A Low Earth orbit (LEO) satellite constellation consists of a large number of small satellites traveling in space with high mobility and collecting vast amounts of mobility data such as cloud movement for weather forecast, large herds of animals migrating across geo-regions, spreading of forest fires, and aircraft tracking. Machine learning can be utilized to analyze these mobility data to address global challenges, and Federated Learning (FL) is a promising approach because it eliminates the need for transmitting raw data and hence is both bandwidth and privacy friendly. However, FL requires many communication rounds between clients (satellites) and the parameter server (PS), leading to substantial delays of up to several days in LEO constellations. In this paper, we propose a novel one-shot FL approach for LEO satellites, called LEOShot, that needs only a single communication round to complete the entire learning process. LEOShot comprises three processes: (i) synthetic data generation, (ii) knowledge distillation, and (iii) virtual model retraining. We evaluate and benchmark LEOShot against the state of the art and the results show that it drastically expedites FL convergence by more than an order of magnitude. Also surprisingly, despite the one-shot nature, its model accuracy is on par with or even outperforms regular iterative FL schemes by a large margin.