## Description

The universal law of gravitation (F=Gmm/r^{2}) is also a force (F) explained as a change in energy over distance. The structure of the force equation for gravitation is similar to Coulomb’s Law with the exception that it has a dimensionless coupling constant that represents the reduction in wave amplitude (energy) which is shown in Eq. 2.5.1. As a particle spins, it loses longitudinal energy which is converted to transverse (magnetic). This was proven with the conversion of energy principle by relating the energy loss (of gravity) to the magnetic energy gain (electron’s magnetic moment – Bohr magneton).

Although the longitudinal amplitude loss is slight, when a large number of particles are together in a large body such as a planet, the effect becomes much greater. This creates a shading effect where amplitude is larger before a wave passes through a large body and smaller after it passes through it. Other particles in the vicinity are attracted to the large body because they move to minimize amplitude. Force is based on wave amplitude difference due to constructive and destructive wave interference.

## Derivation

This derivation begins with the classical form of the gravitational force. The equation contains a dimensionless particle count (Q) which needs to be converted to mass (m) to be consistent with the law of universal gravitation, which uses mass as a method to determine gravitational force. Mass is the total sum of particle mass where Q is the number of particles and m_{e} is the mass of a particle (electron). In other words, m=Qm_{e}.

In this derivation, the Gravitational constant (G) is found. Further information can be found in the *Key Physics Equations and Experiments* paper.

## Proof

**Gravitational Constant**: Solving for the wave constants in Eq. 2.5.9 for the gravitational constant (G) yields the accurate numerical value and units.

**Gravitational Coupling Constant – Electron**: The gravitational coupling constant for the electron is a very slight 2.4 x 10^{-43} when compared to the electric force. It is dimensionless.

The equations use wave constants explained here.

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