The Law of Gravity

Rev. July 31, 2016

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.

integral(NV)dt / integral(t)dTau = dzA/dt  / dt/dTau

integral(NV)dt / ((1/2) t^2) = dzA/dt  / 1

Convert back to seconds:

integral(NV)dt = 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))

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 formula uses mass but the new formula 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.

Rev. 2016.1.8

The Law of Gravity The volume of baryons in a planet equals the volume of a fallen shell in 5 nanoseconds.
NV/tau = zA/t
N = number of baryons in planet
V = proton volume = 3.591364 * 10-45 cubic meters
tau = 5.131534 ns
z = height fallen = 1/2 a t2
A = planet area = 4 π R2
R = planet radius or any larger radius of a sphere centered on a planet
t = time for object falling

Experiments show that dropping an object at a radius R from a planet's center will cause it to fall z meters in t seconds. The average acceleration in that experiment is equal to the average velocity (z/t) in the test for the shell falling into the planet divided by the time growing out of the planet. That is gravity: a volume falling inwards divided by a time passing outwards.
NV/tau = zA/t = the momentum of free-space conservation
NV/tau = ((1/2) a t2) * (4 π R2) / t

End of Law, Revised January 8, 2016, Alan Folmsbee, Wailuku

Matter causes gravity. Protons and neutrons are matter with volume. Mass does not cause gravity; it is an area. The Law of Gravity is defined without mass. The acceleration of gravity (a) near a planet, depends on volumes of free space draining into baryons and time growing out of baryons.
The momentum conservation revealed on the page for "Newton's G Derived" is used to write the law of gravity.
V1/(1 second) = V2/tau
p1 = p2 = momentum conservation = volume per second
V2 is volume of baryons in planet
V1 is a volume calculated after a 1 second experiment dropping an apple
V1 = zA
z = height fallen in 1 second = (1/2 a t2)
z/(1 second) = average velocity in the experiment dropping an apple for 1 second
The derivative of z/(1 sec) is acceleration a
A is area of a sphere centered on the planet's center, with a radius R from the center of the planet (4 pi R2)
tau = 5.131534 nanoseconds = τ
tau = The Universal Constant for the Conservation of Graviticspansive Continuum Graviticspansive Continuum is conserved as the momentum of the vacuum
The momentum in a planet's baryons' volume equals the momentum of any shell around a planet, where a shell is a volume defined as the height fallen times the area of a spheroid centered on the planet's center. This momentum is not mass times velocity. Momentum is also volume divided by time. It's The Law of Gravity. Many distant planets and stars add their volume changes to the planet's local account of continuum fluid.
dp1/dt = dp2/dt = acceleration factors
dp1/dt = 2a pi R2
dp2/dt = MV / mC0

C0 = 5.131534 * 10-9 second2
C0 = capensity of free space = tau * seconds
2a π R2 = MV / mC0
Solve for a = g = gravitational acceleration
g = MV / (2mC0 π R2)

The Acceleration of Gravity from the Law

g = MV / (2 π m C0 R2)

For example, on Mars:
M = 0.641740*1024 kilogram = mass of planet
V = 3.591364*10-45 meter3 = proton volume
m = 1.673800*10-27 kilogram = proton mass
C0 = 5.131534*10-9 second2
C0 = capensity of free space = τ*second
R = 3.396200*106 meter
R = length from the planet center to the apple drop point
g = 3.710000 meters per square second, from NASA experiments and calculations

Use the Law of Gravity to calculate g and compare it with NASA's g.
Multiply mantissa'a alone, then add exponents
g = 0.64174*3.591364/(2*3.141592654*1.673800*5.131534*1.153417)
g = 0.03702555 mantissa
add exponents
x = 24-45+27+9-13 = 2
so g = 3.702555 meter per second squared for Mars
That confirms The Law of Gravity.

g = (M/R2)* (V/(2πC0m)) = (MG/R2)
The momentum in baryons equals the momentum of any shell around a planet, where a shell is a height fallen times the area of a spheroid centered on the planet's center.
The linear momentum in a proton equals the momentum of a shell that surrounds the proton. That is the law of gravity.
December 23, 2015, Alan Folmsbee, Wailuku

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