Lunar flyby transfers to TianQin configuration

The TianQin mission for gravitational wave detection consists of three drag-free spacecrafts deployed in geocentric orbits, and forms an equilateral triangle configuration. In this paper, we investigate lunar flyby transfers to the TianQin configuration. Firstly, a preliminary design method of lunar flyby transfers is proposed in the patched-conic model. Then, lunar flyby transfers in the ephemeris model are constructed through the multiple shooting method. Numerical computation shows that compared to the traditional Hohmann transfer, the lunar flyby transfer can save about 12% of fuel, but its time of flight increases to about 11 days. For the initial deployment of the TianQin configuration, we propose two methods, the phasing method and the direct insertion method. The phasing method uses the phase adjustment when the three spacecraft reach the target orbit. Numerical calculation indicates that the fuel costs of the three spacecraft are identical to that of the nominal transfer, and the total time of flight is about 17 days. Then, the Jet transport tool is applied to find appropriate separation impulses to design the direct insertion orbits. Numerical computation shows that compared to the phasing method, the fuel cost of the direct insertion method is slightly larger than that of the phasing method, but the time of flight of the former is about 5 days shorter than that of the latter.