Experimental Demonstration Of Gravitational Acceleration Measurement With Pendulum Based On Two Fixed-points Method

Gravitational acceleration is a quantity which varies from place to place and whichalso varies with time. High precision gravity measurement is of great significance in manyfields：geophysics, geodesy, metrology and so on. By measuring the length and its periodof a pendulum, the absolute value of gravitational acceleration g can be obtained. Thesimple structure and low cost make the absolute gravimeter with pendulum method ofgreat value in missile guidance and experimental physics.Due to the measuring uncertainty of the center of the test mass, the accurate length ofthe pendulum is difficult to acquire. A variable length pendulum swing method has beenbrought up to measure gravitational acceleration by comparing two swing-periods of twopendulums with different length. Based on this method, they change the pendulum lengthby lifting the test mass. Although this method avoids the direct measurement of theabsolute length of the pendulum, it is limited by the uncertainty of the suspension point,which makes it difficult to accurately measure the pendulum length variance. In addition，its the reproducibility is also poor, which results in a low accuracy of gravitationalacceleration measurement.In order to improve the accuracy for absolute gravity measurement by comparing twoswing-periods of two pendulums with different length, a new method based on onependulum with two suspension fixed points has been proposed in this thesis. Boththeoretical calculation and preliminary experiments have been conducted.Firstly, according to the practical motion of the pendulum, we definite the coordinatereference system, set up a mathematical model, deduce the motion equations and analyzethe pendulum motion common to both modes: double pendulum and compound pendulum.Then we analyze possible systematic error sources for gravity measurement, such as thegeometry parameters, angular, stretching of wire, motion of supporting cage, damping,temperature and et al. Precision requirements of corresponding parameters and their final contributions for mGal-level gravity measurement have been caculated.Secondly, we design and build the demonstrational experimental device formeasuring gravitational acceleration. The functionality of knife-edges control has beenrealized by the fixed swing points system, the knife-edges’ reiteration has been tested. Themotion of the test mass is record by a differential transformer bridge capacitive transducersystem, which has been calibrated carefully. The experimental data is analyzed and thevalue of the gravitational acceleration is obtained as g=(9.7925±0.0056)m/s2, with arelative uncertainty of6.03×10-4. Its main errors are due to the distance measurementbetween the knife-edges and the swing-periods measurement.Finally, based on the analysis of the current experimental result, some improvementscheme for further is discussed and proposed.