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.
