Smooth transfer orbits with minimum fuel consumption

The present paper is concerned with the transfer from one Kepler orbit to another, whereby the transitions from the parking orbit into the transfer orbit, and from the transfer orbit into the terminal orbit are 'smooth', i.e., where the velocity is continuous. An explicit form for the variable thrust is offered that not only guarantees smooth transitions, but also provides design criteria for transfer vehicles in terms of two Eigenvalues that characterize any particular transfer. In addition, it is shown that the most economical transfer with respect to total fuel consumption is achieved if the thrust is applied in near circumferential direction. An application is made to the transfer from a low earth orbit to the geosynchronous orbit.