Online adaptation to distribution shifts in satellite image segmentation stands as a crucial yet underexplored problem. In this paper, we address source-free and online domain adaptation, i.e., test-time adaptation (TTA), for satellite images, with the focus on mitigating distribution shifts caused by various forms of image degradation. Towards achieving this goal, we propose a novel TTA approach involving two effective strategies. First, we progressively estimate the global Batch Normalization (BN) statistics of the target distribution with incoming data stream. Leveraging these statistics during inference has the ability to effectively reduce domain gap. Furthermore, we enhance prediction quality by refining the predicted masks using global class centers. Both strategies employ dynamic momentum for fast and stable convergence. Notably, our method is backpropagation-free and hence fast and lightweight, making it highly suitable for on-the-fly adaptation to new domain. Through comprehensive experiments across various domain adaptation scenarios, we demonstrate the robust performance of our method.