Low Earth Orbit (LEO) constellations, each comprising a large number of satellites, have become a new source of big data "from the sky". Downloading such data to a ground station (GS) for big data analytics demands very high bandwidth and involves large propagation delays. Federated Learning (FL) offers a promising solution because it allows data to stay in-situ (never leaving satellites) and it only needs to transmit machine learning model parameters (trained on the satellites' data). However, the conventional, synchronous FL process can take several days to train a single FL model in the context of satellite communication (Satcom), due to a bottleneck caused by straggler satellites. In this paper, we propose an asynchronous FL framework for LEO constellations called AsyncFLEO to improve FL efficiency in Satcom. Not only does AsynFLEO address the bottleneck (idle waiting) in synchronous FL, but it also solves the issue of model staleness caused by straggler satellites. AsyncFLEO utilizes high-altitude platforms (HAPs) positioned "in the sky" as parameter servers, and consists of three technical components: (1) a ring-of-stars communication topology, (2) a model propagation algorithm, and (3) a model aggregation algorithm with satellite grouping and staleness discounting. Our extensive evaluation with both IID and non-IID data shows that AsyncFLEO outperforms the state of the art by a large margin, cutting down convergence delay by 22 times and increasing accuracy by 40%.