This thesis endeavors to explore and substantiate the utility of a novel approach to Spacecraft Docking Optimization, which integrates Machine Learning methodologies. The research commences by validating the proposed methodology through comprehensive mathematical analysis, grounding the model in well-established mathematical theorems and principles, particularly employing Optimal Control techniques to delineate the underlying framework. Subsequent to establishing the mathematical underpinnings, the study introduces and elucidates the integration of Neural Networks within the proposed framework, highlighting their potential efficacy in addressing the complexities inherent in solving Partial Differential Equations for optimization purposes. Furthermore, the thesis progresses to conduct empirical evaluations utilizing computational simulations implemented in a Python programming environment.