Modeling tethered space systems is critical for advanced orbital operations. Flexible components such as tethers and space nets are integral to these systems but present significant control challenges due to their high dimensional, strongly coupled, and nonlinear dynamics. While data driven methods offer alternative modeling approaches, they frequently struggle with long term predictive stability and spatial generalization. To address this, we propose the Koopman Graph Dynamics (KGD) framework to learn the structural dynamics by integrating the global linear evolution of the Koopman operator with the local topological priors of Graph Neural Networks. Building upon this representation, we develop a KGD based Model Predictive Control strategy for tethered space systems. Subsequently, the ground experiments on flexible tether and space net demonstrate the high precision modeling capabilities of the proposed method. Crucially, the framework exhibits exceptional capacity for spatial transfer without retraining. Models trained exclusively on small configurations successfully predict and control significantly larger, unseen physical scales. Furthermore, the orbit simulations within a physics engine verify the effectiveness of the proposed approach for tethered space systems.

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