Machine learning-based solution of Kepler’s equation

In this study, an analytical solution of elliptical Kepler's equation, which gives the position of a celestial body moving in orbit as a function of time, is designed by using artificial intelligence techniques. For the eccentric anomaly, Kepler’s equation is a transcendental equation with no precise analytical solution. In this paper, a high precision approximate analytical solution is presented to determine eccentric anomaly. The proposed method is based on machine learning where a non-iterative accurate solution is learned from training data. The solution to Kepler’s solution is created using an artificial neural network based on the universal approximation theorem. Simulation results show that this solution is computationally efficient and has a constant complexity.