Abstract
An attempt is presented for the description of the magnitude of Newton’s gravitational force in the experiments with a horizontal torsion balance. There were developed many experimental arrangements in order to find experimentally the value of big G – the Newtonian gravitational constant – after the Michell-Cavendish experiment in 1798. The geometrical configurations of test and source masses play a very important role in these experiments. The old trigonometric function “sagitta” used by Johannes Kepler and Isaac Newton was newly employed as the trigonometric tool for the determination of the magnitude of Newton’s gravitational force between the source mass and the test mass. Based on the known experimental configurations with the horizontal torsion balance we have found that the “true” Michell-Cavendish configuration is not dependent on the space orientation. This “sagitta” function can be experimentally tested in the Karagioz-Izmailov configuration and the Karagioz-Izmailov-Gillies-Gershteyn configuration with the technology available at begin of our century. A proposal for the decomposition of the big G was presented. This concept could not be experimentally tested before the discoveries of the dipole in the cosmic microwave background radiation and the Pioneer anomaly.
Highlights
Gravitational interaction, described by the Newton’s law (1687) of gravitation F = Gm1m2/d2 where F represents force of attraction between two particles having masses m1 and m2 and d is the distance between these particles, continues to attract experimental and theoretical researchers
Based on the known experimental configurations with the horizontal torsion balance we have found that the “true” Michell-Cavendish configuration is not dependent on the space orientation
We can manipulate with the geometrical configurations of two test masses placed on ends of a horizontal torsion balance and two source masses acting on those test masses
Summary
The actual state of the art of the experimental determination of G was recently summarized in the special issue of the Philosophical Transactions A (2014): “Theo Murphy Meeting Issue ‘The Newtonian constant of gravitation, a constant too difficult to measure?” T.J. Quinn and C.C. Speake concluded that main focus should be given to the explanation of the uncertainty of the value G. Speake concluded that main focus should be given to the explanation of the uncertainty of the value G Contributions presented at this Meeting surveyed in details the actual experimental situation of the determination of G and proposed new guidelines for the near future research. A working formula for the possible decomposition of big G is presented
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