Measuring self-gravity of spacecraft for space gravitational wave detection

In space-based gravitational wave detection, the gravitational force generated by the spacecraft itself at the location of the test masses, known as self-gravity, can disrupt the free-fall state of the test masses. The self-gravity effect is one of the main noise sources in gravitational wave detection. Currently, the only established method to estimate this effect before launch is the finite element calculation based on the precise spacecraft computer aided design model. In this paper, we propose a torsion pendulum experiment to measure the dominant gravitational multipole components of spacecraft to assess the self-gravity. This provides an important ground-validation approach for finite element calculations. The results of a proof-of-principle experiment show that the measurement resolution can reach $3.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\text{ }\text{ }\mathrm{m}\text{ }{\mathrm{s}}^{\ensuremath{-}2}$ for differential linear acceleration, $1.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\text{ }\text{ }\mathrm{rad}\text{ }{\mathrm{s}}^{\ensuremath{-}2}$ for angular acceleration, and $4.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\text{ }\text{ }{\mathrm{s}}^{\ensuremath{-}2}$ for linear gradients. These measurement resolutions are sufficient for estimating the self-gravity of Laser Interferometer Space Antenna or TianQin.