ASTROD-GW (ASTROD [Astrodynamical Space Test of Relativity using Optical Devices] optimized for Gravitation Wave detection) is an optimization of ASTROD to focus on the goal of detection of gravitation waves. The detection sensitivity is shifted 52 t
imes toward larger wavelength compared to that of LISA. 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. In order to attain the requisite sensitivity for ASTROD-GW, laser frequency noise must be suppressed 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 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 residual optical path differences in the first and second generation TDI for one-detector case. In our optimized mission orbits for 20 years, changes of arm length are less than 0.0003 AU; the relative Doppler velocities are less than 3m/s. All the second generation TDI for one-detector case satisfies the ASTROD-GW requirement.
In order to attain the requisite sensitivity for LISA, laser frequency noise must be suppressed below the secondary noises such as the optical path noise, acceleration noise etc. In a previous paper (Dhurandhar et al., Class. Quantum Grav., 27, 13501
3, 2010), we have found a large family of second-generation analytic solutions of time delay interferometry with one arm dysfunctional, and we also estimated the laser noise due to residual time-delay semi-analytically from orbit perturbations due to Earth. Since other planets and solar-system bodies also perturb the orbits of LISA spacecraft and affect the time delay interferometry (TDI), we simulate the time delay numerically in this paper for all solutions with the generation number n leq 3. We have worked out a set of 3-year optimized mission orbits of LISA spacecraft starting at January 1, 2021 using the CGC2.7 ephemeris framework. We then use this numerical solution to calculate the residual optical path differences in the second-generation solutions of our previous paper, and compare with the semi-analytic error estimate. The accuracy of this calculation is better than 1 cm (or 30 ps). The maximum path length difference, for all configuration calculated, is below 1 m (3 ns). This is well below the limit under which the laser frequency noise is required to be suppressed. The numerical simulation in this paper can be applied to other space-borne interferometers for gravitational wave detection with the simplification of having only one interferometer.
ASTROD I is a planned interplanetary space mission with multiple goals. The primary aims are: to test General Relativity with an improvement in sensitivity of over 3 orders of magnitude, improving our understanding of gravity and aiding the developme
nt of a new quantum gravity theory; to measure key solar system parameters with increased accuracy, advancing solar physics and our knowledge of the solar system and to measure the time rate of change of the gravitational constant with an order of magnitude improvement and the anomalous Pioneer acceleration, thereby probing dark matter and dark energy gravitationally. It is an international project, with major contributions from Europe and China and is envisaged as the first in a series of ASTROD missions. ASTROD I will consist of one spacecraft carrying a telescope, four lasers, two event timers and a clock. Two-way, two-wavelength laser pulse ranging will be used between the spacecraft in a solar orbit and deep space laser stations on Earth, to achieve the ASTROD I goals. A second mission, ASTROD II is envisaged as a three-spacecraft mission which would test General Relativity to one part per billion, enable detection of solar g-modes, measure the solar Lense-Thirring effect to 10 parts per million, and probe gravitational waves at frequencies below the LISA bandwidth. In the third phase (ASTROD III or Super-ASTROD), larger orbits could be implemented to map the outer solar system and to probe primordial gravitational-waves at frequencies below the ASTROD II bandwidth.
