1-1-08 Cosmogony

0 Contents 1 Background 1-1 Cosmos

 Tools 1-1-10

1-1-09 * Derivation Of The Inverse Square Law Of Gravity
By The Johnson Cosmological Model

Created Dec 3-13, 2003 Stavropol, RU.

 

1 Physical Universe Ruled By The Logos 
           Universe, Aether, Vorton Mechanism
           Logos, Cosmos, Chaos
2 Basic Postulates of Physical Reality
           Postulate 1 Space
           Postulate 2 Aether Matter
           Postulate 3 Motion
3 Basic Operational Definitions
4 Collisions in the Aether
5 Basic Physical Objects
6 The Vortex
7 The Vortex Ring (Toroid)
8 The Shade
Symbols 
Foundation Items
 
Figures 
Observations
Definitions 
Equations 

Appendix

Refractive index
Michelson - Morley experiment
Luminiferous Aether

  

Observe Porpoise vortices!

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Observe a source of basic Insight!

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1. The Physical Universe Ruled By The Logos 

(With Laws And Possibilities)

Universe - All space, matter and motion regarded as a whole.
Logos
- the source of fundamental order of the universe (the eternal laws that govern physical and behavioral reality).
Aether
- The medium that fills all space and supports the propagation of electromagnetic waves which are constructed from vortex rings formed in and of Aether.
Cosmos - the universe regarded as an orderly, harmonious whole.
Chaos - The background random matter in translational equilibrium (an ideal fluid in thermal equilibrium with local fluctuations).

Random background motion of elements of matter in space.

The Physical Universe is the Space, Matter and Motion in which and from which our visible and invisible physical Universe is formed. Aether (matter) is the one and only formless substance of the Cosmos from which and in which all material bodies are formed and exist. The background Matter is in constant motion with collisions from all directions transferring momentum in all directions by the properties of space occupation, lack of cohesiveness, probability of location and conservation of momentum.

Universe

universe (y 'nə-v?s')
The totality of matter, energy, and space, including the Solar System,  the galaxies, and the contents of the space between the galaxies. Current theories of cosmology  suggest that the universe is constantly expanding.

The American Heritage? Science Dictionary Copyright ? 2002. Published by Houghton Mifflin. All rights reserved.
Cite This Source

Aether 

 

Ae?ther
n. Greek Mythology
The poetic personification of the clear upper air breathed by the Olympians.

[Latin Aethr, from Greek aithr, upper air.]

The American Heritage? Dictionary of the English Language, Fourth Edition copyright ?2000 by Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights reserved.

Noun 1. Aether - personification of the sky or upper air breathed by the Olympians; son of Erebus and night or of Chaos and darkness
Greek deity - a deity worshipped by the ancient Greeks
2. aether - a medium that was once supposed to fill all space and to support the propagation of electromagnetic waves
medium - an intervening substance through which signals can travel as a means for communication
Based on WordNet 3.0, Farlex clipart collection. ? 2003-2008 Princeton University, Farlex Inc.

  1. A hypothetical medium formerly believed to permeate all space, and through which light and other electromagnetic radiation were thought to move. The existence of ether was disproved by the American physicists Albert Michelson and Edward Morley in 1887.

The American Heritage? Science Dictionary
Copyright ? 2002. Published by Houghton Mifflin. All rights reserved.
Cite This Source

Vorton Mechanism 

The Aether concept was previously rejected through error in understanding

See : 1-1-9-1 Michelson - Morley experiment

What is so hard to understand?

To the extent that the Aether Chaos is an inviscus, inelastic, infinitely divisable fluid, the Aether vortex rings pass through the Aether chaos with out effect.

Click here to see the video mp4.

To the extent that the rings interact with the chaos we find the cause of the background red shift!

Logos

 *Logos (From Wikipedia, the free encyclopedia)

Logos in ancient Greek philosophy, mathematics, rhetoric, theology, and Christianity.

Logos (pronounced /ˈloʊɡɒs/ or /ˈlɒgɒs/; Greek λόγος Logos) is an important term.

Heraclitus (ca. 535?475 BCE) established the term as meaning the source and fundamental order of the cosmos.

John 1:1-5 In the beginning was the Logos, and the Logos was with God, and the Logos was God. The same was in the beginning with God. All things were made by him; and without him was not any thing made that was made. In him was life; and the life was the light of men. And the light shineth in darkness; and the darkness comprehended it not.

Cosmos

cos?mos (kŏz'məs, -mŏs', -mōs')   n.

1. The universe regarded as an orderly, harmonious whole.
2. An ordered, harmonious whole.
3. Harmony and order as distinct from chaos.

 [Middle English, from Greek kosmos , order .]

The American Heritage? Dictionary of the English Language, Fourth Edition
Copyright ? 2009 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
Cite This Source

Chaos

chaos (kā'ŏs') 
The behavior of systems that follow deterministic laws but appear random and unpredictable. Chaotic systems very are sensitive to initial conditions; small changes in those conditions can lead to quite different outcomes. One example of chaotic behavior is the flow of air in conditions of turbulence. See more at fractal.
The American Heritage? Science Dictionary
Copyright ? 2002. Published by Houghton Mifflin. All rights reserved.
Cite This Source

2. Postulates Of The Physical Properties Of The Universe.

For a founding statement see 1.1.3 Postulates Of Physical Reality - A Foundation Statement

Postulate 1 (The Extensive Property)

The extensive property of the Cosmos exists and is called Space! Space is continuous in three linear, independent, infinite dimensions. 

Note: a vector is an arrow going from a starting point to an end. A vector can be a location (given an arbitrary starting point) or displacement . An example of the use of terms would be the corner stone in a building as the origin. Locations are vectors from the origin to points. Displacements are vectors from one point to another. Displacements subtract out reference to the origin.

In the Figure below Raa and Rbb are locations and r is a displacement. The vector r gives no information about the location of its beginning Raa or its end Rbb

Defining an arbitrary initial, orthogonal Cartesian coordinate system starting point of R00 as the origin with three perpendicular directions (1,2,3).

We define location R in physical space in terms of its components

 R0 ≡ R011 + R022 + R033.

We define displacement rab in physical space in terms of its components

rab ≡ Rbb - Raa.

≡ Rb11 - Ra11 + Rb22 - Ra22 + Rb33 - Ra33

≡ (Rb1 - Ra1)1 + (Rb2 - Ra2)2 + (Rb3 - Ra3)3

rab11 + rab22 + rab33

Location r in an orthogonal Cartesian coordinate system.
Notice that displacement subtracts out reference to R0f and Rii so rfi has magnitude and direction but not location.

We define area A12 as the cross product

A1212r11 x r22.

We define volume V as the dot product of area and extension

V123 ≡ A1212 r33,

= r11 x r22 r33.

Postulate 2 (The Inertial Property)


The inertial property of the Cosmos Aether called Matter exists! Matter is not created or destroyed. Each element of Matter is infinitely divisible. Each element of Matter occupies its own space uniquely. Basic Matter is a non-viscous, inelastic fluid. Out of the Aether Matter all material things formed and in the unformed chaos the move and have their being. The inertial property of Aether is called mass m.

The Aether concept was previously rejected through error in understanding

See : 1-1-9-1 Michelson - Morley experiment

Aether Matter is not just a medium in which electro-magnetic radiation propagates and is effected (like the imagined Aether or Dark Matter). The radiation and all material objects are forms created of the Aether Matter and swimming in the Aether Matter.

Each point of Aether Matter mi occupies it's own unique location Rii in space.

Rii ≡ Ri1i1 + Ri2i2 + Ri3i3.


We define density of a volume of space as the mass divided by the volume of space containing it.

x ≡ mx/Vx

Postulate 3 (The Mobil Property)

Given two elements of Matter ma and mb the displacement between them rabab. Relative motion (velocity) vabab between them exists!


Given two elements of Matter in space separating at a constant velocity vabab and the associated displacement rabab , we operationally define a clock with time t by

tab ≡ |rabab| / |vabab| , where rab ≡ |rabab| and vab ≡ / |vabab|.

With a clock defined we can graph the position of an element of Matter as a function of time. Collisions in the Matter change the position of an element of Matter instantaneously so the graph is jagged as represented in one dimension below.

 Position as a function of time.

This kind of graph has no well defined slope at the points of collision. In calculus terms r(t) is not a differentiable function of time.

3. Basic Operational Definitions 


With a clock to measure time and a length standard to measure distance we operationally define the velocity vector in a given direction va for a period of time in space where there are not any collisions as

varaa/ta.

In the inertial frame of reference the net flow in a given direction is equal to the net flow in the opposite direction because as with the one dimensional physics toy motion flow is possible simultaneously in all directions (meaning + and - directions along each axis).

The magnitude of velocity (speed va) of any element of matter ma in space exists with an average speed v0. The average speed v0 is uniform through out background matter. From this we conclude there exists an inertial frame of reference R0 where the average speed v0 is zero.


Given the random distribution of background matter, with a large enough volume V, we observe the effects of chaotic motion matter is in equilibrium giving an average background density0 that is constant.

  The average background density of matter c is constant.


The dimensionless saturation is the ration of the volume of mass Vm in a volume of space Vs

≡ Vm / Vs 


By Observation 1 we define a universal constant the saturation of the chaos c  for the ratio of a volume of matter Vmc and the volume of confining space Vsc.

c ≡ Vmc / Vsc 


With space, density, and motion we can define momentum passing through a given area or impinging on a given surface. The definition of momentum as mass m times its velocity v needs some insight when talking about a fluid like the Aether Matter. What mass are we talking about and what velocity are we talking about?


flv wmv

Source of basic Insight.

Basic matter is not viscous and not compressible:

This means that if we had two pieces of pure basic matter with no internal motion, in a collision the momentum of one could be transmitted through the other without friction. For example see the diagram below showing a collision.

Basic matter is not viscous and not compressible.

In Figure 3.3 we observe the mechanism for keeping a form in the chaos.

In collision momentum is conserved but instantaneously transferred ahead with a space discontinuity in the path of the center of mass of momentum. In the chaos the shape depends on the shapes and mass distributions in the collision. Since the shape is chaotic so is the outcome.

Momentum can move in opposite directions at the same time in the same pure matter. Below is a model of a Physics Toy with hanging steel balls.

Physics Toy with hanging steel balls.

In Figure 3.3 we observe the mechanism for keeping a form in the chaos.

Matter deposited on one side of a stream is removed by collisions on the opposite side!

When we consider that the pure matter is not viscous and not compressible, we see that momentum freely moves in all directions at the same time. 

Question: In background matter, what is the mass moving in a given direction? 

Considering uniform random motion (similar to a gas) where half the matter has a component moving in any given direction and half the matter has a component moving in the opposite direction.

Elements of matter moving through random collisions.

Answer: At any given time, half the mass has a motion component in any direction and the other half of the mass has a component of motion in the opposite direction. With the infinitesimal sizes in the Aether Matter, this is on a scale large enough that random fluctuations are averaged out.

The expression of the half of the mass mii+ moving in a given direction i+ in terms of the density (by Observation 1) o ≡ mx/Vx is

   mi+ = (1/2)mi

=(1/2)0 Vi+ , ( i+ is direction on the i axis.) 

Question: What is the average component in any given direction at any given time of the average speed?

The average speed associated with any momentum is distributed in all directions equally, so we need to find the average component of the average speed in any given direction (note only one direction along the axis, both ways average to zero). 

Answer: The velocity vk+k+ in a given direction associated with the mass mik+ is the average velocity component of the average speed in any given direction. This ranges from 0 to vo.  An approximate average of this in any direction is half the average speed.

vk+k+ (1/2)vok+, (where k+ indicates the + direction on the k axis.)

The definition of momentum of a mass element mi is mi times its velocity vik+ 

pi+k+ ≡  mi+vk+k+

For a component of momentum passing through a given area in a given direction, we use Equation 2 and Equation 3 in Definition 9 to get:

pi+k+ mi+(1/2)vok+ , Equation 3 in Definition 9
 (1/2)0 Vk (1/2)vok+ , Equation 2 in Definition 9
(?)0 Vk vok+ 

4 Collisions in the Aether

 (The speed of a longitudinal wave as a function of density)

Matter transfers its momentum in collision. The collisions are of incompressible fluid matter. Consider a set of billiard balls in a row. An element of matter traveling with the average background speed *vo=dl/dt (*one dimensional).

Billiard Balls.

From Figure 4.1, momentum is transmitted the distance Lt in time tt.

Lt =  the distance momentum is transmitted.
n =  the numver of elements in length Lt.
d =  the diameter of an element.

The length of matter the momentum traveled through instantaneously was

Lm ≡ nd. 

The length of space the momentum traveled through at *vo

Lf ≡ Lt - Lm , or Lm= Lt -Lf .

The observed time tt for the momentum to be transmitted distance Lt is

tt = observed time to transmit momentum distance Lt

Matter traveled the free space distance Lf  in time tt. By Definition 6 tt ≡ Lt /vt , the speed of the free matter is

vf = Lf /tt.

From Observable 4.1 Lt and Observable 4.4 tt the speed of momentum vp is

vp=Lt /tt

From Equation 4.1 vf =Lf /tt and Equation 4.2 vp=Lt /tt the ratio of the speed of momentum transmission vm to the average background free space speed vf  is

vp /vf =( Lt /tt)/(Lf /tt)
= Lt /Lf .

From Equation 4.3 vp goes to infinity as Lf goes to zero. That is as the density increases the speed of transmission of momentum increases while the speed of free motion is unchanged.

By Definition 5 i ≡ mi/Vi the density of pure matter is its mass divided by its volume

0m =mi/Vm.

We have Observation 1 0 = mx/Vs but here we are varying the background volume to explore the effect on speed of momentum transmission in the Chaos

b = mx/Vb

By taking the ratio of Equation 4.4 0m=mx/Vm and Equation 4.5 b = mx/Vb

0m/b = (mx/Vm)/(mx/Vb) = Vb / Vm = Lm3/Lt3 

Given the average background free space speed vo, consider average speed as a function of density.  We look at this system for an arbitrary unit of distance (large enough that the averages are not invalidated). We use 1000 units of total space and very the free space 1000 to 0.01.

The Table uses a 1000 units total distance Lt and varies the free space Lf 1000 to 0.01.

The graph below represents the data table above.

Graph as the density approaches 100% the speed approaches infinity!

5 Basic Physical Objects

Consider the improbable event of streams forming in the chaos.

A stream forming in the chaos.

Our ideal matter has its own characteristics. To have intuitive insight into behavior of a stream on the chaos we need to have the reality experiences that reflect these characteristics.

A stream is a group organization out of the chaotic matter. A steam travels with a group velocity with respect to the background which averages to zero.

From Observation 3 says that the stream shape will tend to be maintained while Observation 2 says there is a difference in the speed of any element and the external speed of momentum as the momentum advances through transfer. An unverified thought is that the average speed of an element of matter participating in the stream is the same as the ambient average speed. This would mean that there is a direct relationship between that average ambient speed and the speed of any stream.

The next level of organization is a stream forming a vortex. Consider the improbable event of a vortex forming from streams. Below we consider a section of a vortex about the axis of rotation.

Figure 5.2 A vortex forming in a stream.

What is the difference in effect of ambient chaos on the inner vortex boundary and the outer vortex boundary?

The need here is to discover the mechanics that give identity and multiplicity there is some condition (probably density dependent) that gives a size constraint. The spiral form of solar systems and galaxies may also be an outcome of the same mechanics on a larger scale. Here I am not talking about some abstract statistical formulation but a concrete visible mechanics. What is happening differently on the inside surface and the outside surface interaction with the chaos is a focus worth attention.

A vortex cross section.

Consider the improbable event of a vortex ring (toroid) forming from the vortices.

A toroid cut out.

 With vortex rings and multi-ring objects formed from them in the Chaos, we can find objects and observe their position as a function of time. The position as a function of time is smoother than collisions in the Chaos. An example would be throwing a ball. up as shown below.

Position as a function of time.

Using the limit as t 0 in  Definition 7 operationally defines the three-dimensional velocity of and object as the slope of the displacement time graphs.

vii ≡ Limit  (ri/ti)i
t 0 
= Limit  (ri1/t)i1+ (ri2/t)i2 + (ri3/t)i3
t
= (dri1/dt)i1+ (dri2/dt)i2 + (dri3/dt)i3
= vi1i1+ vi2i2 + vi3i3

Velocity as a function of time.

We operationally define the three-dimensional acceleration of and object as the slope of the velocity time graphs

aii ≡ Limit   (vi/ti)i
t

= Limit   (vi1/t)i1+ (vi2/t)i2 + (vi3/t)i3
t

 = (dvi1/dt)i1+ (dvi2/dt)i2 + (dvi3/dt)i3.

= ai1i1+ ai2i2 + ai3i3

We can define the three dimensional force F acting on an element of mass mi with cross section area Ai in the Chaos by time t rate of change matter r0 Vi in the impacting volume moving at average background speed voi .

  Fii ≡ dpii /dt
= dp1i1 /dt + dp2i2 /dt + dp3i3 /dt

Now we need to recognize the infinite divisibility of the Chaos. This means that when two particles of matter collide the momentum of the contacting parts is not lost like in the crash of to cars but as with the physics toy continues in exchange and jumps ahead into the forward element in both directions. Since Chaos is ubiquitous (everywhere like a fog) this continuation of momentum and in fact jumping ahead was accounted for in the average speed in any given direction.

We have the net force Fir+ acting in the r+ direction on an element of mass mir+. The mass is in a volume with cross section area Air. The average momentum pir+r+ of the ith element moving in a given direction (r+) is from Equation 4 pir+r+ (1/4)oVir+vor+. The ambient force Fir+ in any direction r+ on an arbitrary area of obstruction Air is

Fir+r+ ≡ d(pir+r+) /dt ,
d((1/4)0 Vir+ vo)/dtr+ , note (1/4)(0 Air vo) is not a function of time
= (1/4)(0 Air vo)dri/dtr+ , by Definition 7 dri/dtr+ = vir+r+
= (1/4)(0 Air vo) vir+r+ , by Equation 3 vir+r+= (1/2)vor+
= (1/4)(0 Air vo)(1/2)vor+ ,
= (1/8) 0 Air v2or+ .

We can define the average pressure on an element of mass mi in a given direction rr by dividing the average force Fi ave over the area Ar .

P ≡ Fir+aver+●Airr+ / (Airr+ ● Airr+ )   
=  Fir+ / Air ,
 

Using Equation 5 Fir+r+ = (1/8)oAir v2or+  or Fir+ = (1/8) o Air v2o in Definition 13 P = Fir+/Air gives

P = (1/8) oAir v2o / Air
= (1/8) o v2o ,

Note that in the primitive (no vortexes) Chaos this is universal and for a vortex it is the external pressure. 

6 The Vortex

For uniform circular motion we study the diagram below.

A point in uniform circular motion.

We have a point moving at a constant speed vc. At time t1 the point is at r1. At time t2 the point is at r2. In the change of time is dt, the change in position is dr and the change in velocity is dv.

We have similar triangles that give equal ratios for dr/r and dv/v

dr/r = dv/v.

Solving Definition 10 v=dr/dt for dt gives:

dt = dr/v

Rearranging Observation 6 dr/r = dv/v gives vdr/r = dv.
Then dividing both sides by Equation 6.1 dt = dr/v gives (vdr/r)/(dr/v)=dv/dt=a  then reducing gives centripetal acceleration

a=v2/r. 

Consider a vortex section shown below.

A vortex cross section.

The pressure on the surface area exerts the force that is equal to the centripetal (inward) force of rotation. Note that momentum in a stable vortex behaves like an element of matter mi and momentum is associated with the same element as it moves.

We apply Newton's second law to a segment of the vortex cut out

Fi = miai.

Using Equation 6.2 ai=vi2/ri in Equation 6.3 F=ma gives

Fi = mivi2/ri.

Using Equation 4.5 mi = mi/Vmi in Equation 6.4 Fi =mivi2/ri gives

Fi =miVmi vi2/ri.

Looking at the segment in the diagram above we have the volume Vi

Vi = dlAi 

Using Equation 6.6 Vi=dlAi in Equation 6.5 Fi =miVmi vi2/ri gives

Fi =mdlAi vi2/ri.

We have the pressure from the Chaos by Equation 5.2 Pi = (1/8) 0 v2o .
Using this in Definition 13 Pi = Fi /Ai gives the external force as

Fext = PA =(1/8)0v2oA

We apply Newton's third law (to every force there is an equal and opposite force)

Fr-= -Fr+

Using  Definition 5   Density  x ≡ mx/Vx in Equation 6.4 Fc =mv2/r gives

Fc = mdlAivi2 /ri .

Using Equation 6.8 Fext =PA =(1/8)ov2oA and Equation 6.10 Fc = mdlAivi2 /ri  in Equation 6.9 Fr-=-Fr+ gives

mdlAivi2 /ri = (1/8)0vo2Ai ,  

mdl vi2 /ri = (1/8)0vo2 ,

dlvi2 /r = (1/8)(0/m)vo2 .

If we assume that the driving speed of the Chaos vo2 is the same as the tangential speed of the vortex vi2
we have dl/r =(1/8)( o/m), or:

r = 8dl(m/o)

This Equation 6.12 r = 8dl(m/o) would mean that the ratio of the wall radius and the wall thickness would be a constant. Since vortex rings are the building blocks of magnetic fields, this could explain how they can range so much in major radius. That is that as the major radius expands conservation of energy is accomplished by the shrinking the minor radius and wall thickness.

The question remains, what limits the decrease in the radius of the vortex ring? We could speculate on the ratio of the densities, say if the pure density is equal that of the chaos the ratio of  r = 8dl.
If the pure density m was twice that of the chaos the ratio of r = 16dl.
This is a limit. the minor radius r (the minor radius of the vortex must be smaller than 8dl (the thickness of the vortex wall).  We have:

r > 8dl .

The internal energy is kinetic. The energy of a segment is (1/2)mv2, m= 2rdlm ,

K.E.R/z =rdlmv2

7 The Vortex Ring (Toroid)

We start with a toroid cut out shown below. We assume this is a closed system in the sense the the mass is constant and the internal energy is constant.

A toroid cut out.

The total length of z (the axis of the toroid segments) is the center circumference 2R

z = 2R.

Using Equation 7.1 z = 2R in Equation 6.14 K.E.R/z =rdlmv2,  the total energy K.E.R would be

K.E.R = rdlmv2(z) , solving Equation 6.14 for K.E.R
= rdlmv2(2R)
= 22Rrdlmv2.


Using Equation 6.12 r =8dl(m/oin Equation 7.2 K.E = 22Rrdlmv2 gives

K.E=22R {8dl(m/o)} dlmv2
= 162Rd2lv22m /o


This show us the variables while energy is conserved is such large change as the major diameter changes in magnetic fields.

8 The Shade

Consider two groups of vortex rings (making up visible matter) as depicted in the diagram below. The center and top spots represents the cross sectional area of a spherical object.

 

Two groups (center and top) of vortex rings (making up visible matter).

The idea here is that the pressure of the chaos is ubiquitous but clusters of vortex rings deflect the incoming momentum causing a shadow effect. This shadow effect causes the shadowed surface to experience decrease in momentum impacting on the shadowed side. This decrease  in pressure between the objects causes them to experience a net external force toward each other. Groups of rings (objects) are forced toward each other rather than the false concept of "action at a distance" mediated by some imaginary thing called a field.

Given the average cross section area of a single vortex ring is ao. The average cross sectional area for the n center rings is

Acenter = n ao .

We assume that the chaos is fine enough that the cross section area of every ring is seen.

The free vortex rings at the center experience pressure from the momentum of the chaos impacting giving a force Fcenter from all directions. We use Equation 8.1 Acenter = n ao to multiply the pressure in Equation 6  Pi =  (1/8) o v2o get the force impinging on the surface of the center group from any direction. The ambient force on the center object is

  Fo center = P Acenter
=  (1/8) o v2o ncenter ao

What part of that force is missing due to the shielding or shadow effect of the object at the top?

Given the shielding and its shadow the decrease in force in that direction is proportional to the ration of the area of the obstruction divided by the area of the sphere on which it lies with the shadowed object at the center of the sphere and the shadowing object at the top of the sphere.

When object at the top has k vortex rings it casts a shadow of

  Atop = kao .

For a sphere of projection with radius Rs we have the projected spherical surface area of 4R2s or

Asphere = 4R2.

Where the center object has n rings of cross-sectional area of ao. The shadow effect causes reduction in pressure from that direction. The net force pushing the two groups together is proportional to the ratio of the area of the cross section of a single ring ao times the number k of rings and the area of the sphere of projection radius Rs and projected surface area of 4R2s or

Atop / Asphere or kao /(4R2 ) .

Given the mass mo of a single ring (constant mass of a single ring). The mass of the top object with n rings is

mcenter = nmo .

The mass of the center object with k rings is

mtop= kmo .

So the net force from the shielding imbalance is

Fcenter net = Fo center Atop / Asphere , shielding from Equation 8.4
= (1/8) o v2o Acenter Atop / Asphereusing Equation 8.2
= (1/8) o v2o kao nao /(4R2 ) ,  using Equation 7 ,8.5 , and 8.6
= (1/32) o v2o a2o k n / R2 , simplifying
= (1/32) o v2o a2o (mtop/mo) (mcenter/mo) / R2 ,
= (1/32 m2o) o v2o a2o  mtop mcenter  / R2 .

In Equation 8.7 we define the Universal Gravitational Constant

G ≡ (1/32 m2o) o v2o a2o .

Using Definition 14 in Equation 8.7 gives

Fcenter net = G  mtop mcenter / R2 .

This is then a derivation Newton's general law of gravitation!


Symbols  

(a direction in Space)
≡ (is equivalent to)
(is defined to be)
(approximately equal to)

Foundation Items 

Postulate 1    Space R0 Exists!

     Definition 1   Location R0
     R0 ≡ R011 + R022 + R033.
     Definition 2   Displacement rfi
     rfi ≡ Rff ? Rff.
     Definition 3   Area A1212
     A1212 ≡ r11 x r22.
     Definition 4   Volume V123 ,
     V123 ≡ A1212 ? r33,

Postulate 2   Matter m Exists!

     Definition 5   Densityx
     x ≡ mx/Vx .

Postulate 3   Motion v of Matter Exists!

     Definition 6  Time t
     tab ≡ |rabab| / |vabab| .
     Observation 1     Background density o
     o  = constant.

Figure List  

Figure 1.1 Random background motion of
                    Matter in space.
Figure 2.1 Location r in an orthogonal Cartesian
                    coordinate system.
Figure 3.1 Position as a function of time.
Figure 3.2 Basic Matter is not viscous and not
                    compressible.
Figure 3.3 Physics Toy with hanging steel balls
Figure 3.4 Elements of Matter moving through
                    random collisions.
Figure 4.1 Billiard Balls
Figure 4.2 As the density approaches 100%
                   speed approaches infinity!
Figure 5.1 A stream forming in the chaos.
Figure 5.2 A vortex forming in a stream.
Figure 5.3 A vortex cross section.
Figure 5.4 A toroid cut out.
Figure 5.5 Position as a function of time.
Figure 5.6 Velocity as a function of time.
Figure 6.1 A point in uniform circular motion.
Figure 6.2 A vortex cross section.
Figure 7.1 A toroid cut out.
Figure 8.1 Two groups of vortex rings
                     (making up visible Matter)  

Observations  

Postulate 1 Space R0 Exists!
Postulate 2 Matter m Exists in Space!
Postulate 3 Motion v of Matter Exists!
Observation 1 Background density o is constant.
Observation 2 collision momentum with discontinuity
Observation 3 deposited one side removed on opposite!
Observation 4  difference in speed of element and speed of momentum
Observable 4.1
Lt = distance momentum transmitted.
Observable 4.2 n =  number of elements in length Lt.
Observable 4.3 d =  diameter of an element.
Observation 5 What's happening differently inside surface and outside
Observation 6 similar triangles dr/r = dv/v.

Definitions  

       Universe, Aether, Logos, Cosmos, Chaos
Definition 1
Location R0 ≡ R011 + R022 + R033.
Definition 2 Displacement rfi  ≡ Rff ? Rff.
Definition 3 Area A1212 ≡ r11 x r22.
Definition 4 Volume V123 ≡ A1212 ? r33,
Definition 5 Density x ≡ mx/Vx .
Definition 6 Time  tab ≡ |rabab| / |vabab| .
Definition 7 Velocity varaa/ta.
Definition 8 Saturation o ≡ Vm / Vs 
Definition 9 Momentum pi+k+ ≡  mi+vk+k+
Definition 4.1 Lm ≡ nd. 
Definition 4.2 Lf ≡ Lt - Lm , or Lm= Lt -Lf .
Definition 10 vii ≡ Limit t 0 (ri/ti)i
Definition 11 aii ≡ Limit t 0 (vi/ti)i
Definition 12  Fii ≡ dp1i1 /dt + dp2i2 /dt + dp3i3 /dt
Definition 13 Pressure P ≡ Fir+ / Air
Definition 14 G ≡ (1/32m2o)ov2oa2o

Equations  

Equation 1 Rii ≡ Ri1i1 + Ri2i2 + Ri3i3.
Equation 2 mi+ =(1/2)0 Vi+ , ( i+ is direction on the i axis.) 
Equation 3
vk+k+=(1/2)vok+ (where k+ indicates +direction on k axis.)
Equation 3.1 saturation c ≡ Vmc / Vsc 
Equation 4
pi+k+ = (?)0 Vk vok+ 
Equation 4.1 velocity in free space  vf = Lf /tt.
Equation 4.2 velocity of momentum in the chaos  vp=Lt /tt
Equation 4.3  speed of momentum / speed in free space   vp /vf = Lt /Lf .
Equation 4.4 density of pure matter 0m =mi/Vm.
Equation 4.5  varying the background volume  b = mx/Vb
Equation 4.6 ratio of constant and varied density  0m/b = Lm3/Lt3 
Equation 5 Force Fir+r+ ≡ (1/8) 0 Air v2or+ .
Equation 6 Pressure Pi = (1/8) 0 v2o ,
Equation 6.1  dt = dr/v
Equation 6.2  centripetal acceleration a=v2/r. 
Equation 6.3 Newton's second law  Fi=miai.
Equation 7 surface area of a sphere of radius R Asphere = 4R2.
Equation 7.1 Major diameter of ring ztotal = 2R.
Equation 8.1  Acenter = n ao .
Equation 8.2
  Fo center = P Acenter=  (1/8) o v2o ncenter ao
Equation 8.3  Atop = kao .
Equation 8.4 Ratio of view obstruction Atop / Asphere or kao /(4R2 ) .
Equation 8.5  center object mcenter = nmo .
Equation 8.6 top object  mtop= kmo .
Equation 8.7 Force Fcenter net = (1/32 m2o) o v2o a2o  mtop mcenter  / R2 .
Equation 8.8 Force Fcenter net = G  mtop mcenter  / R2

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