Complete energy optimal landing on small and large planetary bodies via theory of functional connections

In this paper, we propose a unified approach to solve the energy optimal landing on a planetary body (e.g., planet, asteroid, comet, etc.). The proposed method accurately computes the energy optimal landing trajectories, including the optimal time of flight, with a computation time on the order of 10-100 milliseconds, using MATLAB. The speed and accuracy of this techniques validate it as a suitable approach for real-time applications. The algorithms developed from this theory are validate for the landing final descent phase in Gaspra and Bennu asteroids and planet Mars.