Orbital transfer in minimum time

Abstract

The problem of orbital transfer discussed here is that of scheduling the direction p of constant momentum thrust of a rocket, which loses mass at a constant rate, so that it transfers to an earth satellite orbit, with known elements of time, position and velocity, in a minimum time T after launching of the rocket. The launching conditions are assumed to be fixed. This situation is illustrated in Figure 1 for the case of a circular orbit. The sector angle B at which the rocket enters orbit will be called the rendezvous angle. To aid the discussion imaginary physical rendezvous of the rocket and satellite is assumed to occur at this angle. The time of rocket launch to achieve actual physical rendezvous can be determined, of course, only after both of the unknowns T and B have been found. The problem is set up as a calculus of variations problem of the Lagrange type, and is solved by an iterative process in which an initial approximation to the angle B is estimated.