Ньютоновская гравитационная постоянная: современные эксперименты и новое значение CODATA В. К. Милюков, ГАИШ МГУ FFK11, 5– 9 декабря, 2011, Дубна, Россия First G value: , Henry Cavendish: G=(6.67±0.07)× m 3 kg -1 s -2 CODATA 2010 value G = ( ± ) G = ( ± ) m 3 kg -1 s -2,

The best world experiments on the measurement of G and CODATA values

The torsion balances and time of swing method The torsion balances and time of swing method No 1 No 2

The new experiment on determination of the gravitation constant in HUST (China)

General and Schematic view of the HUST apparatus for measurement of G 890 mm long, 25 μm diameter tungsten fiber

75.59 g m=75.59 g x x mm The torsion balance and source sphere masses Stainless steel spheres M=778 g; D=5.71 mm

Error Sources Corrections ΔG/G, ppm Pendulum5.07 Dimensions Dimensions1.95 Attitude Attitude0.13 Nonaligment with fiber Nonaligment with fiber0.45 Flatness Flatness0.34 Clamp Clamp1.65 Density inhomogenity Density inhomogenity Coating layer Coating layer Edge flaw Edge flaw Source masses Masses Masses0.82 Distance of GC Distance of GC9.64 Density inhomogenity Density inhomogenity4.50 XYZ positions XYZ positions0.48 Error budget (1)

Error Sources Corrections ΔG/G, ppm Fiber18.76 Nonlinearity Nonlinearity

New value of Gravitational Constant G=( ) m 3 kg -1 s -2 with a standard uncertainty 26 ppm Jun Luo, et al //Phys. Rev. Lett., 102, (2009 ) Liang-Cheng Tu, et al // Phys. Rev. D 82, (2010)

A Simple Pendulum Determination of the Gravitational Constant G. V. Parks and J.E. Faller JILA, University of Colorado and National Institute of Standards and Technology, Boulder, CO 80309, USA

Принцип эксперимента: С помощью интерферометра Фабри- Перо измеряется расстояние между двумя пробными телами относительно точек подвеса Технические характеристики: Маятники: медь, 780 г. Длина подвеса: 72 см Расстояние между центрами пр. масс: 34 см Массы- источники: вольфрамовый сплав, 120 кг., Движение масс на воздушных подшипниках (air bearings). Маятники внутри вакуумной камеры. Используется магнитное демпфирование для подавления маятниковых колебаний He-Ne лазер, 1 μW, finesse 400

General view of the experimental setup

Error Sources ΔG/G, ppm Сritical dimensions measurements Сritical dimensions measurements All other dimensions All other dimensions8 Source mass density inhomogeneities Source mass density inhomogeneities8 Pendulum spring constants Pendulum spring constants7 Total mass measurement Total mass measurement6 Interferometer Interferometer6 Tilt due-to-day mass motion Tilt due-to-day mass motion1 Day-to-day scatter 4 Combined uncertainty Combined uncertainty21 Error budget

New value of Gravitational Constant G=( ) m 3 kg -1 s -2 with a standard uncertainty 21 ppm Harold Parks & James Faller // Phys. Rev. Lett., 105, (2010)

An systematic error of big G due to the anelasticty of the torsion wire (Kuroda effect)

Correction of the G value due to Kuroda effect HUST 2009: Q 1700; ΔG/G= -212 ppm SAI 1979: Q 2500; ΔG/G= -127 ppm

Fig. 1. Schematic of the experiment. J B Fixler et al. Science 2007;315:74-77 Published by AAAS Atom Interferometer Measurement of the Newtonian Constant of Gravity J. B. Fixler 1 J. B. Fixler 1, G. T. Foster 2, J. M. McGuirk 3 and M. A. Kasevich 1G. T. Foster 2J. M. McGuirk 3 M. A. Kasevich 1 1 Stanford University, Stanford, USA. 2 City University of New York, New York, USA. 3 Simon Fraser University, British Columbia,, Canada. We measured the Newtonian constant of gravity, G, using a gravity gradiometer based on atom interferometry. The gradiometer measures the differential acceleration of two samples of laser-cooled Cs atoms. The change in gravitational field along one dimension is measured when a well-characterized Pb mass is displaced

Fig. 3. A typical data sequence showing a modulation of the gradiometer phase output as the Pb source mass is displaced cm from the top of the lower chamber. J B Fixler et al. Science 2007;315:74-77 Published by AAAS

Fig. 4. Data used in the determination of G. J B Fixler et al. Science 2007;315:74-77 Published by AAAS G=( ) m 3 kg -1 s -2 with a standard uncertainty 6100 ppm

Conclusion Henry Gavendish : The apparatus is very simple (Philos. Trans. R. Soc. London, 88, 469, 1798) James Faller: 1.The measurement is very hard (Phys. Rev. Lett., 105, 2010) 2.Big G is the Mt. Everest of precision measurement science, and it should be climbed