The rotating universemodified 20110906
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.

Rotation or vorticity
The angular velocity = tangent velocity/radius= vt/r = c/(c*age) = 1/age in radians/second or Hubble's constant as a rotation rate or fr*c/(fr*c*age) = 1/age

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) = e40.7 = 4.73E17 = age

ln(age*2) = ln(age) + ln(2). Each time the cosmos doubles in age or size the angle of rotation of the cosmos increases by the ln(2) = .693 radians = 39.7 degrees
We are currently at 40.7 radians so 40.7 /(2*pi) = 6.5 revolutions might have been made by the orbiting light and energy in the age of the cosmos. The last revolution started when the cosmos was, e(40.7 - 6.28) = 8.88E14_s = 28.1 million years old.
The previous revolution took 15 billion years.
The next revolution will end in, e(40.7 + 6.28) = 2.53E20_s = 8.017E12_years = 8017 billion years.
The next revolution will take 8000 billion years. The slowly stirring cosmos is slowing down.

The rate of change of the angular velocity (1/age) is the angular acceleration.
angular acceleration = -(1/age2) = -4.46E-36_1/s2. 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, (1/age), as a component of their local angular velocity, as we will see in our galaxy. The cosmos rotated faster when it was younger. This differential rotation might be detected but the angular acceleration is profoundly slow at (1/age2).

Inertial accelerations
To calculate the path of expansion of a particle we need the vector sum of three accelerations; the centrifugal, tangent and coriolis. These are components of the so called fictitious forces which are more properly called forces due to inertia. They are certainly not fictitious if you take the Machian view that inertia is the acceleration dependant gravitational force exerted by the rest of the cosmos. See the article on Inertial Inductance.

Centrifugal acceleration
The centrifugal and gravitational forces are equal. m*c2/r equals the centrifugal force and c2/r is the acceleration felt by light or energy in orbit at the perimeter of the cosmos.
c2/r = c2/(c*age) = c/age = 6.33E-10_m/s2 or c2*fr2 /(c*age*fr) = fr*c/age if fr is less than one

Tangent acceleration:
We can calculate the tangent acceleration using the torque formula.
moment of inertia*angular acceleration = force*radius.
m*r2*angular acceleration = m*a*r.
a = r *angular acceleration = tangent acceleration
a = c*age *(1/age2) = c/age, or
a = fr*c/age if fr is less than one
The direction of deceleration is opposite of rotation. The tangent acceleration can also be calculated from velocity dependent inertial induction with the same result.

Coriolis acceleration:
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.
2 *angular velocity *vr = 2 *vt/r *vr = 2 *c/(c*age) *c = coriolis acceleration
vr is the radial velocity which at the perimeter is c.
2*c/age = coriolis acceleration or
fr*2*c/age if fr is less than one


Click to enlarge! Spirals:
Now that we have calculated the inertial accelerations, we can look at the way the cosmos expands. We have the centrifugal acceleration of c/age, directed radially out. We have the coriolis acceleration of 2*c/age, in the direction of rotation, and the deceleration of c/age, in the direction opposite of rotation. The resultant of these accelerations, is 45 degrees between the direction of rotation and the outward directed radius. It has a value of, 21/2 *c/age = 8.96E-10_m/s2. A particle moving in this way traces out a logarithmic spiral. We have seen that the
angle of rotation = ln(age). This can be written as
age = e(angle of rotation). Now
r = c*age, can be written as
r = c*e(angle of rotation). This is the equation of a logarithmic spiral. It is no coincidence that many galaxies have a spiral shape. Indeed, it is not that space expands, but that the distance between orbiting masses increases as they spiral out and apart from each other, as the cosmos expands and slows in its rotation. The tangent velocity of the stars orbiting in galaxies, stays the same as the galaxies expand and the orbital periods increase. Any velocity change would require force and energy which are absent.
Torque of a spinning black hole
moment of inertia *angular acceleration = torque
M *r2*angular acceleration =
M *vr2 *age2*angular acceleration, but
vr/c = M/Mc, so vr2 = c2*M2/Mc2, therefore substituting for vr2
M *{c2*M2/Mc2} *age2 *angular acceleration =
M3 *c2/Mc2 *age2 *angular acceleration = torque.
If the mass of the black hole is, M = Mc, the mass of the cosmos, then
Mc *c2 *age2 *(1/age2) = Mc *c2
We see that the age2, in the square of the radius, in the moment of inertia, increases at the same rate the angular acceleration 1/(age2) decreases so that the age2 in each cancels and the energy stays constant. We will see the same thing in the torque of a spinning galaxy.

The dynamics of the cosmos:
The radius of the cosmos increases while the rotation of the cosmos slows down, and with it all the blackholes and galaxies, without a change in energy or use of power, always in dynamic equilibrium. Orbits spiral out as the gravitational force decreases with the age of the cosmos.

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