Influence of the Earth’s rotation on measurement of gravitational constant G with the time-of-swing method*

Abstract

In the measurement of the Newtonian gravitational constant G with the time-of-swing method, the influence of the Earth’s rotation has been roughly estimated before, which is far beyond the current experimental precision. Here, we present a more complete theoretical modeling and assessment process. To figure out this effect, we use the relativistic Lagrangian expression to derive the motion equations of the torsion pendulum. With the correlation method and typical parameters, we estimate that the influence of the Earth’s rotation on G measurement is far less than 1 ppm, which may need to be considered in the future high-accuracy experiments of determining the gravitational constant G.