Deployment and simulation of the ASTROD-GW formation
  Constellation or formation flying is a common concept in space Gravitational Wave (GW) mission proposals for the required interferometry implementation. The spacecraft of most of these mission proposals go to deep space and many have Earthlike orbits around the Sun. ASTROD-GW, Big Bang Observer and DECIGO have spacecraft distributed in Earthlike orbits in formation. The deployment of orbit formation is an important issue for these missions. ASTROD-GW (Astrodynamical Space Test of Relativity using Optical Devices optimized for Gravitation Wave detection) is to focus on the goal of detection of GWs. The mission orbits of the 3 spacecraft forming a nearly equilateral triangular array are chosen to be near the Sun-Earth Lagrange points L3, L4 and L5. The 3 spacecraft range interferometrically with one another with arm length about 260 million kilometers with the scientific goals including detection of GWs from Massive Black Holes (MBH), and Extreme-Mass-Ratio Black Hole Inspirals (EMRI), and using these observations to find the evolution of the equation of state of dark energy and to explore the co-evolution of massive black holes with galaxies. In this paper, we review the formation flying for fundamental physics missions, design the preliminary transfer orbits of the ASTROD-GW spacecraft from the separations of the launch vehicles to the mission orbits, and simulate the arm lengths of the triangular formation. From our study, the optimal delta-Vs and propellant ratios of the transfer orbits could be within about 2.5 km/s and 0.55, respectively. From the simulation of the formation for 10 years, the arm lengths of the formation vary in the range 1.73210 +- 0.00015 AU with the arm length differences varying in the range +- 0.00025 AU for formation with 1 degree inclination to the ecliptic plane. This meets the measurement requirements. 
An-Ming Wu and Wei-Tou Ni
gr-qc astro-ph.CO astro-ph.IM physics.space-ph