Studying The Influence Of Squeeze-film Damping Testing The Newtonian Inverse-square-law At Close Range In Using A Torsion Pendulum

Gravity is one of the four fundamental interaction forces in nature, it is very weak. The torsion pendulum has been widely used in various gravity experiments. With the development of technology, the sensitivity of the torsion pendulum detection is higher and higher, in these gravitational experiments various noises have become the important factor to limit the improvement of experimental accuracy, such as air damping, electrostatic force, temperature, magnetic field, vibration and so on.This paper analyze the problem of the squeeze-film damping in testing Newtonian inverse-square-law experiment at submillimeter range using density modulation method in our laboratory, namely the torque noise from gas molecular collisions of Brownian motion. The torsion pendulum in the vacuum container can lose itself energy from the residual gas molecular collisions, which make the torsion pendulum's noise increase. Firstly, We calculate quantitatively the gas damping of our torsion pendulum in a isolated space, when the pressure is 3×10-5Pa in the container, we found that the gas damping torque noise of the torsion pendulum isn't dominant.Secondly, We calculate the gas Brownian motion torque noise of our torsion pendulum in a infinite space. In order to understand the characteristics of Brownian motion from gas molecules better, we have a numerical simulation for the process of gas molecules collision with torsion pendulum in a infinite space, the relative error of the simulation and theoretical result of gas Brownian motion torque noise is agreement within the range of 0.3-4.8%. when the pressure is 3×10-5Pa in the container and the separation between a torsion pendulum and a thin film is less than 25?m, the gas Brownian motion torque noise is larger than thermal noise with internal damping for Q-factor 2500 tungsten fiber. If the torsion pendulum is suspended by the quartz fiber with Q-factor 50000, the gas Brownian motion torque noise is larger than thermal noise with internal damping when the separation between a torsion pendulum and a thin film is less than 150?m. These studies provide guidance for testing the Newtonian inverse-square-law at close range using a more ultra-sensitive torsion pendulum.