This thesis explores a novel Physics-Informed Machine Learning (PIML) approach to solve the minimum-time rest-to-rest reorientation problem in satellite attitude dynamics and control. The problem of satellite reorientation consists in maneuvering a satellite from an initial rest state to a desired rest state within the shortest possible time. It is critical for a wide range of space missions, including Earth observation, scientific research, and defense applications. While traditional optimization methods are effective, they are computationally intensive and sensitive to initial conditions, posing challenges for real-time applications. To address these limitations, this research investigates a Physics-Informed Neural Network (PINN) architecture specifically designed to solve the minimum time reorientation problem.