Hohmann-Hohmann and Hohmann-Phasing Cooperative Rendezvous Maneuvers

We consider the problem of cooperative rendezvous between two satellites in circular orbits, given a fixed time for the rendezvous to be completed, and assuming a circular rendezvous orbit. We investigate two types of cooperative maneuvers for which analytical solutions can be obtained. One is the case of two Hohmann transfers, henceforth referred to as HHCM, while the other, henceforth referred to as HPCM, is the case of a Hohmann transfer and a phasing maneuver. For the latter case we derive conditions on the phasing angle that make a HPCM rendezvous cheaper than a cooperative rendezvous on an orbit that is different than either the original orbits of the two participating satellites. It is shown that minimizing the fuel expenditure is equivalent to minimizing a weighted sum of the ΔVs of the two orbital transfers, the weights being determined by the mass and engine characteristics of the satellites. Our results show that, if the time of rendezvous allows for a Hohmann transfer between the orbits of the satellites, the optimal rendezvous is either a noncooperative Hohmann transfer or a Hohmann-phasing cooperative maneuver. In both of these cases, the maneuver costs are determined analytically. A numerical example verifies these observations. Finally, we demonstrate the utility of this study for Peer-to-Peer (P2P) refueling of satellites residing in two different circular orbits.