# “Vortex Gravitation” Model — Gradient Gravitational Field — Kepler’s Third Law is a System Body Constant

The “Inertial Gravitation Evolutionary Attraction Rate” (${K_{Gravity}}$) is constant throughout the total extent of the “gradient gravitational field” and  is a parameter that quantifies and generalizes an Inertial Mass Gradient Gravitational Field, and describes a specific quantity of the Gravitational Attraction that is directly proportional to the Net Inertial Mass of the Gravitational Field Vortex system body.

The “Gravitational Vortex” is modeled as being comprised of an infinite series of Euclidean Spherical Volumes of “Gravitational Potential” of the “Gradient Gravitational Field” which are spherical layers or shells of “Gravitational Potential Energy” which originate with Schwarzschild Radius (${r_{Schwarzschild}}$) Black Hole Event Horizon, as described by the following equation and shown in the image below.

Schwarzschild Radius – (Scalar)

${r_{Schwarzschild}} \,\, = \frac{2\,{m_{Net}}\,G}{c^2_{Light}} \,$  $---> {m}$

The Inertial Gravitation Evolutionary Attraction Rate – (Scalar)

${K_{Gravity}} \,\, = {m_{Net}}\,G \, \, = ( {m_{1}} + {m_{2}} + {m_{3}} + ...... + {m_{N}})G \,\,$   $---> \frac{m^3}{s^2}$

${K_{Gravity}}= \, 4\pi^2 (\frac{r^3_{Schwarzschild}}{T^2_{Schwarzschild}}) \, = \, 4\pi^2 (\frac{r^3_{1}}{T^2_{1}}) = 4\pi^2 (\frac{r^3_{2}}{T^2_{2}})= ...=4\pi^2 (\frac{r^{3}}{T^{2}_{Period}}) \,$

Next, any and every “Vortex” has rotational flow in three dimensions of space and one dimension of time. The vortex is modeled as having three independent components: Radial, Tangential, and Orthogonal.

Below is described some various components that describe the “Inertial Mass Gravitational Spherical Sink Vortex”

Gravitational Spherical Sink Vortex – Radial Vortex Parameters (Terms)

1) Semi-Major Radius Distance – – > ${r}$ —–> ${m}$

It is well known from Kepler’s First law that the planets or bodies in gravitational fields orbit in elliptical and not circular orbits.

Semi-Major Radius – (${r}$)
Semi-Minor Radius – (${r_{Minor}}$)
elliptical eccentricity – (${e}$)

${r_{Minor}} = {r}\,\, \sqrt{1\,\,\, - \,\,\, e^2}$ $\,\,\,\,----> \,\, {m}$

2) Inertial Mass Gravitational Evolutionary Attraction Rate – – >

${K_{Gravity}} \, = \, {m_{Net}\,G} \, = 4\pi^2 (\frac{r^{3}}{T^{2}_{Period}}) \, \,$  —> $\frac{m^3}{s^2}$

3) Inertial Mass Gravitational Acceleration – – >

${g_{Gravity}} \, = \, \frac{K_{Gravity}}{r^2}\, = \, \frac{m_{Net}\,G}{r^2}$ —–> $\frac{m}{s^2}$

4) Inertial Mass Gravitational Force – – >

${F_{Gravity-Force}} \, \, = \, \frac{m_{Mass}\,{K_{Gravity}}}{r^2} \, = \, \frac{m_{Mass}\,{m_{Net}}\,G}{r^2} \, = \, \, {m_{Mass}}{g_{Gravity}}$ —> $\frac{kg m}{s^2}$

Gravitational Spherical Sink Vortex – Tangential Vortex Parameters (Terms)

1) Gravitational Tangential “Orbital” Velocity – – >

${v_{Gravity}} \, = \, \sqrt{\frac{K_{Gravity}}{r}} = \, \sqrt{\frac{m_{Net}\,G}{r}}$   $---> \frac{m}{s}$

2) Gravitational Vorticity “Vortical” Velocity – – >

${\Omega_{G-Vorticity}} \, = \, \sqrt{\frac{K_{Gravity}}{r^5}} \, = \, \sqrt{\frac{m_{Net}\,G}{r^5}}$ —-> $\frac{1}{m\, s}$

Gravitational Spherical Sink Vortex – Orthogonal Parameters (Terms)

1) Gravitational Angular Velocity – – >

${\omega_{Gravity}} \, = \, \sqrt{\frac{K_{Gravity}}{r^3}} \, = \, \sqrt{\frac{m_{Net}\,G}{r^3}}$ —> $\frac{1}{s}$

2) Gravitational Aerial Velocity – – >

${(\frac{dA_{rea}}{dt})_{Gravity}} \, = \, \frac{1}{2}\sqrt{{K_{Gravity}}\,\,{r}} \, = \, \frac{1}{2}\sqrt{({m_{Net}\,G})\,\,{r}}$ —–> $\frac{m^2}{s}$

3) Gravitational Angular Momentum – – >

${L_{Angular-Momentum}} \, \, = \,\, 2{m_{Mass}}\,\,[{(\frac{dA_{rea}}{dt})_{Gravity}}]$ —–> $\frac{kg\, m^2}{s}$

Gravitational Spherical Sink Vortex – Cross Product Rules

Wiki – Cross Product Rules

Gravitational Tangential “Orbital” Velocity – (Tangential Vector)

$\vec{v_{Gravity}} \,\, = \, \, \vec{r} \,\, \times \,\, \vec{\omega_{Gravity}}$ —–> $\frac{m}{s}$

$\vec{v_{Gravity}} \,\, = \, \, {r^2} \,\, \vec{\Omega_{Gravity}}$ —–> $\frac{m}{s}$

Gravitational Acceleration – (Radial Vector)

$\vec{g_{Gravity}} \,\, = \, \, \vec{\frac{F_{Gravity-Force}}{m_{Mass}}} = \, \, \vec{\omega_{Gravity}} \,\, \times \,\, \vec{v_{Gravity}}$ —–> $\frac{m}{s^2}$

$\vec{g_{Gravity}} \,\, = \, \, \vec{\frac{F_{Gravity-Force}}{m_{Mass}}} = \, \, {\omega^2_{Gravity}} \,\, \vec{r}$ —–> $\frac{m}{s^2}$

Gravitational Aerial Velocity – (Orthogonal Vector)

$\vec{(\frac{dA_{rea}}{dt})_{Gravity}} \,\, = \,\, \vec{\frac{L_{Angular-Momentum}}{2\,m_{Mass}}} \,\, = \, \, \frac{1}{2}(\vec{r} \,\, \times \,\, \vec{v_{Gravity}})$ —–> $\frac{m^2}{s}$

$\vec{(\frac{dA_{rea}}{dt})_{Gravity}} \,\, = \,\, \vec{\frac{L_{Angular-Momentum}}{2\,m_{Mass}}} \,\, = \, \, \frac{1}{2}({r^2} \,\, \vec{\omega_{Gravity}})$ —–> $\frac{m^2}{s}$

Gravitational Vorticity “Vortical” Velocity – (Tangential Vector)

$\vec{\Omega_{G-Vorticity}} \, = \, \frac{\vec{v_{Gravity}}}{r^2} \,\, = \, \, \frac{\vec{r} \,\, \times \,\, \vec{\omega_{Gravity}}}{r^2}$ —–> $\frac{1}{m\,s}$

$\vec{\Omega_{G-Vorticity}} \, = \, \frac{\vec{\omega_{Gravity}}}{r} \,\, = \, \, \frac{\vec{r} \,\, \times \,\, \vec{v_{Gravity}}}{r^3}$ —–> $\frac{1}{m\,s}$

Inertial Mass Gravitational Evolutionary Attraction Rate – (Radial Vector)

$\vec{K_{Gravity}} \,\, = \, \, 2\vec{(\frac{dA_{rea}}{dt})_{Gravity}} \,\, \times \,\, \vec{v_{Gravity}}$   —–> $\frac{m^3}{s^2}$

$\vec{K_{Gravity}} \,\, = \, \, {r^2}\,\,[2\vec{(\frac{dA_{rea}}{dt})_{Gravity}} \,\, \times \,\, \vec{\Omega_{Gravity}}]$   —–> $\frac{m^3}{s^2}$

$\vec{K_{Gravity}} \,\, = \, \, 2\vec{(\frac{dA_{rea}}{dt})_{Gravity}} \,\, \times \,\, \vec{r} \,\, \times \,\, \vec{\omega_{Gravity}}$   —–> $\frac{m^3}{s^2}$

$\vec{K_{Gravity}} \,\, = \, \, {r^2}\,\,(\vec{g_{Gravity}})$   —–> $\frac{m^3}{s^2}$

The above rules are used to model the Inertial Mass Gravitational Spherical Sink Vortex.

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### Citation

Robert Louis Kemp; The Super Principia Mathematica – The Rage to Master Conceptual & Mathematical Physics – The General Theory of Relativity – ““Vortex Gravitation” Model — Gradient Gravitational Field — Kepler’s Third Law is a System Body Constant– Online Volume – ISBN 978-0-9841518-2-0, Volume 3; July 2010

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Author: Robert Louis Kemp

http://www.SuperPrincipia.com

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