Optimal many-revolution orbit transfer

In the last decades, the problem of low-thrust, minimum-time orbit transfer has been studied analytically several times. Several authors used the method of two time variables. Edelbaum (1961) solved the optimal one-orbit control problem for the first time, and obtained a suboptimal solution for the long time scale problem. The present investigation also makes use of the method of two time scales, taking into account the separation of the optimal control problem into a 'fast' time scale problem over one orbit, and a 'slow' time scale problem over the entire transfer. For the first time, a detailed closed-form solution to the low-thrust circle to circle orbit transfer problem is obtained. The solution is exact for an infinite number of revolutions during the transfer. The solution is simple enough to be implemented in the onboard control system of an orbit transfer vehicle.