Approximate Optimization of Low-Thrust Transfers Between Low-Eccentricity Close Orbits

An approximation of the optimal control law for low-thrust transfers between low-eccentricity orbits with small changes of orbital elements is introduced. Transfers with a small number of revolutions around the main body are considered; in this case, Edelbaum's approximation, which is commonly adopted to analyze longer missions, provides unsatisfactory results. The novel approach presented here allows for analytic integration of the differential equations which describe the change of the orbital elements. Numerical solution of an algebraic system provides the control law that is required to obtain the prescribed orbit change. Results for different test cases are shown in comparison to the exact optimal solutions obtained with an indirect method. The mission costs that are evaluated with the approximate control law, provide a very accurate estimation of the actual optima, with a computational cost which is orders of magnitude lower.