TianQin is a planned space-based gravitational wave (GW) observatory consisting of three Earth-orbiting satellites with an orbital radius of about $10^5 \, {\rm km}$. The satellites will form an equilateral triangle constellation the plane of which is nearly perpendicular to the ecliptic plane. TianQin aims to detect GWs between $10^{-4} \, {\rm Hz}$ and $1 \, {\rm Hz}$ that can be generated by a wide variety of important astrophysical and cosmological sources, including the inspiral of Galactic ultra-compact binaries, the inspiral of stellar-mass black hole binaries, extreme mass ratio inspirals, the merger of massive black hole binaries, and possibly the energetic processes in the very early universe and exotic sources such as cosmic strings. In order to start science operations around 2035, a roadmap called the 0123 plan is being used to bring the key technologies of TianQin to maturity, supported by the construction of a series of research facilities on the ground. Two major projects of the 0123 plan are being carried out. In this process, the team has created a new-generation $17 \, {\rm cm}$ single-body hollow corner-cube retro-reflector which was launched with the QueQiao satellite on 21 May 2018; a new laser-ranging station equipped with a $1.2 \, {\rm m}$ telescope has been constructed and the station has successfully ranged to all five retro-reflectors on the Moon; and the TianQin-1 experimental satellite was launched on 20 December 2019—the first-round result shows that the satellite has exceeded all of its mission requirements.

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We consider the relativistic tidal effects on frequency shift of clockcomparison experiments. The relativistic formulation for frequency shift and time transfer is derived in the gravitational field of a tidal, axisymmetric, and rotating Earth. With the help of Love numbers describing the tidal response of solid Earth, we formulize the mathematical connection between tidal effects from the ground-based clock-comparison experiments and the local gravity tides from the gravimeters, which in turn provides us an approach to eliminate tidal influences on clock comparison with the local gravity tides data. Moreover, we develop a method of the perturbed Kepler orbit to determine relativistic effects of clock comparison for space missions, which allows more precise calculations comparing to the conventional method of unperturbed Kepler orbit. With this perturbed method, it can give the perturbation of relativistic effects due to the orbital changes under the influences of tidal forces, Earth's oblateness etc. In addition, as the applications of our results, we simulate tidal effects in frequency shift for the clock comparison on the ground and also give some estimates for TianQin mission and GPS.

Given the high-precision modern space mission, a precise relativistic modeling of observations is required. By solving the eikonal equation with the post-Newtonian approximation, the light propagation is determined by the iterative method in the gravitational field of an isolated, gravitationally bound N-body system. Different from the traditional N bodies that are independent with each other in the system, our system includes the velocities, accelerations, gravitational interactions and tidal deformations of the gravitational bodies. The light delays of these factors then are precisely determined by the analytical solutions. These delays are significant and are likely to reach a detectable level for the strong gravitational fields, such as binary pulsars and some gravitational wave sources. The result's application in the vicinity of the Earth provides a relativistic framework for modern space missions. From the relativistic analysis in the TianQin mission, we find the possible tests for the alternative gravitational theories, such as a possible determination for the post-Newtonian parameter γ in the level of some scalar-tensor theories of gravity.

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