Mega-constellations of small-size Low Earth Orbit (LEO) satellites are currently planned and deployed by various private and public entities. While global connectivity is the main rationale, these constellations also offer the potential to gather immense amounts of data, e.g., for Earth observation. Power and bandwidth constraints together with motives like privacy, limiting delay, or resiliency make it desirable to process this data directly within the constellation. We consider the implementation of on-board federated learning (FL) orchestrated by an out-of-constellation parameter server (PS) and propose a novel communication scheme tailored to support FL. It leverages intra-orbit inter-satellite links, the predictability of satellite movements and partial aggregating to massively reduce the training time and communication costs. In particular, for a constellation with 40 satellites equally distributed among five low Earth orbits and the PS in medium Earth orbit, we observe a 29x speed-up in the training process time and a 8x traffic reduction at the PS over the baseline.