  The proposed space-borne laser interferometric gravitational wave (GW)
observatory TianQin adopts a geocentric orbit for its nearly equilateral
triangular constellation formed by three identical drag-free satellites. The
geocentric distance of each satellite is $\approx 1.0 \times 10^{5}
~\mathrm{km}$, which makes the armlengths of the interferometer be $\approx
1.73 \times 10^{5} ~\mathrm{km}$. It is aimed to detect the GWs in $0.1
~\mathrm{mHz}-1 ~\mathrm{Hz}$. For space-borne detectors, the armlengths are
unequal and change continuously which results in that the laser frequency noise
is nearly $7-8$ orders of magnitude higher than the secondary noises (such as
acceleration noise, optical path noise, etc.). The time delay interferometry
(TDI) that synthesizes virtual interferometers from time-delayed one-way
frequency measurements has been proposed to suppress the laser frequency noise
to the level that is comparable or below the secondary noises. In this work, we
evaluate the performance of various data combinations for both first- and
second-generation TDI based on the five-year numerically optimized orbits of
the TianQin's satellites which exhibit the actual rotating and flexing of the
constellation. We find that the time differences of symmetric interference
paths of the data combinations are $\sim 10^{-8}$ s for the first-generation
TDI and $\sim 10^{-12}$ s for the second-generation TDI, respectively. While
the second-generation TDI is guaranteed to be valid for TianQin, the
first-generation TDI is possible to be competent for GW signal detection with
improved stabilization of the laser frequency noise in the concerned GW
frequencies.
