In this talk, we present an application of the optimal control theory to orbital transfer of Low Earth Orbit satellites. The optimal control problem is treated with Dynamic Programming techniques which require solving the Hamilton–Jacobi– Bellman equations on a suitable state space, with the reconstruction of the optimal controls in a static feedback form. This study sets the problem first in planar form, thus working in a four-dimensional state space, and then in the three-dimensional case (thus working in a six-dimensional state space). We will focus on the implementation of various techniques to speed up the computation, and asses the accuracy of the numerical solution.