Thermal noise limit in measuring the gravitational constant G using the angular acceleration method and the dynamic deflection method

• A comparison is made between the angular acceleration method and the dynamic deflection method.
• Selection of driving signal frequency should avoid resonance to reach a lower thermal noise limit in the dynamic deflection method.
• The ultimate thermal noise limit for the angular acceleration method and the dynamic deflection method is obtained.
• Both have advantages and can be performed with one and the same device, making measurement of G more convenient and reliable.

A general comparison is made between two methods of measuring the gravitational constant G. The angular acceleration method can avoid the anelasticity effect since the torsion fiber is not twisted. The dynamic deflection method is similar in principle but it does not use feedback, therefore a major noise introduced by the feedback control system in the angular acceleration method can be avoided. Both methods have their advantages and can be performed with the same device. Based on different expressions of G, we have expressed the signal-to-noise ratio and calculated the thermal noise limit for both methods. In order to get a lower thermal noise limit, the dynamic deflection method should avoid resonance.