Orbit optimization for ASTROD-GW and its time delay interferometry with two arms using CGC ephemeris

Abstract

Astrodynamical space test of relativity using optical devices optimized for gravitation wave detection (ASTROD-GW) is an optimization of ASTROD to focus on the goal of detection of gravitation waves. The detection sensitivity is shifted 52 times toward larger wavelength compared with that of laser interferometer space antenna (LISA). The mission orbits of the three spacecrafts forming a nearly equilateral triangular array are chosen to be near the Sun—Earth Lagrange points L3, L4, and L5. The three spacecrafts range interferometrically with one another with an arm length of about 260 million kilometers. In order to attain the required sensitivity for ASTROD-GW, laser frequency noise must be suppressed to below the secondary noises such as the optical path noise, acceleration noise, etc. For suppressing laser frequency noise, we need to use time delay interferometry (TDI) to match the two different optical paths (times of travel). Since planets and other solar-system bodies perturb the orbits of ASTROD-GW spacecraft and affect the TDI, we simulate the time delay numerically using CGC 2.7 (here, CGC stands for center for gravitation and cosmology) ephemeris framework. To conform to the ASTROD-GW planning, we work out a set of 20-year optimized mission orbits of ASTROD-GW spacecraft starting at June 21, 2028, and calculate the differences in optical path in the first and second generation TDIs separately for one-detector case. In our optimized mission orbits of 20 years, changes of arm lengths are less than 0.0003 AU; the relative Doppler velocities are all less than 3 m/s. All the second generation TDI for one-detector case satisfies the ASTROD-GW requirement.