The research project, in collaboration with Thales Alenia Space Italia SpA, aims to study, develop and numerically simulate innovative methods for optimizing the orbital transfer of small satellites in LEO (Low Earth Orbit) using Low-Thrust engines, to be deployed in constellations for Earth observation applications. We developed the controlled dynamics of a single satellite, using the Dynamic Programming approach, based on the characterization of the value function via the Hamilton-Jacobi-Bellman equation. We have built an algorithm that fits a specific physical problem of industrial interest, applying numerical techniques as the Policy Iteration to make the algorithm faster, and using a more suitable grid to save memory. The main challenge is to build a solid control model to satisfy mission objectives and requirements, e.g. the time needed to reach the target orbit, or the use of propellent.