  In this paper, 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 equation on a suitable state space, with the
reconstruction of the optimal controls made in the form of a static feedback.
In order to validate the numerical scheme without the complexity of the full
model, this first study sets the problem in planar form, thus working in a
four-dimensional state space. We will study various techniques to speed up the
computation, and assess the accuracy of the numerical solution.
  This project is born from the attempt of evaluating and applying direct
method of optimal control techniques based on Dynamic Programming as a
complementary approach to the well known indirect methods, as Pontryagin or
Lawden. In particular, the final aim is to treat the case of low thrust engines
from real use cases, in the full 3-D problem.
