using these data. However, when applying FL in satellite networks, it is necessary to consider the unique challenges brought by satellite networks, which include satellite communication, computational ability, and the interaction relationship between clients and servers. This study focuses on the siting of parameter servers (PSs), whether terrestrial or extraterrestrial, and explores the challenges of implementing a satellite federated learning (SFL) algorithm equipped with client selection (CS). We proposed an index called “client affinity” to measure the contribution of the client to the global model, and a CS algorithm was designed in this way. A series of experiments have indicated the advantage of our SFL paradigm—that satellites function as the PS—and the availability of our CS algorithm. Our method can halve the convergence time of both FedSat and FedSpace, and improve the precision of the models by up to 80%.