## 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. 2.5.2. 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 Force Equation, which is derived from the Longitudinal Energy Equation. This was originally proven to have its roots in the Energy Wave Equation. In short, all of the energy and force equations can be traced back to a simple energy wave equation.

The Force Equation contains a particle count (Q) which needs to be converted to mass (m) to be consistent with the universal law of 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. This constant is no longer necessary when using the Force Equation. References to** Eqs. 1.10 and 1.5.2 **come from the *Key Physics Equations and Experiments* paper.

## Proof

The gravitational constant (G) was calculated on this site and also in *Forces*: **6.674E-11 m ^{3} / s^{2} kg**.

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