The rapid growth in low-Earth-orbit satellites enables providing Earth observation applications to public users via a shared platform. However, the limited satellite-ground communication resources present a major challenge in downloading and fully utilizing satellite-captured Earth observation data on the ground. As a new edge computing paradigm, orbital edge computing allows satellites to host deep learning models with on-board computing resources for in-orbit data analysis, reducing downlink data volume and response time. However, the limited generalizability of in-orbit models and data distribution shifts across geographical locations severely impact the accuracy of in-orbit analytics. In this work, we design a framework, AdaOrb, which dynamically schedules online model retraining for location-specific Earth observation tasks. Scheduling decisions are made with a model predictive control-based algorithm that allocates limited satellite downlink capacity among onboard tasks to download model retraining data. By developing and using a hardware-in-the-loop orbital edge computing testbed, we show that our method achieves superior overall accuracy of in-orbit analytics tasks compared to alternative methods.