A Possible Exact Solution for the Newtonian Constant of Gravity

Abstract

Compared with our knowledge of other fundamental constants, the exact value of the Newtonian constant of gravity (G) has long been enigmatic, and there is currently no ocially accredited exact solution for G. Dierent from the widely adopted experimental approach and unlike other theoretical ways in resolving the value of G, by applying to the eld equation of general relativity two newly developed tensor-based mathematical approaches (one is referred to as \eigen-modulus" to show the converging ability of a tensor, the other is called \the law of tensorial determination" to evaluate indeterminate forms involving tensors), we provide a possible exact solution to G that only relates to the electrical permittivity (ϵ0) and magnetic permeability (μ0) of free space, and  is the corresponding mass density with constant value, with η = 1 (kg·m −3). This research casts doubt on the prevailing hypothesis that G is an independent constant. Our nding may place the theory of gravity and many related researches on a more objective and quantitative footing. The result not only aects the theory of gravity but also plays a key role in maintaining theories of classical mechanics, cosmology, general relativity and astrophysics.