Fundamentals of the orbit and response for TianQin

Abstract

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