The Study Of Correlative Effects In Measuring G By The Time-of-swing Method With Large Amplitude Of Pendulum

Since Cavendish successfully measured the gravitational constant G by the torsion pendulum for the first time in 1798, a great many experimental groups from all around the world have been devoting great efforts to the optimization of experiment designs and the improvements of measure techniques in the field of measuring the Newtonian constant G in the past 200 years, which aim to achieve measurement results with higher precision. At present, there are 8 claimed measurement results of G with relative uncertainty less than 50 ppm. The respectively claimed values of G are extremely accurate, but these values are still in poor agreement with each other. which is maybe caused by the unfound or unrecognized system errors among different methods.The Center of Gravitational Experiment have carried out the gravitation research of precise torsion balance since 1980 s. In the field of measuring G, our achieved results of HUST-99, HUST-05 and HUST-09 have been recorded by the CODATA. The time-of-swing method we used to determine G is based on the pendulum motion amplitude of mrad, and hence the intrinsic thermal noise of the torsion pendulum is relatively large. Then, the precision of period extraction is relatively low, and thus determining the period of pendulum with enough high precision is at the cost of very long cycle of the whole measurement. Besides, the long cycle demands much higher stability and consistency of ambient environment and experimental apparatus. Based on the above considerations and combined with the existing measurement condition of our laboratory, this thesis makes preliminary analysis and discussion of correlative effects in the time-of-swing method with large amplitude, which is proposed and improved by Newman et al. 1. Via the two different methods of gravitational potential and multipole moment expansion, the simulation model of torsional torque of the pendulum in the time-of-swing method with large amplitude is established. 2. After some simplification, the curve of torsional torque versus torsional amplitude is given when the source masses is placed at the “near” or “far” positions, and then the characteristic curve of the frequency squared versus torsional amplitude is obtained. This thesis also calculates the influence of the amplitude effect on the value of G, which in the condition that the torsional amplitude of the pendulum is large up to the order of rad. Compared to the experiment of HUST-09, the contribution of the amplitude effect to the relative uncertainty of determining G is 10~100 times larger than before. 3. The correlation method is used to calculate the intrinsic thermal noise limit of the pendulum on the period extraction, which occurs in the time-of-swing method with large amplitude. Due to the significant large amplitude, the relative contribution of thermal noise on the precision of the period extraction improves one order than that of HUST-09, and meantime, the cycle of the whole measurement we need is effectively shortened to 1/6~1/70 of that of HUST-09.