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 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 - The Rotating Universe**- Measured tangent velocity within our galaxy
- Flat rotation curves of galaxies
- Torque of the spinning galaxy
- The dynamics of the galaxy
- Hubble in the solar system
- Inertial accelerations
- Centrifugal acceleration
- Tangent acceleration
- Coriolis acceleration
- Spirals
- Torque in the solar system
- The dynamics of the solar system
**Go to - Chapter 5 - The Uniformity of the CMB**

The mass/radius ratio,

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 21_cm, if it is dense enough along their line of sight. Cold molecular hydrogen which is more stable, is probably much more common but is unfortunately invisible at radio wavelengths. It may be detected in the future as the unseen dark matter.

In reference to galaxies,

vt

vt

vt

vt*age = R

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

vt

vt

mass *r

mass *vr

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

The radius of the galaxy increases while the rotation of the galaxy slows down without a change in energy or use of power. Orbits spiral out as the gravitational force decreases with the age of the cosmos.

If the Hubble expansion extends to the solar system, then all the planets share the same very small precession rate, of their major axis within the planet's elliptic plane. An expanding ring slows in its rotation. We calculate a change in angular velocity, which is due to a radial Hubble velocity. This effect may be currently overwhelmed by the noise of the changing gravitational forces exerted by the planets and moons. It may be detected by large ring laser gyroscopes which detect absolute rotations.

The length of the orbit, when divided by,

We see that the r's cancel so that this rate of precession is universally true for the entire solar system and is not tied to any radius.

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

To calculate the path of expansion of a planet we need the vector sum of three accelerations; the centrifugal, tangent and coriolis.

Centrifugal force uses the tangent velocity, but here, we are looking for the precessional component or factor, of the centrifugal force which is due to the Hubble expansion. The tangent and radial velocity due to precession are equal.

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.

The direction of deceleration is opposite of rotation.

vr is the radial velocity.

2*vr/age = coriolis acceleration

Now that we have calculated the inertial accelerations we can look at the way the solar system expands. We have the centrifugal
acceleration of **vr/age** directed radially out. We have the coriolis acceleration of **2*vr/age** in the direction of rotation and the deceleration of **vr/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 **2 ^{1/2}*vr/age**. A planet moving in this way
traces out a logarithmic spiral.

mass *r

mass *vr

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

Expansion and rotation rates are linked. The radius from the sun, to the planets, increases while the orbital periods of the planets slow down, without a change in energy or use of power. Orbits spiral out as the gravitational force decreases with the age of the cosmos.