Systems consisting of a massive black hole and a stellar-origin compact object (CO), known as extreme-mass-ratio inspirals (EMRIs), are of great significance for space-based gravitational-wave detectors, as they will allow for testing gravitational theories in the strong field regime, and for checking the validity of the black hole no-hair theorem. In this work, we present a calculation of the EMRI rate and parameter estimation capabilities of the TianQin observatory, for various astrophysical models for these sources. We find that TianQin can observe EMRIs involving COs with a mass of $10M_{\odot }$ up to redshift $\sim 2$. We also find that detections could reach tens or hundreds per year in the most optimistic astrophysical scenarios. Intrinsic parameters are expected to be recovered to within fractional errors of $\sim {10}^{-6}$, while typical errors on the luminosity distance and sky localization are 10% and $10{\mathrm{deg}}^2$, respectively. TianQin observation of EMRIs can also constrain possible deviations from the Kerr quadrupole moment to within fractional errors $\lesssim {10}^{-4}$. We also find that a network of multiple detectors would allow for improvements in both detection rates (by a factor $\sim 1.5–3$) and in parameter estimation precision (20-fold improvement for the sky localization and fivefold improvement for the other parameters).

TianQin is a future space-based gravitational wave (GW) observatory targeting the frequency window of 10⁻⁴–1 Hz. A large variety of GW sources are expected in this frequency band, including the merger of massive black hole binaries, the inspiral of extreme/intermediate mass ratio systems, stellar-mass black hole binaries, Galactic compact binaries, and so on. TianQin will consist of three Earth orbiting satellites on nearly identical orbits with orbital radii of about 10⁵ km. The satellites will form a normal triangle constellation whose plane is nearly perpendicular to the ecliptic plane. The TianQin project has been progressing smoothly following the ‘0123’ technology roadmap. In step ‘0’, the TianQin laser ranging station has been constructed and it has successfully ranged to all the five retro-reflectors on the Moon. In step ‘1’, the drag-free control technology has been tested and demonstrated using the TianQin-1 satellite. In step ‘2’, the inter-satellite laser interferometry technology will be tested using the pair of TianQin-2 satellites. The TianQin-2 mission has been officially approved and the satellites will be launched around 2026. In step ‘3’, i.e. the TianQin-3 mission, three identical satellites will be launched around 2035 to form the space-based GW detector, TianQin, and to start GW detection in space.

In future geocentric space-based gravitational-wave observatory missions, eclipses due to passing through the Moon’s and Earth’s shadows can negatively impact the sciencecraft’s thermal stability and steady power supply. The occurrence should be reduced as much as possible in orbit design. In regard to TianQin’s circular high orbits, we tackle the combined challenges of avoiding eclipses and stabilizing the nearly equilateral-triangle constellation. Two strategies are proposed, including initial phase selection and orbit resizing to $1:8$ synodic resonance with the Moon, where the latter involves slightly raising TianQin’s preliminary orbital radius of $1\times {10}^5\mathrm{km}$ to $\sim 100900\mathrm{km}$. As the result, we have identified pure-gravity target orbits with a permitted initial phase range of $\sim 15°$, which can maintain eclipse-free during the $3+3$ month observation windows throughout a 5-year mission started in 2034, and meanwhile fulfill the constellation stability requirements. Thereby the eclipse issue for TianQin can be largely resolved.

TianQin is a proposed space-borne gravitational-wave detection mission using circular high Earth orbits. The geocentric concept has raised questions about the disturbing effect of the nearby gravity field of the Earth-Moon system on the highly sensitive intersatellite ranging measurements. Here we examine the issue through high-precision numerical orbit simulations with detailed gravity-field models. By evaluating range accelerations between distant free-falling test masses, the study shows that the majority of the Earth-Moon’s gravity disturbances are not in TianQin’s detection frequency band above ${10}^{-4}\mathrm{Hz}$, and hence present no showstoppers to the mission.