Determination of the gravitational constant at an effective interaction distance of 112 m

Cornaz, A.; Hubler, B.; Kündig, W.

doi:10.1103/physrevlett.72.1152

Cited by 30 publications

(23 citation statements)

References 20 publications

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“…It is based on a beam balance which is a suitable device for measuring the gravitational force [12]. The idea of this experiment and the experience on how to operate the balance is based on our successful storage lake experiment, where the gravitational force of water has been measured in order to test Newton's inverse-square law [13,14]. This new experiment is a modern variation of the method used by von Jolly [5] and Richarz and Krigar-Menzel [6].…”

Section: (Received 19 August 1997)mentioning

confidence: 99%

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Gravitational Constant Measured by Means of a Beam Balance

1998

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We present a new method to measure the gravitational constant G. A beam balance compares the weight of two 1-kg test masses and measures the gravitational force of two field masses with a statistical uncertainty of 10 ng. Two vessels in a refined arrangement are used as field masses. They have been filled with water as a test. G has been determined with an uncertainty of 240 ppm. The next step is to fill the vessels with mercury. Because of the larger signal and further refinement of our experiment, we hope to reach the design uncertainty of 10 ppm. [S0031-9007 (97)05223-X] PACS numbers: 04.80.CcThe gravitational constant G is known with a relative uncertainty of only 128 ppm (part per million) while the uncertainty of all other fundamental constants is rapidly decreasing to values considerably below 1 ppm [1][2][3]. The most precise device for measuring the gravitational force is the torsion balance, first applied by Cavendish 200 years ago. Until 1890 beam balances were also used to measure the gravitational force [4][5][6]. The accuracy was limited to 0.16% at best [6], and these measurements were given up in favor of the torsion balance. During past few decades, no essential progress of the technique for measuring G has been made. Recent attempts with different techniques failed to improve the uncertainty of G [7-9]. The current results, as well as several former results, show unexplained discrepancies. No significant deviations from Newton's gravitational law were found experimentally. The most obvious explanation is, therefore, systematic errors even for the traditional torsion balance technique [10,11].In order to overcome this situation, we proposed a new experiment. It is based on a beam balance which is a suitable device for measuring the gravitational force [12]. The idea of this experiment and the experience on how to operate the balance is based on our successful storage lake experiment, where the gravitational force of water has been measured in order to test Newton's inverse-square law [13,14]. This new experiment is a modern variation of the method used by von Jolly [5] and Richarz and Krigar-Menzel [6]. Our first results have already provided a significant accuracy improvement over the earlier beambalance experiments. This is possible because of a different method and the general progress grained in mechanics, automation, and weighing techniques.The principle of our new experiment is shown in Fig. 1: To large masses are moved in the vertical direction and alternately positioned in one of two states. Their gravitational field acts on two small test masses which are separately suspended on wires. The suspension devices of the test masses are alternately connected to a single-pan beam balance which measures the weight change due to the gravitational force. The arrangement of two test and field masses is symmetrical and en-ables a differential measurement such that many disturbing forces and drift effects cancel each other out.The field masses have a cylindrical shape. They have an axial bore in orde...

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Section: (Received 19 August 1997)mentioning

confidence: 99%

“…The balance and the basic weighting technique is discussed in more detail in Refs. [12][13][14][15][16], for example.…”

Section: (Received 19 August 1997)mentioning

confidence: 99%

Gravitational Constant Measured by Means of a Beam Balance

1998

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“…Interest in the value of the Newtonian gravitational constant, G, has increased recently with the publication of several disparate results [1][2][3][4]. This discrepancy, as much as 50 standard deviations, is an error unheard of in the measurement of any other of the fundamental constants.…”

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confidence: 94%

Preliminary Results of a Determination of the Newtonian Constant of Gravitation: A Test of the Kuroda Hypothesis

1997

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Two preliminary determinations of the Newtonian constant of gravitation have been performed at Los Alamos National Laboratory employing low-Q torsion pendulums and using the time-of-swing method.Recently, Kuroda has predicted that such determinations have an upward bias inversely proportional to the oscillation Q, and our results support this conjecture. If this conjecture is correct, our best value for the constant is ͑6.6740 6 0.0007͒ 3 10 211 m 3 kg 21 s 22 .Interest in the value of the Newtonian gravitational constant, G, has increased recently with the publication of several disparate results [1][2][3][4]. This discrepancy, as much as 50 standard deviations, is an error unheard of in the measurement of any other of the fundamental constants. A torsion pendulum instrument has been assembled at Los Alamos National Laboratory which determines G by the method of Heyl, also called the time-of-swing method, and preliminary results of this effort are reported herein. Kuroda has shown [5] that popular models of anelasticity predict a bias in these determinations where the damping of the pendulum is caused by losses in the suspension fiber, and this upward fractional bias should be 1͞pQ. Two determinations were carried out employing systems which differ in Q by a factor of 2, and the disagreement of their results is consistent with that predicted by Kuroda.In a time-of-swing, or Heyl-type, measurement, the oscillation frequency of a torsion pendulum is perturbed by the presence of source masses. In their absence, the free oscillation frequency, squared, is related to the moment of inertia, I, and fiber torsion constantThe interaction potential energy of the pendulum and source masses, U g ͑w͒, contributes a "gravitational torsion constant,"where w is the angle between the axis of the pendulum and that of the source masses. Therefore, the frequency of small oscillations of the pendulum isThe gravitational torsion constant is at a maximum when the pendulum is in line with the source masses (w 0, or "near" position), and at a minimum when it is perpendicular (w p͞2, or "far" position). It is proportional to G, and is calculable from the geometry and densities of the pendulum and masses, so the gravitational constant is given bywhere k g K g ͞G, and D͑v 2 ͒ is the difference of the square of the frequencies recorded at the two orientations.The above derivation assumes that k g remains the same at each orientation, but this assumption has been called into question recently. Interest in gravitational wave detectors has spurred research into the anelastic properties of suspension materials at low frequencies, and one model of anelasticity has been shown [6-8] to predict accurately the behavior of several different materials. This model treats a physical spring as a perfectly elastic spring in parallel with a continuous number of Maxwell units, characterized by a spectrum of relaxation times. The model predicts that the torsion constant is a function of oscillation frequency. Kuroda [5] has shown that, for a Heyl-type measu...

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“…33 6.674215 ± 0.000092 Sevres (BIPM) [27,28] 48.8 2.13 6.67559 ± 0.00027 6.683 ± 0.011 Fribourg [29] 46.8 7.15 6.6704 ± 0.0048 (Oct. 84) 6.6735 ± 0.0068 (Nov. 84) 6.6740 ± 0.0053 (Dec. 84) 6.6722 ± 0.0051 (Feb. 85) Magny-les-Hameaux [30] 49 2 6.673 ± 0.003 Wuppertal [31] 51.27 7.15 6.6735 ± 0.0011 ± 0.0026 Braunschweig (PTB) [8,32] 52.28 10.53 6.71540 ± 0.00056 6.667 ± 0.005 Moscow [33,34] 55.1 38.85 6.6729 ± 0.0005 6.6745 ± 0.0008 Dye 3, Greenland [35] 65.19 -43.82 6.6726 ± 0.0027 Lake Brasimone [36] 43.75 11.58 6.688 ± 0.011 Table 1 : Results of the most precise laboratory measurements of G published during the last sixty years and location of the laboratories. [17] - [20], [23], [14], [29] - [31], [32] - [35]). The line indicates the best fit G lab versus the mixed variable x (χ published in 1999 [16], one would obtain with the sample S1 :…”

Section: Comparison With Laboratory Measurementsmentioning

confidence: 99%