Dynamical response of the Galileo Galilei on the ground rotor to test the equivalence principle: Theory, simulation, and experiment. I. The normal modes

Recent theoretical work suggests that violation of the equivalence principle might be revealed in a measurement of the fractional differential acceleration η between two test bodies—of different compositions, falling in the gravitational field of a source mass—if the measurement is made to the level of η≃10−13 or better. This being within the reach of ground based experiments gives them a new impetus. However, while slowly rotating torsion balances in ground laboratories are close to reaching this level, only an experiment performed in a low orbit around the Earth is likely to provide a much better accuracy. We report on the progress made with the “Galileo Galilei on the ground” (GGG) experiment, which aims to compete with torsion balances using an instrument design also capable of being converted into a much higher sensitivity space test. In the present and following articles (Part I and Part II), we demonstrate that the dynamical response of the GGG differential accelerometer set into supercritical rota...