Étude et réalisation d'un procédé expérimental novateur dédié à la mesure de la constante universelle de gravitation G
(2009)
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- (en) Remains of systematic errors in recent experiments dedicated to the measurement of the universal constant of gravitation lead the 2006 CODATA comity to promote the development of new experiments relying on conceptually different principles. In this work we propose to study the feasibility of a new approach based on an astatic vertical pendulum driven in position feedback loop by means of an electrostatic actuator. The very close position between the center of mass of the pendulum and his axis of rotation provides a low sensitivity of the angular position of pendulum's arm to the local micro-seismic ground acceleration while its one degree of rotational freedom enables a very precise position feedback loop control. The use of the position feedback loop enables to achieve linearity and stability of the balance by compensating the mechanical work of pendulum's hinge, cause of various biases due to anelastic effects which are hard to manage. Calibration factor of gravitational torques applied on the pendulum's arm is set by two independent ways: the electrostatic torque used for the position feedback loop and a small calibration mass applied with a variable cantilever around the pendulum's axis of rotation. This one is materialised on our apparatus by the horizontal rotation of the weight of the needle of a watch fixed on the pendulum's arm. We will detail the main concepts of our approach and corresponding theoretical models in parallel with the description of our experimental apparatus. This one is designed to achieve a theoretical precision of few percent on the measurement of the gravitational torque. The resolutions of our capacitive position sensor and our electrostatic actuator are respectively about 10-9 rad and 10-9 Nm. We will also introduce the effect of the main background noises factors related to this kind of experiment as well as a very simple algorithm enabling us to compute gravitational effects for any geometry of masses. The conclusions coming from our theoretical and experimental study will allow us to provide a set of suggestions and recommendations to reach a resolution of a few ppm in the measurement of the gravitational torque.
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Naslin, S. (2009). Étude et réalisation d’un procédé expérimental novateur dédié à la mesure de la constante universelle de gravitation G. https://hdl.handle.net/2078.5/131241