The emergence of mega-constellations of interconnected satellites has a major impact on the integration of cellular wireless and non-terrestrial networks, while simultaneously offering previously inconceivable data gathering capabilities. This paper studies the problem of running a federated learning (FL) algorithm within low Earth orbit satellite constellations connected with intra-orbit inter-satellite links (ISL), aiming to efficiently process collected data in situ. Satellites apply on-board machine learning and transmit local parameters to the parameter server (PS). The main contribution is a novel approach to enhance FL in satellite constellations using intra-orbit ISLs. The key idea is to rely on predictability of satellite visits to create a system design in which ISLs mitigate the impact of intermittent connectivity and transmit aggregated parameters to the PS. We first devise a synchronous FL, which is extended towards an asynchronous FL for the case of sparse satellite visits to the PS. An efficient use of the satellite resources is attained by sparsification-based compression the aggregated parameters within each orbit. Performance is evaluated in terms of accuracy and required data transmission size. We observe a sevenfold increase in convergence speed over the state-of-the-art using ISLs, and $10\times$ reduction in communication load through the proposed in-network aggregation strategy.