  In the detection of gravitational waves in space, the arm lengths between
spacecraft are not equal due to their orbital motion. Consequently, the equal
arm length Michelson interferometer used in Earth laboratories is not suitable
for space. To achieve the necessary sensitivity for space gravitational wave
detectors, laser frequency noise must be suppressed below secondary noise
sources such as optical path noise and acceleration noise. To suppress laser
frequency noise, time-delay interferometry (TDI) is employed to match the two
optical paths and retain gravitational wave signals. Since planets and other
solar system bodies perturb the orbits of spacecraft and affect TDI
performance, we simulate the time delay numerically using the CGC2.7 ephemeris
framework. To examine the feasibility of TDI for the ASTROD-GW mission, we
devised a set of 10-year and a set of 20-year optimized mission orbits for the
three spacecraft starting on June 21, 2028, and calculated the path mismatches
in the first- and second-generation TDI channels. The results demonstrate that
all second-generation TDI channels meet the ASTROD-GW requirements. A geometric
approach is used in the analysis and synthesis of both first-generation and
second-generation TDI to clearly illustrate the construction process.
