The dynamic case for an expanding spinning

black hole universe modified 20110926

black hole universe modified 20110926

Rosman, North Carolina USA

john.erich.ebner@gmail.com

26 September 2011

Abstract and purpose. We explore a simple classical model of the universe in dynamic equilibrium. Our purpose is to solve the problems of the flat rotation curves of galaxies, prevalence of dark matter in galaxy dynamics and uniformity of the cosmic microwave background. Wiki calls these "unsolved problems of physics." They are shown to be a consequence of this model of the dynamic universe. The age, radius, mass, expansion rate and density of the universe are unambiguously shown to apply to a black hole and are in the range of mainstream values frequently quoted.

This is the first of five chapters.

Chapter 2 - Black holes

Chapter 3 - Rotation of the Cosmos

Chapter 4 - Dark matter

Chapter 5 - Uniformity of the CMB

Introduction

There is a lot of math detail so that the ideas are more accessible. The math is written to be copied into a spread sheet or calculator. One may reason as to its correctness. There is no one above you. You are the authority who must decide.The Cosmos has the radius, mass and density quoted for the observable universe. The Cosmos is an entity which rotates and expands with respect to something larger and outside itself. It is a subset of the universe. The universe is the totality of all things that exist and the source of the material for our Cosmos. Our Cosmos continues to expand and slow in its rotation according to the rules of dynamics.

Postulates or Assumptions

- Our
**observable universe**is an**entity**, a**dynamic unit**. Once you see the expanding spinning black hole universe as an entity as a dynamic unit, it has a more local personal character. You are a part of something. You no longer see it in isolation. It is a ball in play in a much larger game. The cosmos is the universe regarded as an orderly, harmonious whole. The universe is the totality of all things. Cosmos deals with structure, it has more the clockwork dynamic quality which seems to fit an object of study better than the existential term universe. Here Cosmos will be the name preferred for our local dynamic unit. - It is
**rotating**and**blowing up**like a balloon but very slowly in relation to its size. Like a spinning ice skater slows her spin, by extending her arms, the spinning universe slows in its rotation while expanding. Each circle is a cross section of the cosmos at a different time. The triangle shows the way it expands and rotates. Light orbits at the perimeter of the cosmos. As the cosmos increases in size, light orbits farther out. Most observers would look out in any direction and see the cosmos expanding faster at greater distances. This is a Hubble expansion. We rotate with respect to that which is very far away and is outside our dynamic unit. The length of the hypotenuse of the triangle

**Click image to animate!****r**is the**radius of the Cosmos**. It is the velocity of light times the age of the cosmos, at that particular time, or**r = c*age.**The hypotenuse expands and has a tangent velocity of the speed of light,**v = c.**The base of the triangle expands and rotates at its fixed fraction**fr**of the speed of light,**v = fr*c.**This**fraction "fr"**is the cosine of the triangle. We can see that a location, the circled point in the corner of the triangle, where we might be located, expands radially outward and rotates at a constant velocity, proportional to its fraction of the radius of the cosmos according to the rules of dynamics. -
Every location within this Cosmos, has a
**constant tangent**and**radial velocity**which are**proportional**to its**radius**. Since the velocity is constant, the acceleration is zero, and no force and no power is required for it to continue on its journey.**Energy is conserved**. - A location
**spirals out**as the Cosmos expands and rotates. The location stays at the same constant**fraction**"**fr**" of the radius of the Cosmos**r = fr*c*age**and a constant velocity**v = fr*c**. Here**fr**at the location is**.7**and the velocity is,**v = fr*c = .7*c.**This is a Hubble expanding Cosmos.

**Click image to animate!**. Everything spirals apart as the cosmos grows and slows in its rotation. Spiral galaxies are no surprise if they are part of the Hubble expansion. The Cosmos rotates at*Everything spirals out***c**at a radius of**r = c*age**. Everything has the same tiny**angular velocity = c/(c*age) = fr*c/(fr*c*age) = 1/age = 2.11E-18_1/s**, radians per second. Age is the**age of the cosmos**. Hubble's constant is also**1/age**. Pluto orbits at**4753_m/s**at a radius of**5.913E12_m**. Pluto's angular velocity is**4753_m/s / 5.913E12_m = 8.038E-10_1/s**, radians per second. The cosmos rotates**831 million**times slower than Pluto. This tiny angular velocity will be very hard to detect. The angular velocity was larger in the past. It is changing with a very small**angular acceleration = -1/age**or radians per second squared.^{2}= -4.46E-36_1/s^{2} - Our universe has sufficient mass for light to orbit at its perimeter. Orbiting light or energy makes it a black hole universe. From inside the void, left by the departing perimeter, we see the
very nearly uniform microwave background radiation, also known as the cosmic microwave background, CMB. The CMB which is heat or low energy light may come from the spherical region where light
orbits. The fact that the CMB appears uniform, implies that we might be near the center of the CMB and the Cosmos, an unlikely occurrence, which we will revisit later. The glow of the CMB is
dimming since the perimeter's area,
**4*pi*r**is proportional to the^{2}= 4*pi*c^{2}*age^{2}**age**and luminosity to^{2}**1/age**. The luminosity is decreasing at the same rate as the Cosmos is slowing down in its rotation and increasing in surface area. Its glow is also greatly reduced by the inverse square nature of radiation in its immense travel thru space. It can be described, by the equation for a sphere expanding at the speed of light, like the spherical wave front of an electromagnetic wave with a radius of^{2}**r=c*age**so that**x**but this is beyond the scope of our simple dynamics.^{2}+y^{2}+z^{2}= c^{2}*age^{2}

Edwin Hubble determined from the linear Doppler red shift of galaxies that they are receding at a rate proportional to distance. It is called Doppler because of the familiar Doppler frequency shift of sound with the velocity of the sound source. Here the frequency shift is in the light toward the red with increasing velocity of recession. Think of a sine wave appearing stretched as it moves away. The peaks of the sine wave seem stretched farther apart as it moves away. There is a longer duration between the peaks as the sine wave moves away. The longer duration is the sum of the natural original duration between the peaks of the sine wave plus the duration between the peaks added by the recession of the sine wave. The sine wave seems to have a lower red shifted frequency. The sine wave is unchanged only our point of view and relative velocity has changed. Does space stretch? How could it? Space is empty. How could we see billions of light years with telescopes unless space is empty? Is it more likely that our point of view has changed or that space has changed by becoming stretched? Some people mistake abstraction for reality.

Edwin Hubble determined from the linear Doppler red shift of galaxies that the velocity of recession at a certain distance, divided by that distance is a constant. Hubble's constant,
**Ho**, is about **65 km/(s*Mpc),** kilometers per second per million parsecs. In smaller units, this is **2.11E-18_m/s per meter,** 2.11 times 10 to the minus 18 meters per
second per meter or **2.11E-18_1/s.** * Using these smaller more familiar units may lead you to wonder if the expansion is also local. Does the Hubble expansion extend to the galaxy, to the
solar system, to atoms? If it exists, was it missed because the size of the expansion is so small?* Hubble's constant has units of

Four examples are;

130_km/(s*Mpc) = 1/7.5 billion years

65_km/(s*Mpc) = 1/15 billion years

32.5_km/(s*Mpc) = 1/30 billion years

16.25_km/(s*Mpc) = 1/60 billion years

130_km/(s*Mpc) = 1/7.5 billion years

65_km/(s*Mpc) = 1/15 billion years

32.5_km/(s*Mpc) = 1/30 billion years

16.25_km/(s*Mpc) = 1/60 billion years

Binary star systems and galaxies show rotational Doppler red shift. The approaching star in a binary system is more blue and the receding star is more red. The approaching side of a galaxy is
more blue and the receding side of a galaxy is more red. The color change is due to velocity. Vera Rubin found that in many galaxies the velocity seen in the red shift spectrum in the rotation of the
galaxy does not follow Kepler's laws by decreasing with radius but stays the same at greater radius. The galaxies are said to have **flat rotation curves**. Radio telescopes extended these flat
rotation curves out to the dust clouds that orbit galaxies. We will extend these flat rotation curves even further when we look at **dark matter**.

Non-Doppler red shift is red shift unrelated to the velocity of recession. The much hotter star in a binary system shows non-Doppler red shift. Since the binary stars are receding at a common velocity, the substantial non-Doppler red shift of the hotter star is not due to velocity. The sun also shows non-Doppler solar red shift. There is an unknown ratio between the Doppler and non-Doppler red shift components of Hubble's constant.

- If
**1/2**the Hubble constant is due to non-Doppler red shift then the Doppler Hubble constant should be,**32.5_km/(s*Mpc)**not**65_km/(s*Mpc)**and the cosmos is**30 billion years old**not**15 billion years old**. - If
**3/4**the Hubble constant is due to non-Doppler red shift then the Doppler Hubble constant should be,**16.25_km/(s*Mpc)**and the cosmos is**60 billion**not**15 billion years old**.

The cosmos must be much older and larger when non-trivial, non-Doppler red shift is included since the calculated radius is proportional to the age of the cosmos. If most or all of the red shift is non-Doppler and the CMB is the ambient temperature of the star lighted universe, as in the strong case presented by Marmet and Reber, then the universe is infinitely old, large and massive. I assume for now that some of the Hubble constant is Doppler and that the Cosmos slows in its rotation as it expands. The next section might be clearer after reading Gravity, rosettes, binary systems and inertia.

This is

This means that either

We see that the

gravitational force = G*Mc *m /r

Since

The orbital forces equal the orbiting energy divided by the radius of the cosmos. The

**m *vt ^{2} /r = G*M *m /r^{2}**, the centrifugal force equals the gravitational force.

fr

If

.9

The gravitational energy = **G *M *m /r = c ^{3}*age/Mc *fr^{3}*Mc *m /(fr *c*age) = fr^{2}*m*c^{2}**The gravitational energy is constant if

The centrifugal force =

The gravitational force =

We see that the mass “

Density of the Cosmos

The density within a fraction of the radius of the cosmos isfr

3*Mc/(4*pi*c

References

- Unsolved problems of physics @ http://www.answers.com/topic/unsolved-problems-in-physics#Cosmology_and_Astronomy
- Bohr's planetary atom @ http://blackholeformulas.com/files/BohrAtom.html
- Ring electron @ http://blackholeformulas.com/files/RingElectron.html
- Helical electromagnetic waves @ http://blackholeformulas.com/files/helicalelectromagneticwaves.html
- Triangle graphic gif @ http://blackholeformulas.com/files/dctri.10.gif
- Spiral graphic gif @ http://blackholeformulas.com/files/dcconccirc.10.gif
- Hubble @ http://en.wikipedia.org/wiki/Hubble%27s_law
- Age of the universe @ http://hypertextbook.com/facts/1999/RachelHoover.shtml
- Radius of the universe @ http://hypertextbook.com/facts/2002/CarmenBissessar.shtml
- Non-Doppler red shift @ http://www.newtonphysics.on.ca/hubble/index.html
- Binary system and solar non-Doppler red shift @ http://www.newtonphysics.on.ca/chromosphere/index.html
- Marmet and Reber @ http://www.newtonphysics.on.ca/universe/universe.html
- Gravity theory @ http://blackholeformulas.com/files/gravity.html
- Mass of the universe @ http://hypertextbook.com/facts/2006/KristineMcPherson.shtml
- New Scientist @ http://space.newscientist.com/article/mg19425994.000-axis-of-evil-a-cause-for-cosmic-concern.html
- Goodness in the axis of evil @ http://arxiv.org/PS_cache/arxiv/pdf/0802/0802.3229v2.pdf
- Sloan study @ http://arxiv.org/astro-ph/0703325
- WMAP data @ http://arxiv.org/abs/astro-ph/0605325
- Quasars @ http://arxiv.org/abs/astro-ph/0507274v1
- Density of the universe @ http://hypertextbook.com/facts/2000/ChristinaCheng.shtml

Chapter 2 - Black hole universe modified 20110925

Introduction

There are two ways of defining a black hole and two black hole formulas. The original black hole definition goes back centuries where Go back to Chapter 1 - Introduction

Goto Chapter 3 - Rotation of the Cosmos

The orbiting energy equals the gravitational energy. If

All the terms cancel, telling us that our Cosmos is a black hole.

If

- For a
**ten solar mass**black hole or**1.99E31_kg, vr = 3.12E-14_m/s**

- For a
**billion solar mass**black hole or**1.99E39_kg, vr = 3.12E-6_m/s**. This expands at**98_m/year**.

- For a
**9.61E22 solar mass**black hole or**1.91E53_kg, the mass of the Cosmos Mc, vr=299792458_m/s = c**

The gravitational force was stronger in the past.

We take

Four examples of black hole density using the mass formula;

ten solar mass = 1.47E18_kg/m

five solar mass = 5.90E18_kg/m

1.4 solar mass = 7.52E19E19_kg/m

1.4 solar mass = 6.6E25_kg/m

The mass of a proton or hydrogen atom is

While we would expect to see an approaching object to be seen as blue-shifted on the outside of our Cosmos, an approaching black hole emits no light, as all its perimeter light is in orbit. We would only see an approaching black hole when it merged with our own and suddenly appeared inside the perimeter of our Cosmos.

Little ones merge to make big ones. Two soap bubbles merge to make a larger soap bubble. In eggland, two eggs touch. Their shells merge much like soap bubbles merge. Their contents merge. Where there was two eggs, there is now one larger egg with two merged yokes. Over time, there is a very big egg with many yokes merged together. The yokels, being unaware of the mechanics of merging, make up odd stories of their creation and their importance to the creator.

There are groupings of mass in space so great, that gravity in the age of the Cosmos, would be inadequate for their formation from hydrogen gas. These are called large-scale structure. An example is the Sloan Great Wall. Their great mass should have been reflected in the observed inhomogeneities in the CMB, if the conventional theory is right. The merging of black holes, does however, explain these structures. The smaller black hole has a much higher density. The merged contents are enclosed in a much larger volume. From within, one sees only the merged contents. The smaller black hole leaves behind a higher residual mass density, in the stretched out, merged contents, which is the artifact or footprint of their merging.

**M/r = mass/radius = c ^{2}/G = 1.35E27_kg/m
radius = r = mass *G/c^{2}surface area = mass^{2} *4*pi* G^{2}/c^{4}volume = mass^{3} *4*pi*G^{3}/(3*c^{6})
density = mass /volume = 3*c^{6}/(mass^{2} *4*pi*G^{3})**

Two times mass equals; two times radius, four times surface area, eight times volume, density divided by four, and two times vr.

**Spherical caps of merging spheres:** See the figure above.

A spherical cap is a part cut off a sphere. When two spheres merge they create a lense shaped merged region. The volume of the lense shaped merged region includes twice the volume of the spherical caps of each sphere. The volume of a spherical cap is,

**1/3*pi*r ^{3}*(3-fr)*fr^{2}, with fr,** being the fraction of r, that is the height of the cap. The volume of a sphere equal to four spherical caps would be

When the spherical caps of merging black holes of the same size reach .6527 of their radius, the volume and the mass of the merged portions satisfies the mass/radius formula for a black hole.

The new velocity distribution in the merged black hole will cause all the orbits to relocate over time but these are small acceleration forces in a low density Cosmos like our own. Light and energy will eventually occupy a circular orbit at the new now larger radius of the black hole. The masses within will seek their own new orbits. The acceleration at the edge of the Cosmos is

There was a super nova relatively near our solar system around the time that the Earth formed. It left the Earth with its radioactive materials. It would not be surprising if it also left the Earth seeded with life in the form of rocks with embedded bacteria or spores from the nova stars solar system.

There are two ways of defining a black hole and two black hole formulas. In the traditional black hole

If the escape velocity only

The centrifugal force equals twice the gravitational force, so light can not be restrained to an orbit.

Using escape velocity has problems with the fixed velocity of light,

**.5*m*vr ^{2} = G*m*M/r**, kinetic energy equals gravitational energy

If

If

Other characteristics of the traditional black hole are:

**M/r = c ^{2}/(2*G) = 6.73E26_kg/m
c^{2}*r/(G*M) = 2**

density = mass /volume =

Two times mass equals two times radius, four times surface area, eight times volume and density divided by four.

Energy in orbit black holes

Energy in orbit black holes are The mass/radius ratio of traditional black holes is half that of energy in orbit black holes. This difference may be detectable with the measurement of orbital periods of x-ray emitting clouds that orbit some black holes in binary systems of a black hole and star as reported, in this edited excerpt from May 12, 2001, Science News.

"The Rossi satellite detected X rays that flicker 300 times per second, from the region around GRO J1655-40. Astronomers would expect this from a blob of hot gas orbiting 64 km from the 6.3 solar mass black hole. Rossi also recorded an X-ray signal flickering 450 times per second. A radiating blob of gas orbiting a black hole is like a lighthouse beacon sweeping past Earth hundreds of times per second, suggests Strohmayer. The closer the blob gets to the black hole, the faster it orbits. The most rapid oscillation detected by Rossi can best be explained by blobs of gas that are orbiting 15 km nearer to the hole than indicated by the slower flickering, he says. The material could maintain itself at this closer distance only if the black hole spins, Strohmayer asserts."

References

- Traditional black holes @ http://blackholeformulas.com/files/GSJBlackHoles.html#Appendix
- Hubble @ http://blackholeformulas.com/files/Introduction.html#Hubble (age, radius, radial velocity)
- Nuclear density @ http://en.wikipedia.org/wiki/Nuclear_density
- Neutron star mass @ http://www.lsw.uni-heidelberg.de/users/mcamenzi/NS_Mass.html
- Neutron star radius @ http://www.astro.washington.edu/users/ben/a510/NSTARS.new.html
- Density of the universe @ http://hypertextbook.com/facts/2000/ChristinaCheng.shtml
- Photon-photon scattering @ http://www.hep.ucl.ac.uk/opal/gammagamma/gg-tutorial.html
- Large scale structure of the Cosmos @ http://en.wikipedia.org/wiki/Large-scale_structure_of_the_Cosmos
- Sloan great wall @http://en.wikipedia.org/wiki/Sloan_Great_Wall
- Inhomogeneities in the CMB @ http://www.newton%20physics.on.ca/BIGBANG/Bigbang.html
- Panspermia @ http://en.wikipedia.org/wiki/Panspermia
- Planetary exposions @ http://metaresearch.org/solar%20system/eph/eph2000.asp
- Rossi satellite @ http://www.sciencenews.org/articles/20010512/toc.asp

Chapter 3 - The rotating universe modified 20110924

Introduction

As the light and energy orbit the expanding Cosmos, it takes longer to reach a reference point against the background universe. Newton would call this reference
point absolute space. Mach would call it the fixed stars. The Cosmos, galaxy and solar system all rotate, with respect to that which is outside our cosmic dynamic unit. If the background universe
has features which are close enough, and these features are not black holes, then they may be visible through the intense orbiting energy and light around the Cosmos. Seeing through this orbital
energy seems possible since stars are visible near the sun during an eclipse as starlight perpendicular to the huge energy flow from the sun. We might be seeing such features in the Hubble
telescope deep field photographs. It would not be remarkable if the background universe looks the same as it does within our dynamic unit Cosmos.Go back to - Chapter 2 - Black holes

Goto Chapter 4 - Dark matter The

The **rate of change **of the **angle of rotation **is the **angular velocity.**

The **rate of change **of the **angle of rotation** is **1/age.**

The **rate of change **of the **ln(age)** is **1/age.**

The **angle of rotation = ln(age)** = the natural logarithm of the age = **ln(4.73E17) = 40.7 radians**.

The base of the natural logarithms is **e**.

**e ^{(angle of rotation)} = e^{40.7} = 4.73E17 = age**

The previous revolution took

The next revolution will end in,

The next revolution will take

The rate of change of the angular velocity **(1/age)** is the angular acceleration.

**angular acceleration = -(1/age ^{2}) = -4.46E-36_1/s^{2}.** This is the second derivative of the angle of rotation. This very small rate that the Cosmos is decelerating in its
rotation is necessary for the equilibrium between rotation and expansion. We are rotating with the Cosmos. Everything has the same universal angular velocity

m*r

a = r *angular acceleration = tangent acceleration

a = c*age *(1/age

The direction of deceleration is opposite of rotation. The tangent acceleration can also be calculated from velocity dependent inertial induction with the same result. Inertia will cause an outward directed mass, on a rotating platform, to lag behind in a direction opposite to the rotation. This is the reaction. The action which is the coriolis acceleration is in the direction of the rotation. A person in an accelerating car is pushed back against the seat. This is a reaction to the acceleration. The acceleration is in the direction of the velocity. The reaction is in the direction opposite the velocity.

vr is the radial velocity which at the perimeter is c.

M *r

M *vr

M

If the mass of the black hole is, M = Mc, the mass of the Cosmos, then

We see that the age

References

- Machian view @ http://www.bun.kyoto-u.ac.jp/~suchii/mach.pr.html
- Inertial inductance @ http://blackholeformulas.com/files/InertialInductance.html
- Spiral png @ http://blackholeformulas.com/files/unfigspiral2.png

Chapter 4 - Dark matter modified 20110926

Introduction

Dark matter can be explained by matter present farther out from the galaxy than is seen in the optical spectrum. The orbiting atomic hydrogen clouds are also in this region. Each meter of radius in moving out from the center of a galaxy adds a fixed amount of mass to a bigger volume so the density decrease with radius. The galaxy extends to the radius at which the galaxy is the same density as the Cosmos.Go Back to Chapter 3 - Rotation of the Cosmos

Goto Chapter 5 - Uniformity of the CMB We have a tangent velocity

The mass/radius ratio,

The mass added by the next meter of radius,

I suspect that this low density of matter or dark matter, would usually be hard to detect for example with 21_cm radiation, but it is obviously still probably matter not some mysterious stuff. Radio telescopes can detect the atomic hydrogen at

In reference to galaxies,

If the galaxy increases with a constant

vt

vt

vt*age = R

The total galactic mass when divided by the visible mass within the

For

vt

vt

mass *r

mass *vr

We see that the square of the radius in the moment of inertia for the galaxy

The length of the orbit when divided by

We see that the

1.375E-5_arcs/year = 1.375E-3_arcs/century

For the earth,

For the moon,

vr

This is the radius divided by the angular acceleration of the Cosmos. This is a clue that the ultimate source of the centrifugal force is the Cosmos. We can calculate the tangent acceleration using the torque formula.

m*r

a = r *angular acceleration =

a = vr*age *(1/age

The direction of deceleration is opposite of rotation.

vr

mass *r

mass *vr

We see that the square of the radius in the moment of inertia for the planet,

References

- Galaxy tangent velocity @ http://www.astronomynotes.com/ismnotes/s7.htm
- Atomic hydrogen 21 cm radiation @ http://en.wikipedia.org/wiki/Hydrogen_line
- Molecular hydrogen @ http://www.newtonphysics.on.ca/hydrogen/index.html
- Galactic flat rotation curves @ http://en.wikipedia.org/wiki/Galaxy_rotation_curve
- Precession @ http://en.wikipedia.org/wiki/Precession
- Large laser gyroscopes @ http://www.wettzell.ifag.de/LKREISEL/G/LaserGyros.html
- Interferometer detects the aether drift @ http://www.21stcenturyideas.com/interferometer.html
- Natural Philosophy Alliance world science data base @ http://www.worldsci.org/php/index.php?tab0=Experiments&tab1=Display&id=3

Chapter 5 - The uniformity of the CMB modified 20110926

Introduction

The cosmic microwave background Go back to - Chapter 4 - Dark Matter

Go back to - Chapter 1 - Introduction The ellipse is the path of point that moves, so that the

Light acts the same, with the same geometry, with ellipsoidal mirrors. The two foci can be called the origin and the destination. Light leaves the origin as an expanding sphere and reflects at the ellipsoidal surface as a ring. It is a ring because it is the intersection of a sphere and ellipsoid. This reflection focuses the light on to the destination. The overall travel time from the origin, to reflection, to destination, is always the same for all angles of light departing from the origin.

If we retain the origin and destination and change to a luminous expanding sphere we can eliminate the mirror and reflection while keeping the geometry of the intersection of an expanding sphere and ellipsoid. The

A ray of **CMB** reaches us, after **two distinct intervals**.

The **first interval** starts at the center focus, at the origin, at point **o**, on figure 3. It is with the expanding and cooling spherical
shell, before the ray of CMB, which we will be observing, is emitted. Examples on figure 3; are the lines **oa**, **ob** and **oc**. The **temperature **and** watts/meter ^{2}**, of the expanding sphere is
proportional to the inverse square of the radius.

The **second interval**, is the travel of the ray of CMB through space, after it leaves the expanding spherical shell. Examples on figure 3; are the lines **ad**, **bd** and **cd**. It ends with the
reception of the CMB, at the observer at point **d**. The temperature and watts/meters^{2}, of the CMB during the second interval is also proportional to the inverse square of the
radius.

The two intervals always add up to, **c*age** meters in **age** seconds, in any direction the observer looks. For CMB emitted early in the cosmos, there is a shorter interval with the expanding
sphere, and a much longer path through space interval to reach the observer. For CMB emitted later, there is a longer spherical expansion interval, before the CMB is emitted, but a shorter path
through space interval to the observer. The expanding spherical shell, the CMB which it emits, and the CMB during its travel through space, all have a temperature proportional to, the inverse
square of the distance traveled from the origin, **o**.

When the radius of the cosmos was **oa**, it emitted CMB from the entire spherical surface. Only that from the ring, on the sphere at **aa**, will reach **d** at the same time, as the other rings on the
same ellipsoid. A similar argument can be seen in the rings bb and cc. All the CMB from the various rings, which intersect the ellipse, arrive at point **d**, at the same time and temperature. **oa +
ad = ob + bd = oc + cd = or = c*age**.

The formulas in the next section, show the relationship between radius and temperature in the CMB.

The temperature at point **a** when the cosmos was **1/4** its age and size was **5.4_K**.

The CMB arrived at point **d** **at 2.7_K** after expanding for **3/4** the age of the cosmos.

The temperature at point **b** when the cosmos was **1/2** its age and size was **3.8_K**.

The CMB arrived at point **d** **at 2.7_K** after expanding for **1/2** the age of the cosmos.

The temperature at point **c** when the cosmos was **3/4** its age and size was **3.2_K**.

The CMB arrived at point **d** **at 2.7_K** after expanding for **1/4** the age of the cosmos.

When one sees something, it is in terms of

The ** W/m^{2} times the area of the cosmos = wattage of the CMB**, because as we saw in figure 3, the temperature at point

The CMB has the luminosity of a

This is the same as

The CMB is emitted from the expanding radiant shell which is where light orbits at the perimeter of the Cosmos. The scattering of photons along this thin spherical shell is the source of the CMB. The light was accumulated as the Cosmos gained mass and light through the merging of Black holes. The energy emitted in 15 billion years by the CMB, if the energy output is constant, is **7.9E47_Watts*age = 3.7E65_J**. For comparison, the energy of the cosmos, **Mc*c ^{2}=1.7E70_J is
46,000 times bigger**. If the CMB is the remnant energy from the Big Bang, why is it so feeble? However, if the CMB is emitted instead throught the scattering of photons at the perimeter of the Cosmos then this small value of energy makes sense.

The gravitational and centrifugal accelerations on the photon in orbit are **c/age**. As the cosmos expands, the photons orbit at a larger radius and the orbital accelerations decrease. The rate
of change of the acceleration is **1/age ^{2}**. The

We can map the power of the CMB onto the smaller spheres and higher temperature when the cosmos was younger, as long as we keep well clear of infinities.

**(7.9E47/(5.5698E-8*4*pi)) ^{1/2} /(temperature_K^{2}) = radius in meters**

1.0615E27_m/(temperature_K^{2}) = radius in meters

The radius, of the expanding sphere of the shell, is proportional to the inverse square of the temperature.

The following examples map temperature and radius.

At a temperature of

Another way of looking at it is;

Conclusions

A ledger might have beliefs on the left side, and evidence for those beliefs on right side. The dynamics described here are mathematically consistent beliefs, which don’t require
physical infinities. The evidence is the values presented by the mass, radius and density of the cosmos, uniformity of the CMB, the flat rotation curves of galaxies and prevalence of dark
matter. All the parts slip together seamlessly, and the dynamics locks all the parts together. There are no free parameters which might be adjusted to reflect a point of view.
References

- Ellipse graphic @ http://blackholeformulas.com/files/ellipse2.png
- Polarized in a non-random direction @ http://www.spie.org/web/oer/june/jun97/axis.html
- WMAP satellite @ http://map.gsfc.nasa.gov/m_mm.html