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

Abstract

ASTROD-GW (ASTROD [Astrodynamical Space Test of Relativity using OpticalDevices] optimized for Gravitational Wave detection) is a gravitational-wave mission with the aim of detecting gravitational waves from massive black holes, extreme mass ratio inspirals (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 spacecrafts 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 precession-period. 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 is 0° (no inclination), 0.5°, 1.0°, 2 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 example to show the orbit optimization and TDI simulation.

Alternative LISA-TAIJI networks

“…These three combinations should cover all the possible dual detector scenarios except the LISA with a co-located TAIJI having a −60 • inclination which would be insipid because neither the large separation benefiting for the compact binary observation nor strong cross-correlation for the SGWB observation is expected. The numerical orbits for the TAIJIp and TAIJIc are from our work in [24,32], and the orbit for TAIJIm is newly obtained from our optimization method in [32][33][34][35][36][37].…”

Gravitational wave detection in space

“…41 Time delay interferometry has been worked out for LISA much more thoroughly on various aspects since 1999. 88,89 First-generation and second-generation TDIs are proposed.…”

“…Schematic orbit configuration of LISA-type mission design 9 and ASTROD-GW mission design 41 are shown in Fig. 1 and Fig.…”

“…2. 3,41 Before the ASTROD-GW proposal, Super-ASTROD which was proposed in 1996 23 with S/C's in Jupiter-like orbits was studied as a dual mission for GW measurement and for cosmological model/relativistic gravity test in 2008. 42 With the proposal of ASTROD-GW, the baseline GW configuration of Super-ASTROD makes 3 out of 4-5 S/C orbiting near Sun-Jupiter Lagrange points L3, L4 and L5 respectively.…”

Gravitational wave astronomy: the current status

“…Since then we have worked out the same things numerically for LISA [305], eLISA/NGO [306], NGO-LISAtype with 2 × 10 6 km arm length [306], ASTROD-GW with no inclination [307,308], and ASTROD-GW with inclination [309]. Schematic orbit configuration of ASTROD-GW mission design [309] and LISA-type mission design (http://sci.esa.int/lisa/35596-schematic-of-lisa-orbit/) are shown in Figures 39 and 40. For the numerical evaluation, we take a common receiving time epoch for both beams; the results would be very close to each other numerically if we take the same start time epoch and calculate the path differences.…”