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

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 3m/s. All the second generation TDI for one-detector case satisfies the ASTROD-GW requirement.

Orbit optimization and time delay interferometry for inclined ASTROD-GW formation with half-year precession-period

ASTROD-GW （ASTROD [astrodynamical space test of relativity using optical devices] optimized for gravitational wave detection） is a gravitational-wave mission with the aim of detecting gravitational waves from massive black holes, extreme mass ratio inspirais （EMRIs） and galactic compact binaries together with testing relativistic gravity and probing dark energy and cosmology. Mission orbits of the 3 spacecrafts forming a nearly equilateral triangular array are chosen to be near the Sun-Earth Lagrange points L3, L4, and L5. The 3 space, crafts range interferometrically with one another with arm length about 260 million kilometers. For 260 times longer arm length, the detection sensitivity of ASTROD- GW is 260 fold better than that of eLISA/NGO in the lower frequency region by assuming the same acceleration noise. Therefore, ASTROD-GW will be a better cosmological probe. In previous papers, we have worked out the time delay interferometry （TDI） for the ecliptic formation. To resolve the reflection ambiguity about the ecliptic plane in source position determination, we have changed the basic formation into slightly inclined formation with half-year precessionperiod. In this paper, we optimize a set of 10-year inclined ASTROD-GW mission orbits numerically using ephemeris framework starting at June 21, 2035, including cases of inclination angle with 0° （no inclination）, 0.5°, 1.0°, 1.5°, 2.0°, 2.5°, and 3.0°. We simulate the time delays of the first and second generation TDI configurations for the different inclinations, and compare/analyse the numerical results to attain the requisite sensitivity of ASTROD-GW by suppressing laser frequency noise below the secondary noises. To explicate our calculation process for different inclination cases, we take the 1.0° as an example to show the orbit optimization and TDI simulation.