Newton's Force Formula Derived

The calculus of the vacuum is summarized mathematically:

The Theory:
The volume of the protons and neutrons in a planet is equal to the volume of a fallen shell. The shell is zA where A is the planet area (4 pi R2) and z is the height fallen. Since the proton shrinks its own volume out of space every 5ns, the fallen shell, in one second of falling, has a volume 200 million times the volume of the protons and neutrons. Volume per second is momentum of free-space. z is (1/2)at2.

The acceleration is equal to the average velocity given above for a fallen shell, z/t, divided by the time growing out of the planet. Protons and neutrons shrink space and grow time. That is gravity. It is from a contraflow momentum of continuum, V/tau.

First, derive the 5.1 nanosecond universal constant, tau

p2 = p1

p2 is momentum into baryons

p2 = NV/(a constant time) = a constant

p1 is momentum of free-space, gravity is available here, potentially

p1 = d(zA)/dt

zA is called a shell fallen, it is a volume

NV is the planet’s baryon volume

V = proton volume = 3.591364 x 10^-45 cubic meters

N = number of protons and neutrons in planet

N = M/m(proton)

M = mass of planet

m(proton) = 1.6738 x 10^-27 kilogram = proton mass

5.1ns = The Universal Constant for the Conservation of Graviticspansive Continuum (derived below)

z = height fallen in an experiment

z = (1/2) g t^2

z/t = average velocity during acceleration

A = area of a sphere with radius R from the planet's center to the height where gravitational acceleration is g

A = 4 pi R^2


Equation 1 was created from conservation of momentum considerations. Momentum has two forms, mass times velocity and volume per second.

p1 = zA / (1 second test) = momentum of free space

zA = (1/2 g t^2) * ( 4 pi R^2)

zA = 2 pi (9.8 meter/sec^2) (1 second)^2 R^2

zA = 2 pi 9.8 meter R^2

V1 = zA = volume of free space

p1 = d(zA)/dt = momentum of the vacuum

p1 = (2 pi 9.8 meter R^2) / second

V2 = NV = volume of baryons in planet


Theory proposed for the cause of gravity:

V2 per (a constant time) = V1 per second

“The volume consumed by baryons per second equals the volume of free space fallen per second for gravity. Find a constant time (t2) for baryon volumes to equal free-space volume fallen at planet surface.”

(V2/t2) = (V1/t1)

t2 and t1 are times to be determined. Let t1=1 second for the experiment dropping an apple. (It falls 4.9 meters). Find t2, a constant time.

V2/t2 = p2 = momentum

V1/t1 = p1 = momentum (meter^3/second = Lug)

Lug is the new unit name for momentum of the vacuum

p2 = p1

V2/(a constant time) = p1 = zA/(1 second)

dV2/dt = dV1/dt

“The rate of volume change into baryons equals the rate of volume change out of free space. Replenishment occurs from outer space.”


p2 = p1

p2 = V2/(a constant time tau)

V2/tau = p1

V2/p1 = tau = a constant time

p1 = zA/(1 second)

zA = (1/2 g t^2) * ( 4 pi R^2)

p1 = (g t^2) * ( 2 pi R^2)

tau = NV / ((g t^2) * ( 2 pi R^2))

tau = MV / ((m g t^2) * ( 2 pi R^2))

tau = 5.1ns for Earth’s (M, g, R)


Now that tau was found to be a universal constant for 5 planets, it is used to derive Newton’s Force Law, next...

d(NV/5.1ns)/dt = d^2(zA)/dt^2 ...Equation 1

NV/(5.1 x 10^-9 seconds^2) = d^2(zA)/dt^2

zA = (1/2 g t^2) * ( 4 pi R^2)

zA = 2 pi g t^2 * R^2

d(zA)/dt = 2 pi gtR^2

d^2(zA)/dt^2 = 2 pi g R^2


NV/(5.1 x 10^-9 seconds^2) = 2 pi g R^2

Solve for g

g = NV/(5.1 x 10^-9 seconds^2) / (2 pi R^2)

g = (M/m(proton))*V/(5.1 x 10^-9 seconds^2) / (2 pi R^2)

force = mass times g

f = mg

m = test mass

f = (mM/R^2) (V/m(proton)) /(5.1 x 10^-9 seconds^2 * 2 pi R^2)

f = (mM/R^2) * (V / (2 pi m(proton)* 5.1 x 10^-9 seconds^2)


G = V / (2 pi m(proton)* 5.1 x 10^-9 seconds^2)


f = GmM/R^2


Newton’s Force Formula was derived from basic facts of nature.

Alan Folmsbee, December 29, 2015, Wailuku

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