Optimal low-thrust transfers to synchronous orbit

The general problem of circle-to-circle transfer is examined for chemical rocket spacecraft, following Lawden's 'primer vector' theory. Impulsive and near-impulsive transfers are analyzed to predict initial conditions for low-thrust transfers. A computer solution of the low-thrust problem is described. Results are presented for the low earth orbit to geosynchronous orbit case, showing behavior of the optimal thrust direction, and developing transfer efficiency figures for a range of acceleration limits. Both fixed-thrust and fixed-acceleration propulsion systems are considered. The effect of multiple burns is discussed. Robbins's approximation for gravity loss is shown to be good for a large class of maneuvers.