Study On The Slow Drift Effect In The Experiment Of Measuring G

The precise measurement of the Newtonian gravitational constant G is of great significance in the many fields such as geophysics,accuracy guidance,precision measurement,cosmology,astronomy and so on.G is the earliest known and measured fundamental universe constant in history,but it is still measured with least precision among all physical constants.Although several recently published G values are obtained with high precision,these values are not in good agreement with each other within respective uncertainties,and it means that there are some possible unknown or incorrectly evaluated systematic errors in different measuring methods.In order to explore these possible systematic errors for improving the reliability of measurement results,the Center for Gravitational Experiments in Huazhong University of Science and Technology adopts the time-of-swing method and the angular acceleration method to measure G in the meantime.The accurate determination of G not only depends on ingenious experiment design and precise machining,but also needs the effective processing of experiment data.In the measurements of G,due to the properties of fiber material and the variation of ambient environment,some physical quantities undergo slow drifts.These above slow drift effects have significant influences on the parameter estimation of the useful experimental signals.In the measurement of G with time-of-swing method,the accurate determination of G depends on the period extraction of torsion balance with high precision.The slow drift effects of ambient environment temperature and the torsion balance period,and the thermoelastic effect between the two physical quantities affect the period extraction directly.In order to effectively correct the influences of the slow drift effects of the temperature and period on the period extraction,this thesis establishes the theoretical model of partial linear correlation to analyze the complicated relation between the temperature change and period variation,proposes the frequency-time-temperature model to fit the pendulum's motion frequency variation at the near and far positions,and adopts this developed model to process typical experiment data.The thermoelastic coefficient is obtained 101(2)×10-6/?,which is in good agreement with that obtained by the independent temperature modulation experiment,and the temperature data recorded by the sensor nearest to the pendulum reflects the temperature sensed by the torsion fiber best.The difference of the frequencies squared at the near and far positions is given as 1.662751(14)×10-6s-2 with the relative uncertainty of 8 ppm.The error influence of the thermoelastic effect on the difference is 9.16(0.18)ppm,and its precision influence on the G value is less than 1 ppm.Therefore,the developed model is able to obtain a reliable thermoelastic coefficient and an accurate difference of the frequencies squared in the meantime,and judge which sensor's temperature data can best reflect the temperature change sensed by the fiber.In the measurement of G with angular acceleration method,the determination of G with high precision is dependent on the accurate amplitude estimation of the usefulgravitational signal,and furthermore,the accurate extraction of the useful gravitational signal depends on the effective corrections of the slow drift effect of the pendulum equilibrium position and the coupling effect between the slow drift and background gravitational signal.Besides,the correction of the coupling background gravitational effect needs the highly precise determination of the background gravitational signal.In order to effectively correct the slow drift effect and the coupling effect,this thesis analyzes the slow drift effect of the pendulum equilibrium position and the coupling effect between the slow drift and background gravitational signal,linearizes the nonlinear objective function on the experimental signal into the multiple linear regression,which is able to precisely estimate the amplitudes of the useful gravitational signal and the background gravitational signal meanwhile,and adopts the developed method to process typical experiment data.The result shows that the bias influence of the slow drift effect on the G value is about 7ppm,and the influence of the coupling effect on the G value is less than 1ppm.According to the stretch processing of time,this thesis proposes an improved correlation method to accurately determine the amplitudes of the prominent harmonic components of the spurious background gravitational signal with time-varying angular frequency in the meantime,calculates the uncertainty of the determined amplitudes based on the Gaussian white noise model,and adopts the improved correlation method to process typical experiment data.The result shows that the amplitudes of the basic frequency and second harmonic components of the background gravitational signal are given as 1.444(11)nrad/s2 and 45.255(11)nrad/s2 respectively,and the uncertainty based on the Gaussian white noise model is in good agreement with the statistical error of the amplitude sequence obtained by the data segment processing.Finally,this thesis analyzes the influence of the cosine oscillation in the time-varying frequency on the background gravitational signal.The bias of the cosine oscillation on the amplitudes of the background gravitational signal obtained by the improved correlation method are given as the difference of the amplitudes with and without the cosine oscillation effect corrected.The result shows that the amplitude biases of the basic frequency and second harmonic components of the background gravitational signal are 0.005 nrad/s2 and 0.002 nrad/s2 respectively,which are within the respective uncertainties.Therefore,the improved correlation method is able to accurately determine the amplitudes of the prominent harmonic components of the background gravitational signal with time-varying angular frequency in the meantime,the uncertainty based on the Gaussian white noise model is correct and reliable,and the bias influence of the cosine oscillation in the time-varying frequency on the amplitudes obtained by the improved correlation method can be negligible.