Ньютоновская Ньютоновская гравитационная гравитационная

постоянная:постоянная: современные современные

эксперименты и новое эксперименты и новое значение значение CODATACODATA

В. К. МилюковВ. К. Милюков, , ГАИШ МГУГАИШ МГУ

FFK11, 5– 9 декабря, 2011,Дубна, Россия

First G value:First G value:1797-98, Henry 1797-98, Henry Cavendish:Cavendish:

G=(6.67±0.07)×10G=(6.67±0.07)×10-11-11 mm33kgkg-1-1ss-2-2CODATA 20CODATA 201010 value value

GG  ==  (6.67384(6.67384  ±±  0.00080)0.00080)1010-11-11 m m33kgkg-1-1ss-2-2,,

The best world experiments on The best world experiments on the measurement of G andthe measurement of G and

CODATA valuesCODATA values

Authors, year of publication

Value of G10-11

м3kg-1s-2

STD 10-11 m3kg-1s-

ppm

[1] Facy and Ponticis,Ffrance 1972 6.6714 0.0006 90 [2] Sagitov, Milyukov, et al. Moscow University 1979 6.6745 0.0008 120 [3] Luther and Towler, Nat. Bur. of Stand., Washington 1982 6.6726 0.0005 75 CODATA 1986 6.67259 0.00085 128 [4] Michaelis, et al.,Physik Technische Bundesanstalt 1995 6.7154 0.0006 90 [5] Karagioz, Izmailov, Committee of Standards, Moscow 1996 6.6729 0.0005 75 [6] Bagley and Luther, Los Alamos National Lab 1997 6.6740 0.0007 105 CODATA 1998 6.673 0.010 1500 [7] Jun Luo, et al., HUST, China 1999 6.6699 0.0007 105 [8] Fitzgerald and Armstrong Meas.St.Lab, New Zealnd 1999 6.6742 0.0007 105 [9] Gundlach and Merkowich, University of Washington, 2000 6.674215 0.000092 14 [10] Quinn, Speake et all. University of Birmingham 2001 6.67559 0.00027 41 [11] Schlamminger et all. University of Zurich 2002 6.67407 0.00022 33 CODATA 2002 6.6742 0.0010 150 [12] Armstrong and Fitzgerald, Meas.St.Lab, New Zealnd 2003 6.67387 0.00027 40 [13] Schlamminger et all. University of Zurich 2006 6.674252 0.000109 16 CODATA 2006 6.67428 0.00067 100 [14] Jun Luo, et al. HUST, China 2009 6.67349 0.00018 26 [15] Parks and Faller, University of Colorado 2010 6.67234 0.00014 21 CODATA 2010 6.67384 0.00080 120

1975 1980 1985 1990 1995 2000 2005 2010

6.668

6.67

6.672

6.674

6.676

6.678

6.68

Year

G

10-1

1 [m3

kg-1

s-2

]

[1]

[2]

[3] CODATA-86

[5]

[6]

CODATA-98

[7]

[8]

[9]

[10]

[11]

CODATA-02

[12]

[13]

CODATA-06

[14]

[15]

CODATA-10

Authors, year of publication

Value of G10-11

м3kg-1s-2

STD 10-11 m3kg-1s-

ppm

[9] Gundlach and Merkowich, University of Washington, 2000 6.674215 0.000092 14 [10] Quinn, Speake et all. University of Birmingham 2001 6.67559 0.00027 41 [11] Schlamminger et all. University of Zurich 2002 6.67407 0.00022 33 CODATA 2002 6.6742 0.0010 150 [12] Armstrong and Fitzgerald, Meas.St.Lab, New Zealnd 2003 6.67387 0.00027 40 [13] Schlamminger et all. University of Zurich 2006 6.674252 0.000109 16 CODATA 2006 6.67428 0.00067 100 [14] Jun Luo, et al. HUST, China 2009 6.67349 0.00018 26 [15] Parks and Faller, University of Colorado 2010 6.67234 0.00014 21 CODATA 2010 6.67384 0.00080 120

2000 2002 2004 2006 2008 2010 20126.672

6.6725

6.673

6.6735

6.674

6.6745

6.675

6.6755

6.676

Year

G

10-1

1 [m3

kg-1

s-2

]

[9]

[10]

[11]

CODATA-02

[12]

[13]

CODATA-06

[14]

[15]

CODATA-10

0)]/([ GkJ J

Gk /21

21

22

112

1

//

J

G

The torsion balances and The torsion balances and time of swing method time of swing method

No 1

No 2

2000 2002 2004 2006 2008 2010 20126.672

6.6725

6.673

6.6735

6.674

6.6745

6.675

6.6755

6.676

Year

G

10-1

1 [m3

kg-1

s-2

]

[9]

[10]

[11]

CODATA-02

[12]

[13]

CODATA-06

[14]

[15]

CODATA-10

2000 2002 2004 2006 2008 2010 20126.672

6.6725

6.673

6.6735

6.674

6.6745

6.675

6.6755

6.676

Year

G

10-1

1 [m3

kg-1

s-2

]

[9]

[10]

[11]

CODATA-02

[12]

[13]

CODATA-06

[14]

[15]

CODATA-10

2000 2002 2004 2006 2008 2010 20126.672

6.6725

6.673

6.6735

6.674

6.6745

6.675

6.6755

6.676

Year

G

10-1

1 [m3

kg-1

s-2

]

[9]

[10]

[11]

CODATA-02

[12]

[13]

CODATA-06

[14]

[15]

CODATA-10

2000 2002 2004 2006 2008 2010 20126.672

6.6725

6.673

6.6735

6.674

6.6745

6.675

6.6755

6.676

Year

G

10-1

1 [m3

kg-1

s-2

]

[9]

[10]

[11]

CODATA-02

[12]

[13]

CODATA-06

[14]

[15]

CODATA-10

2000 2002 2004 2006 2008 2010 20126.672

6.6725

6.673

6.6735

6.674

6.6745

6.675

6.6755

6.676

Year

G

10-1

1 [m3

kg-1

s-2

]

[9]

[10]

[11]

CODATA-02

[12]

[13]

CODATA-06

[14]

[15]

CODATA-10

2000 2002 2004 2006 2008 2010 20126.672

6.6725

6.673

6.6735

6.674

6.6745

6.675

6.6755

6.676

Year

G

10-1

1 [m3

kg-1

s-2

]

[9]

[10]

[11]

CODATA-02

[12]

[13]

CODATA-06

[14]

[15]

CODATA-10

The newThe new experimentexperiment on determination of theon determination of the gravitation constant in HUST (China)gravitation constant in HUST (China)

General and General and Schematic view of the Schematic view of the HUST apparatus for HUST apparatus for measurement of Gmeasurement of G

890 mm long, 25 μm diameter tungsten fiber

75.59 g

m=75.59 g91.52 x 12.01 x 27.58 mm

The torsion balance and source The torsion balance and source sphere massessphere masses

Stainless steel spheresM=778 g; D=5.71 mm

Error SourcesError Sources CorrectionsCorrections ΔΔG/G, ppmG/G, ppm

PendulumPendulum 5.075.07 DimensionsDimensions 1.951.95

AttitudeAttitude 0.130.13

Nonaligment with fiberNonaligment with fiber 0.450.45

FlatnessFlatness 0.340.34

ClampClamp 1.651.65

Density inhomogenityDensity inhomogenity ≤≤0.210.21

Coating layerCoating layer -24.28-24.28 4.334.33

Edge flawEdge flaw -0.12-0.12 0.170.17

Source massesSource masses 10.6810.68 MassesMasses 0.820.82

Distance of GCDistance of GC 9.649.64

Density inhomogenityDensity inhomogenity 4.504.50

XYZ positionsXYZ positions 0.480.48

Error budget (1)

Error SourcesError Sources CorrectionsCorrections ΔΔG/G, ppmG/G, ppm

FiberFiber 18.7618.76 NonlinearityNonlinearity <0.70<0.70

ThermoelasticityThermoelasticity -39.83-39.83 1.521.52

AnelasticityAnelasticity -211.80-211.80 18.6918.69

AgingAging <0.01<0.01

Gravitation Gravitation NonlinearityNonlinearity

0.300.30

Magnetic damperMagnetic damper 0.310.31

Magnetic fieldMagnetic field 0.400.40

Electrostatic fieldElectrostatic field 0.100.10

Statistical Statistical ΔΔ((ωω22)) 14.1814.18

TotalTotal 26.3326.33

Error budget (2)

New value of Gravitational New value of Gravitational ConstantConstant

G=(6.67349 0.00018)10-11 m3kg-

1s-2

with a standard uncertainty 26 ppm

Jun Luo, et al //Phys. Rev. Lett., 102, 240801 (2009)

Liang-Cheng Tu, et al // Phys. Rev. D 82, 022001 (2010)

2000 2002 2004 2006 2008 2010 20126.672

6.6725

6.673

6.6735

6.674

6.6745

6.675

6.6755

6.676

Year

G

10-1

1 [m3

kg-1

s-2

]

[9]

[10]

[11]

CODATA-02

[12]

[13]

CODATA-06

[14]

[15]

CODATA-10

A Simple Pendulum Determination A Simple Pendulum Determination of the Gravitational Constantof the Gravitational Constant

G. V. Parks and J.E. FallerG. V. Parks and J.E. Faller

JILA, University of Colorado and JILA, University of Colorado and National InstituteNational Institute

of Standards and Technology, of Standards and Technology, Boulder, CO 80309, USABoulder, 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 SourcesError Sources ΔΔG/G, ppmG/G, ppm ССritical dimensions measurementsritical dimensions measurements 1144

All other dimensionsAll other dimensions 88

Source mass density inhomogeneitiesSource mass density inhomogeneities 88

Pendulum spring constantsPendulum spring constants 77

Total mass measurementTotal mass measurement 66

InterferometerInterferometer 66

Tilt due-to-day mass motionTilt due-to-day mass motion 11

Day-to-day scatterDay-to-day scatter 44 Combined uncertaintyCombined uncertainty 2121

Error budget

New value of Gravitational New value of Gravitational ConstantConstant

G=(6.67349 0.00014)10-11 m3kg-

1s-2

with a standard uncertainty 21 ppm

Harold Parks & James Faller // Phys. Rev. Lett., 105, 110801 (2010)

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

)(

1)()/(

)()(//

))()(()(2

2222

JK

CJKJKKJ

Ggfn

fnfn

QJK

GG

1

)()(2

21

2211

21

//

J

G

2000 2002 2004 2006 2008 2010 20126.672

6.6725

6.673

6.6735

6.674

6.6745

6.675

6.6755

6.676

Year

G

10-1

1 [m3

kg-1

s-2

] [SAI 1979]

[9]

[10]

[11]

CODATA-02

[12]

[13]

CODATA-06

[14]

[15]

CODATA-10

[SAI corr]

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

Authors, year of publication

Value of G10-11

м3kg-1s-2

STD 10-11 m3kg-1s-

ppm

[2] Sagitov, Milyukov, et al. Moscow University 1979 6.6745 0.0008 120 CODATA 1986 6.67259 0.00085 128 [14] Jun Luo, et al. HUST, China 2009 6.67349 0.00018 26 [15] Parks and Faller, University of Colorado 2010 6.67234 0.00014 21 [2] Sagitov, Milyukov, et al. Moscow University corr 6.6736 0.0008 120 CODATA 2010 6.67384 0.00080 120

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. Fixler1, G. T. Foster2, J. M. McGuirk3 and M. A. Kasevich1

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 27.940 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=(6.693 0.041)10-11 m3kg-1s-2

with a standard uncertainty 6100 ppm

ConclusionConclusionHenry 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.”

1798

2010