A Free-Fall Determination of the Newtonian Constant of Gravity

Abstract

Recent determinations of the Newtonian constant of gravity have produced values that differ by nearly 40 times their individual error estimates (more than 0.5%). In an attempt to help resolve this situation, an experiment that uses the gravity field of a one-half metric ton source mass to perturb the trajectory of a free-falling mass and laser interferometry to track the falling object was performed. This experiment does not suspend the test mass from a support system. It is therefore free of many systematic errors associated with supports. The measured value was G = (6.6873 ± 0.0094) × 10 −11 m 3 kg −1 sec −2 .

5D gravity and the discrepant G measurements

“…[19,20] 38.9 -77.02 6.6726 ± 0.0005 6.6720 ± 0.0041 Boulder (JILA) [21] 40 -105. 27 6.6873 ± 0.0094 Gigerwald lake [22,23] 46.917 9.4 6.669 ± 0.005 (at 112 m) 6.678 ± 0.007 (at 88 m) 6.6700 ± 0.0054 Zurich [24,25] 47.4 8.53 6.6754 ± 0.0005 ± 0.0015 6.6749 ± 0.0014 Budapest [26] 47.5 19.07 6.670 ± 0.008 Seattle [14] 47.63 -122.…”

Measuring the Newtonian constant of gravitation with a differential free-fall gradiometer: A feasibility study

“…In a cold atom gravimeter version of the G-measurement the relative standard uncertainty-mainly from positioning errors-was of about 4.6 × 10 −4 9 for a total source mass of about 500 kg of tungsten. Schwarz et al reported a relative standard uncertainty of 160 × 10 −6 due to positioning errors and source mass density variations 7 . In a beam balance experiment at the University of Zurich two cylindrical vessels, filled with 14 metric tons of mercury were used 3 .…”

“…Our plan is to use numerous small metal spheres instead of big cylinders as done by Schwarz et al 7 or Lamporesi et al 9 Let us make some basic considerations in order to compare solid cylinder source masses with approximately the some volume filled with spheres. Assume twelve identical solid cylinders with a height of h = 15 cm and radius of 5 cm.…”

“…It follows that the software used for the gravimeter can be directly applied to obtain the differential acceleration; no modifications need to be done. A calculation of the peak field strength produced by tungsten cylinders, such as used by Schwarz et al 7,8 , give 27 µGal (5 cylinders with a diameter of about 16.6 cm and a height of about 10.4 cm and a mass of 39.7 kg each, in a torus-like arrangement). Assume that one torus of 5 cylinders were placed as the source mass T in figure 3.…”

“…The idea is based on a former experiment where a free-fall absolute gravimeter F G5, from Micro-g LaCoste 6 Inc., was used 7 , 8 . The reported uncertainty of Schwarz et al 8 was 1410 ppm.…”