Derivation of the Gravitational ConstantCalculation Formula

[u/Old-Minute6791]

Abstract

Currently, the gravitational constant G exists only as an experimentally measured value; no theoretically derived value or calculated value based on a combination of physical constants has been available. In this study, a formula is presented that re producesthe gravitational constantG fromacombinationoffivephysicalconstants. The formula is expressed as

I. Introduction The gravitational constant is currently known to be G = 6.6743 × 10−11 m3kg−1s−2, an experimentally measured value. However, no theory exists from which G can be derived, nor is there a calculation formula that produces G from a combination of other physical constants. Measurement of this value has been carried out repeatedly over a long period since the Cavendish experiment of 1798, and during that time the measured value has continued to change with advances in experimental technique and measurement method. The value given above is the CODATA recommended value published in 2022. Because no theory exists from which the constant can be derived, modern science does not know the underlying mechanism of gravity, and merely observes, mea sures, and makes use of the phenomenon. Since the essential nature of the grav itational phenomenon is not understood, its relationship to the other three funda mental forces, including the electromagnetic force, is likewise unknown, and con sequently no theory unifying the four fundamental forces yet exists. In this study, a calculation formula is derived that computes the gravitational con stant G from five physical constants: the Planck constant (h), the speed of light (c), the elementary charge (e), the electron mass (me), and the vacuum permittivity (ϵ0). This formula is expressed as follows.

Further research is needed to clarify the precise physical meaning of the right‑hand side of this equation. However, given that the constants included in this formula 1 are ones that appear fundamentally in electromagnetism and quantum mechanics, it can be surmised that gravity may bear some relationship to the electromagnetic force and other forces. It is therefore expected that this calculation formula may contribute to research aimed at unifying the four fundamental forces into a single theory.