Autonomous free-flying robots in orbital environments require controllers that are both versatile and resource-efficient, yet maintaining a separate, task-specific policy for each mission profile is architecturally brittle and limits operational flexibility as requirements evolve. We introduce HYPER-GNC, a multi-task reinforcement learning framework in which a hypernetwork maps physics-informed task embeddings to the weights of a shared actor-critic policy, enabling a single compact controller to master four distinct GNC tasks: velocity tracking, docking, inspection, and navigation with obstacle avoidance. The continuous embedding space allows the controller to generalize to novel mission configurations at deployment time without any retraining. Extensive experiments demonstrate that HYPER-GNC achieves sample efficiency comparable to single-task specialists while maintaining stability under significant inertial perturbations and external body wrenches. We further validate the framework on a physical satellite emulator, successfully bridging the simulation-to-reality gap across all mission profiles. Code, trained models, and deployment scripts are made publicly available to support reproducibility.

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