Influence of the Earth's Rotation on Measurement of Newton's Constant by using the Angular Acceleration Method

Using the relativistic Lagrangian expression, we develop a method to derive the equation of motion of the torsion balance in a non-inertial reference frame, which is used to analyze the gravitational experiment in measuring Newton's constant G with the angular acceleration method. Our calculation shows that the Earth's rotation couples with the vibration, which should be considered in the high?accuracy experiments of determining the gravitational constant G.