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Due to the difficulty of acquiring large sets of real images, spacecraft pose estimation networks are exclusively trained on synthetic ones. However, because those images do not capture the illumination conditions encountered in orbit, pose estimation networks face a domain gap problem, e.g., they do not generalize to real images. Our work introduces a method that bridges this domain gap. It relies on a novel, end-to-end, neural-based architecture as well as a novel learning strategy. This strategy improves the domain generalization abilities of the network through multitask learning and aggressive data augmentation policies, thereby enforcing the network to learn domain-invariant features. We demonstrate that our method effectively closes the domain gap, achieving state-of-the-art accuracy on the widespread SPEED+ dataset. 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