A Possible Exact Solution for the Newtonian Constant of Gravity

Compared with our knowledge of other fundamental constants, the exact value of the Newtonianconstant of gravity (G) has long been enigmatic, and there is currently no o�cially accreditedexact solution forG. Di erent from the widely adopted experimental approach and unlike othertheoretical ways in resolving the value ofG, by applying to the eld equation of general relativitytwo 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 toGthatonly relates to the electrical permittivity (ε0) and magnetic permeability (μ0) of free space, andG=116(m·s−3)·[(ε0μ0)12/ηπ(m2·kg−1·s)] = (ε0μ0)12/16πη(m3·kg−1·s−2).ηis the correspondingmass density with constant value, withη= 1 (kg·m−3). This research casts doubt on the prevailinghypothesis thatGis an independent constant. Our nding may place the theory of gravity andmany related researches on a more objective and quantitative footing. The result not only a ectsthe theory of gravity but also plays a key role in maintaining theories of classical mechanics,cosmology, general relativity and astrophysics.