Newton's G Derived

The force of gravity is f, and G is Newton's Universal Gravitational Constant.

f = GmM/RR

The proposed formula for Gravity Volume Theory is modified to show where the new universal constants come from (p, Tau, C), which are replacing the lumped G Universal Gravitational Constant.

integral of Volume of baryons = derivative of Volume of fallen shell, times a constant

∫NVdt = d/dt (zA) * C/2
Where N is number of baryons in a star, V is baryon volume 3.6*10^-45 meter^3, z is height fallen in an experiment, A is area of star at distance R from the center of the star, C is 5.131534*10^-9 second^2, m is a test mass, M is a star mass, (mp) is proton mass:

N = M/(mp)

Newton's force of gravity formula uses mass but the new Law for Gravity does not, it uses Volumes. The mass of matter is proportional to the Volume of matter, so some people mistake mass for a source of gravity. Mass does not cause gravity. Mass is proportional to something that causes gravity. Understanding how things really work allows progress beyond that which is allowed after overloading a mass concept with excessive apotheosis.

Here is how Newton's force formula is derived from The Gravity Volume Theory.

Run an experiment, normalized to 1 second. This allows simple algebra to get an answer that calculus can get for any time span. The answer that is sought is a time constant Tau that describes something for gravity. Tau is how long it takes for the volume of a fallen shell to equal the volume V1 of the baryons in the planet or star. A fallen shell V2 is the height fallen (z) multiplied by the area of the planet(A). The momentum of free space p is V/Tau. That is a universal constant for protons and neutrons that make gravity.

z = 1/2 a t^2

t = 1 second

NV/Tau = zA/t

V1 / Tau = V2 / time

NV = 1.4*10^7 meter^3

zA = 2.7*10^15 meter^3

Tau = 5.131534*10^-9 second

END OF PRECALCULUS END OF PRECALCULUS


The Conservation of 4D Continuum and continuity of continuum fluid is modeled as follows. Normalize Tau to be 1.000 econd instead of 5 nanoseconds. Or just consider time to be normalized in a way described elsewhere. This step allows the magnitude 5 nano to be separated from the second and second^2.

The time integral of baryon space divided by the integral of baryon time equals the derivative of baryon space divided by the derivative of baryon time.

A Law For Gravity

∫NVdt / ∫(t)dTau = dzA/dt  / dt/dTau

∫NVdt / ((1/2) t^2) = dzA/dt  / 1

Convert back to seconds:

∫NVdt = d/dt (zA) * C/2

NVt =  d((1/2) a t^2)/dt * CA/2

NVt =  a t * CA/2

NVt =  a t * C(4 pi RR)/2

a = NV / C(4 pi RR)/2

a = NV / (C 2 pi RR)

a = MV / (2 pi C RR (mp))

f = ma

f = mMV / (2 pi C RR (mp))

f = mM/RR * V/(2 pi C (mp))

f = mM/RR * G

G = V/(2 pi C (mp))

G = 10^(-45+8+27) = correct magnitude

Conclusion

G equals the volume of a proton every 5ns per second per proton mass. Newton did not get that far. G is a conversion factor so mass can be used for a gravity calculation. Mass is not needed for the proposed Law For Gravity.

integral(NV)dt = d/dt (zA) * C/2

For Newton, G was measured but he knew of no facts of nature that determined G. Now you know a theory for that. Baryons set the strength of gravity as they shrink space and grow time.

G can be defined two ways: without using mass, or using the mass of a proton:

G = pi cuberoot(V)/(sqrt(5*10^-9 second second) second)

G = V/(2 pi C (mp))

Newtons force formula was derived to get Newton's Universal Gravitational Constant in terms of basic facts of nature. By doing that, a more fundamental constant was discovered: the radial linear momentum of free space, p.

p = V/Tau = 7*10^-37 meter^/second momentum into baryon

V = 4/3 pi r^3

r = 0.95fm proton radius

Tau = 5 nanoseconds

C = 5 * 10^-9 second^2

July 31, 2016 by Alan Folmsbee

Begin 2015 Pre-Calculus Version

The Big G is finally derived, after 331 years of using a measured number:
G = 6.67 * 10^-11 Newton meter*meter / (kg*kg)

G = V / ((2 π m τ) * second)

Here is how that formula was derived, unintentionally:
Find the cause of gravity. More detail is in this link.
V = proton volume
m = proton mass
It will be revealed in this geometry and algebra that:
τ= The Universal Constant for Conservation of Graviticspansive Continuum
τ = tau = 5.13 nanoseconds, verified for five planets, the Sun, and Vesta, within 1%
g = GM / R² was already known from Newton's teachings
M = mass of planet
R = distance from planet's center to where g is known
z = 1/2 at² + v₀t + z₀
a = acceleration = g = gravitational acceleration
N = M/m
N = number of baryons in planet
A = 4πR²
A = area of sphere under the experiment to drop an apple 1 second, planet-centric
V1 = zA
V1 = volume of shell of potential falling of apples
z = height fallen in 1 second
V2 = NV
V2 is the volume of the baryons in the planet
τ = V2 / (V1 per second)
Above, find a time constant for space shrinkage, τ. That formula can be re-arranged to be momentum equals momentum. But not mass times velocity, momentum is also equal to volume per second.
V1 / (1 second) = V2 / tau
p₁ = p₂
That is the conservation of momentum.
z = 1/2 at²

V1 = 1/ 2 at² 4πR²
V2 / V1 = NV / ( 1/2 at² ∗ 4πR2)
t = 1 second
τ = NV ∗ second /( 2a((1 second)²)πR²)
Since τ (tau) was found to be a universal constant, the formula allows a, acceleration, to be found:
a = NV ∗ second / (2τ ((1 second)²)πR²)
N = M / m
It was noticed that this formula can be re-arranged to isolate M/R², like in a Newtonian equation. From memory, that looked like an old law with a new constant:
a = ( M / R² ) ∗ ( V ∗ second / (2 m τ second²π)
G = V ∗ second / (2 m τ second²π)
G = V / ((2 π m τ) * second)

Observation
Many people ask, "Where does the 1 / R² come from for the inverse square laws of force and acceleration?"
There are two steps to get the inverse square law. First, the area of a sphere is 4 pi R². The second step is to take a momentum equation and solve for a, acceleration and that R² is always a multiplier of a. The R² for area multiplies a height fallen, z. That area times z is a volume for a momentum on one side of the equation. After a derivative, the z/(1 second) becomes z/(second²). So the acceleration and R² are always multiplied on one side of an equation, so when solving for a, the R² must divide both sides. That isolates the desired "a" on the left while sending 1/R² to the other side. That is why the inverse square law happens: spherical geometry and a momentum conservation theory where the volume of baryons equals a volume of a fallen shell. Each of those volumes are divided by a time to get momentum. Momentum is now including volume per time in addition to the mass times velocity as momentum. The conservation of continuum is conservation of momentum.
z 4 pi R² per second = NV/tau
p₁ = p₂ momentum
December 21, 2015 Alan Folmsbee, Wailuku

G is a universal gravitational constant that is oriented
to use mass in the formula. The Gravity Volume Theory provides this:

m = proton mass = 1.6738*10^-27 kg

N = number of baryons in planet Earth = 3.5692*10^51

z = height fallen in 1 second test = 4.9033 meters

A = area of Earth = 5.111855*10^14 meter^2

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

G = zA / (2 * pi * N * second * m * second)

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

mantissa

4.9*5.1 / (1 * 3.14 * 3.5 * 1.67) = 0.66762999

exponent

10^(14-51+27) = 10^-10

G = 6.6762 * 10^-11 cubic meters per kg second^2

Confirmed

G = zA / (2 * pi * N * second * m * second)

because V/5ns = zA/(N seconds) where V is proton volume, and 5ns is time to conserve continuum

11/25/2016