Transfers with a rendezvous lasting one to two orbits between near-circular coplanar orbits

The paper discusses orbit transfers involving spacecraft rendezvous which belong to the class of coplanar non-intersecting orbits of a spacecraft and a space station. The duration of the rendezvous is assumed to be limited to two orbits, because for longer durations there is a known optimal solution algorithm, where phasing is achieved through the optimal orbit-to-orbit transfer between coplanar orbits. The proposed programs include in the final leg of the transfer a three-impulse rendezvous program lasting one orbit, which was determined using the method of splitting the impulse burns for the optimal orbit-to-orbit transfer. The phasing needed to achieve the phase difference required at the start of the three-impulse rendezvous program is attained through maneuvering during the previous leg of the transfer and the splitting of the orbit transfer pulses, not resulting in an increased propellant consumption. The structure of the optimal rendezvous program as function of its duration was determined and computing formulas were obtained. The range of phase differences at the start of maneuvering was determined, within which the characteristic velocity of the rendezvous is equal to the characteristic velocity of the orbit-to-orbit transfer. The paper presents simulation results for «quick» rendezvous profiles that use the proposed programs.