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.

TianQin is a proposed space-based gravitational-wave observatory mission to be deployed in high circular Earth orbits. The equilateral-triangle constellation, with a nearly fixed orientation, can be distorted primarily under the lunisolar perturbations. To accommodate science payload requirements, one must optimize the orbits to stabilize the configuration in terms of arm-length, relative velocity, and breathing angle variations. In this paper, we present an efficient optimization method and investigate how changing the two main design factors, i.e. the orbital orientation and radius, impacts the constellation stability through single-variable studies. Thereby, one can arrive at the ranges of the orbital parameters that are comparatively more stable, which may assist future refined orbit design.

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