Monitoring space objects is crucial for space situational awareness, yet reconstructing 3D satellite models from ground-based telescope images is super challenging due to atmospheric turbulence, long observation distances, limited viewpoints, and low signal-to-noise ratios. In this paper, we propose a novel computational imaging framework that overcomes these obstacles by integrating a hybrid image pre-processing pipeline with a joint pose estimation and 3D reconstruction module based on controlled Gaussian Splatting (GS) and Branch-and-Bound (BnB) search. We validate our approach on both synthetic satellite datasets and on-sky observations of China’s Tiangong Space Station and the International Space Station, achieving robust 3D reconstructions of low-Earth orbit satellites from ground-based data. Quantitative evaluations using SSIM, PSNR, LPIPS, and Chamfer Distance demonstrate that our method outperforms state-of-the-art NeRF-based approaches, and ablation studies confirm the critical role of each component. Our framework enables high-fidelity 3D satellite monitoring from Earth, offering a cost-effective alternative for space situational awareness.