Coupling effect of vibrations and residual electrostatic force in short-range gravitational experiments

In the short-range test of the gravitational inverse-square law (ISL) using a torsion pendulum, the residual electrostatic force is usually the major disturbance. We have built a torsion pendulum apparatus to verify the coupling effect of the residual electrostatic force with the separation variation between the test mass and the shielding membrane due to the environmental vibrations. We present an alternative solution for reducing the disturbance by suspending the shielding membrane, which has a common mode response as the torsion pendulum to the seismic translational motion and ground tilt. The experimental results with a fixed membrane are in good agreement with the theoretical calculations. By replacing the fixed membrane with a suspended membrane, the sensitivity of the torsion pendulum has been improved by at least a factor of 3 from 0.5 to 20 mHz, which is very useful for the further improvement of the ISL test in short range. This work may be helpful for other small-force measurement experiments.