Analysis Of Several Related Effects In Determination Of Newtonian Gravitational Constant G

The gravitational constant G is the first fundamental constant to be introduced and measured in history.Its precision measurement became very important because it is closely related to theoretical physics,astrophysics and geophysics,etc.Since Cavendish reported the first experimental value of G in 1798,many efforts have been put into measurement of G during past two centuries.However,the accuracy of G is still the worst one among all the fundamental constants.Besides,the values of G obtained by different experimental groups in the world are in poor consistent in their claimed uncertainties, which show that there must be unknown systematical errors in these measurements.Our laboratory had determined G by a high-Q torsion pendulum with the time-of-swing method,and obtained a value in 1999,which has been adopted by CODATA-1998 and named as HUST-99.In order to improve the precision of the measurement,we designed a new scheme and analyzed the errors in this experiment.This paper mainly analyzes the systematical errors in this experiment,such as the effect from the density inhomogeneities of the pendulum body and the source masses,the distribution of the coating layer on the pendulum,and the effect of the ambient magnetic field around the pendulum.The gravitational constant G has to be measured based on Newtonian law of gravitation.One of the difficulties is that the point mass does not exist actually.Therefore, the pendulum and the source masses with certain dimension must be considered by the integral computation and the mass distributions should be known accurately.For the glass pendulum,we use an optical interference method to detect the variations of the refractive index of the pendulum.According to the relationship between the refractive index and density of the glass,we can obtain the relative variation of the density over a volume with sizes of 5×5×5mm³ is about 10^-5,which will contribute to G value with an uncertainty of about 0.2ppm.For the SS316 stainless steel spherical source masses,we cut one of the spheres into small blocks and use the scanning electron microscopy to scan the defects in different sections and then obtain the density inhomogeneity.The relative variation of the density over a volume with dimensions of 0.272×0.234×0.005mm³ is about 5.9×10^-4.If the density inhomogeneity of the spheres used in our measuring G is the same as that of the sphere sampled,it will contribute to G value with an uncertainty of less than 0.034ppm.In order to minimize the electrostatic interaction between the pendulum and its surroundings,the pendulum was coated with gold layer,which was found to have a significant correction to G value due to its density much larger than that of the pendulum. A sample with the same dimension as the pendulum was cut into 19 small blocks,and the distribution of the coating layer was determined by measuring the mass differences of the blocks in different position before and after coating.The experimental results show that the gold layer on the pendulum would contribute a correction of -24.3ppm to our G measurement and with an uncertainty of 4.3ppm.Besides,the influence of ambient magnetic field on the period of the torsion balance was analyzed theoretically.The relative variable of the period was about 7×10^-9 with our selected parameters.If the period of the torsion balance is seleted for 530s and the magnetic field is selected for 10^-5T,the variation of magnetic field will contributed an uncertainty of 0.15ppm to G measurement.