The inverse-square distance dependence of the gravitational force has been tested over a range of approximately 2 to 5 cm, by use of a test mass suspended from a torsion balance to probe the gravitational field inside a mass tube. The result supports an inversesquare law. Assuming a force deviating from inverse square by a factor ll + e lnr(cm)] it is found that e = (1± 7)x 10' 5 .PACS numbers: 04.90.+e, 06.30.-k A number of different ideas have recently been discussed which suggest the existence of forces which could manifest themselves as a deviation from inverse-square distance dependence of the gravitational force on a laboratory distance scale (1 cm-1 km). These ideas include modified theories of gravity 1 ; exchange of a low-mass axion, of a variety undetectable in other tests 2 ; and a long-range component of the strong interaction, arising from two-gluon exchange. 3 Of particular interest is the observation by Scherk 4 that supergravity unification theories lead naturally to an effective weakening of the gravitational force at short distances, possibly on a laboratory scale, so that inverse-square tests might provide evidence for such theories.An experiment indicating a breakdown of the inverse-square law has, in fact, been reported by Long. 5 Comparing the effective gravitational constant at two distances, Long finds G(4.5 cm) to be smaller than G(30 cm) by (0.37±0.07)%. This result has inspired a number of other inverse-square tests, 6 but to our knowledge no result with sensitivity comparable to Long's has been reported. We report here an experiment defining a range of distances (close to Long's) and a condition (null experiment) in which, with sensitivity greater than Long's, we find no anomaly.Our experiment uses a torsion balance (Fig. 1) to measure the change in the force acting on a test mass suspended inside a long hollow cylinder, as the cylinder is moved laterally. For an infinitely long perfect cylinder and exact inversesquare force law, the gravitational field due to the cylinder vanishes everywhere inside it, just as inside a spherical mass shell. For our finite cylinder of length L = 60 cm and inside diameter D = 6 cm there exists a small net "end-effect" force on a test mass located near an inside wall, smaller than the nearly balanced opposing forces due to near and far walls by a factor (D/L) 2 = 10" 2 . Thus to compare the gravitational force at the distances from the near and far walls in our cylinder, to a level of 1 part/10 5 , we need measure the end effect force to only 1 part/10 3 . Furthermore, the residual field in the cylinder is such that we need measure only the relative motion of the cylinder to just 1 part/10 3 , while the absolute position of the cylinder relative to the test mass need only be known to a few millimeters. (The homogeneity and geometry of the cylinder itself must be known with precision on the order of 1 part/10 5 .) By averaging data taken at a set of equally spaced azimuthal orientations of the cyl-
The simultaneous exchange of two pseudoscalars between fermions leads to a spin-independent force between macroscopic objects. Previous work has demonstrated that one can combine this interaction with tests of the weak equivalence principle, gravitational inverse square law, and studies of laser beam propagation in magnetic fields, to set significant new constraints on the Yukawa couplings of massless pseudoscalars to nucleons. Here we extend these results to massive pseudoscalars, and derive new constraints which relate the strengths of these couplings to the pseudoscalar mass.
A recent publication (J.D. Anderson et. al., EPL 110, 1002) presented a strong correlation between the measured values of the gravitational constant G and the 5.9 year oscillation of the length of day. Here, we compile published measurements of G of the last 35 years. A least squares regression to a sinusoid with period 5.9 years still yields a better fit than a straight line. However, our additions and corrections to the G data reported by Anderson et al. significantly weaken the correlation.
A measurement of Newton's gravitational constant G has been made with a cryogenic torsion pendulum operating below 4 K in a dynamic mode in which G is determined from the change in torsional period when a field source mass is moved between two orientations. The source mass was a pair of copper rings that produced an extremely uniform gravitational field gradient, whereas the pendulum was a thin fused silica plate, a combination that minimized the measurement's sensitivity to error in pendulum placement. The measurement was made using an as-drawn CuBe torsion fibre, a heat-treated CuBe fibre, and an as-drawn Al5056 fibre. The pendulum operated with a set of different large torsional amplitudes. The three fibres yielded high Q -values: 82 000, 120 000 and 164 000, minimizing experimental bias from fibre anelasticity. G -values found with the three fibres are, respectively: {6.67435(10),6.67408(15),6.67455(13)}×10 −11 m 3 kg −1 s −2 , with corresponding uncertainties 14, 22 and 20 ppm. Relative to the CODATA2010 G -value, these are higher by 77, 37 and 107 ppm, respectively. The unweighted average of the three G -values, with the unweighted average of their uncertainties, is 6.67433(13)×10 −11 m 3 kg −1 s −2 (19 ppm).
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