## Description

Sir Isaac Newton’s **universal law of gravitation (F=Gmm/r ^{2})** is an equation representing the attractive force (F) of two masses (m) separated at distance (r). It was first published as a part of Newton’s works on classical mechanics in the late 1600s. Force is proportional to mass and distance, related by a proportionality symbol known as the gravitational constant (G). The force of gravity occurs even at the smallest of particles, yet at this scale, force and motion is dominated by the electric force. Only when the electric force is neutralized, such as in atoms, can the presence of gravity be detected. Gravity is so weak, that it takes trillions and trillions of atoms, such as large bodies like planets, before the force is significant.

In energy wave theory, gravity results from a shading effect of the electric force between the particles. Although the longitudinal amplitude loss of gravity is slight, when a large number of particles form in a large body such as a planet, the total amplitude loss 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, causing an attractive force. Other particles in the vicinity are attracted to the large body because of motion to minimize amplitude. Further information is available in the section on gravity.

## Derivation – Classical Constants

The universal law of gravitation can be derived using only Planck constants (classical constants). The derivation is very similar to Coulomb’s law as they are both related to the electron’s energy at distance. Where it differs from Coulomb’s law is an additional geometry for the spin at the particle core of a second particle, as gravity is a shading effect between two or more particles. The geometric ratios from the geometry of spacetime page (α_{1 }and α_{2}) are used in Eq. 1.5.3. When all of the variables in the α_{2} ratio are the electron’s classical radius (r_{e}), with the exception of slant length (l), which is πr_{e}, it resolves to be the fine structure constant (described in Eq. 1.5.6). When the x and y variables in the α_{2} ratio are Planck length (l_{P}), cone radius is electron’s classical radius (r_{e}) and slant length is πr_{e}, it resolves to be the gravitational coupling constant for the electron (described in Eq. 1.5.7). Further details can be found in the *Geometry of Spacetime* paper.

## Proof

**Gravitational Constant**: Solving for the classical constants in Eq. 1.5.14 for the gravitational constant (G) yields the accurate numerical value and units.

## Derivation – Wave Constants

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, including the reference to Eq. 1.12, 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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