Effect of celestial body gravity on Taiji mission range and range acceleration noise

Abstract

The Taiji project is a space gravitational-wave detection mission consisting of three satellites that form a giant equilateral triangle with a side length of approximately $3\ifmmode\times\else\texttimes\fi{}{10}^{6}\text{ }\text{ }\mathrm{km}$ in the heliocentric orbit. The target of the mission is to detect gravitational-wave signals in the 0.1 mHz to 1 Hz band. However, its intersatellite distances are affected by celestial bodies in the solar system, introducing changes that may reach levels of 30,000 km in magnitude. Thus, it is important to investigate whether the gravitational fields of celestial bodies in the detection frequency band will have an impact on the realization of ultrahigh-sensitivity intersatellite ranging measurements. In this study, a high-precision orbit propagator with an accuracy of 0.03 pm on the 1 AU scale is developed. Based on this orbit propagator, the impact of the major large celestial bodies in the solar system on the detection sensitivity in the intersatellite measurements are analyzed. Detailed numerical studies show that the linear spectral density of the range and range acceleration are approximately $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\text{ }\text{ }\mathrm{m}/\sqrt{\mathrm{Hz}}$ and $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23}\text{ }\text{ }\mathrm{m}/{\mathrm{s}}^{2}/\sqrt{\mathrm{Hz}}$, respectively, at 0.1 mHz, indicating that the gravitational disturbance generated by the major celestial bodies in the solar system will not affect the aim of the Taiji mission to detect gravitational waves in the frequency band 0.1 mHz to 1 Hz.