In recent space missions, the more complicated the missions become, the moreimportant autonomous spacecraft controllers are. In this study, we focus on aprecise autonomous orbit prediction of LEO (Low-Earth Orbit) satellite. ThePhysics Informed Machine learning (PIML) enables us to predict the satellite orbitwith compatible accuracy to the numerical simulation but more efficiently. Theproposed physics informed machine learning algorithm is based on modelling theorbital trajectory as Partial Differential Equation (PDE) and using deep NeuralOperator (NO) to model the dynamic of the system. We also analyse the limitationsin terms of prediction errors with respect to noisy measurements, sample frequency and computational requirements for satellite onboard operation.