  TianQin is a space-based laser interferometric gravitational wave detector
aimed at detecting gravitational waves at low frequencies (0.1 mHz -- 1 Hz). It
is formed by three identical drag-free spacecrafts in an equilateral triangular
constellation orbiting around the Earth. The distance between each pair of
spacecrafts is approximately $1.7 \times 10^{5} ~\rm{km}$. The spacecrafts are
interconnected by infrared laser beams forming up to three Michelson-type
interferometers. The detailed mission design and the study of science
objectives for the TianQin project depend crucially on the orbit and the
response of the detector. In this paper, we provide the analytic expressions
for the coordinates of the orbit for each spacecraft in the
heliocentric-ecliptic coordinate system to the leading orders. This enables a
sufficiently accurate study of science objectives and data analysis, and serves
as a first step to further orbit design and optimization. We calculate the
response of a single Michelson detector to plane gravitational waves in
arbitrary waveform which is valid in the full range of the sensitive
frequencies. It is then used to generate the more realistic sensitivity curve
of TianQin. We apply this model on a reference white-dwarf binary as a proof of
principle.
